From dad1b2c3a776d99ec9cef99d76c321013ac95b4a Mon Sep 17 00:00:00 2001 From: Ruge Lin Date: Thu, 8 Oct 2026 00:16:39 +0800 Subject: [PATCH] Present the complete logarithmic-return result and trim progress narration --- README.md | 26 ++-- STATUS.md | 177 ++++++++---------------- TUTORIAL.md | 6 +- WORKSPACE.md | 3 + archive/README.md | 18 +++ docs/README.md | 16 +-- literature/ASSUMPTIONS.md | 71 ++++------ literature/DEVDARIANI_COMPARISON.md | 36 +++-- literature/PHYSICAL_PRECEDENTS.md | 68 ++++----- literature/SCIENTIFIC_CONTEXT.md | 59 ++++---- literature/SOKOLOVSKI_PONS_MUGA_2014.md | 37 ++--- llms.txt | 22 +-- research/AMPLITUDE_IDENTIFICATION.md | 31 ++--- research/CLAIMS.md | 113 ++++++--------- research/FINITE_VOLUME.md | 28 ++-- research/LIMITS_AND_ACCURACY.md | 6 +- research/MODEL_RESIDUAL.md | 29 ++-- research/PREPARATION_READOUT.md | 23 ++- research/PROOF_STATUS.md | 92 +++--------- research/REFLECTION_MATCHING.md | 44 +++--- research/SCIENTIFIC_PREPARATION.md | 119 ++++++---------- research/TUTORIAL_BRIDGE.md | 11 +- research/UNIFORM_MINIMUM.md | 30 ++-- work_orders/CURRENT.md | 142 ++++++------------- 24 files changed, 442 insertions(+), 765 deletions(-) diff --git a/README.md b/README.md index 5e9d440..3c0f9c9 100644 --- a/README.md +++ b/README.md @@ -12,7 +12,7 @@ is how much returns to the original bound orbital after this coherent, closed cy | [Physical account](research/CORE.md) · [Proof and quantifiers](research/PROOF_STATUS.md) · [Claim map](research/CLAIMS.md) | Follow the return law and its proof dependencies | | [Limits and accuracy](research/LIMITS_AND_ACCURACY.md) · [Assumptions](literature/ASSUMPTIONS.md) · [Prior-work comparison](literature/SCIENTIFIC_CONTEXT.md) | Check the asymptotic domain, physical premises and attribution | | [Evidence and reproduction](#evidence-and-reproduction) · [Scope and evidence](STATUS.md) | Inspect the checks and their interpretation | -| [LLM guide](llms.txt) · [Workspace](WORKSPACE.md) | Identify relevant questions and authoritative files | +| [LLM guide](llms.txt) | Identify relevant questions and authoritative files | ## The fixed question @@ -34,15 +34,16 @@ The probability is unconditional; population that escapes remains in continuum s ## The logarithmic return law -At exact touching, the recorded author-side derivation gives +The leading slow-cycle law at exact touching is ```math \boxed{P_\infty(T,0)\sim\frac{\pi^2}{4\ln^2T}\longrightarrow0.} ``` -This is a leading slow-cycle asymptotic. With units restored, the logarithm is -$`\ln(T_{\rm physical}J/\hbar)`$. It is not a precision percentage formula at every -finite duration. [The proof map](research/PROOF_STATUS.md) gives the exact quantifiers. +With units restored, the logarithm is +$`\ln(T_{\rm physical}J/\hbar)`$. [The proof map](research/PROOF_STATUS.md) gives the +exact quantifiers, and [limits and accuracy](research/LIMITS_AND_ACCURACY.md) explains +the remainder and finite-duration interpretation. A trap with a shrinking positive minimum also retains the effect. Define @@ -101,10 +102,9 @@ The selected learning foundation is: > [Publisher record](https://link.springer.com/book/10.1007/978-1-4684-5451-2) · [DOI](https://doi.org/10.1007/978-1-4684-5451-2) The [single-book route](TUTORIAL.md) focuses on Chapters 1–2 and 8–10, with precise -section locations, checkpoints and an access ledger. The [tutorial bridge](research/TUTORIAL_BRIDGE.md) -supplies the lattice threshold, normalization, matching and joint-limit steps locally. -The book's contents and available previews were inspected; complete chapter reading -is not claimed. No second external tutorial is required for this route. +section locations, checkpoints and an access ledger covering the publisher contents +and inspected previews. The [tutorial bridge](research/TUTORIAL_BRIDGE.md) supplies +the lattice threshold, normalization, matching and joint-limit steps locally. ## Boundaries and prior work @@ -117,11 +117,11 @@ observable from an implemented device. Fixed positive anisotropy has a supportin Threshold-touching loss, static essential binding and the energy-domain method have predecessors. A local power-law tangent predicts the leading prefactor; the contribution -under assessment is the controlled logarithmic physical limit and its joint domain. +is the controlled logarithmic physical limit and its joint domain. [Scientific context](literature/SCIENTIFIC_CONTEXT.md), the [Devdariani comparison](literature/DEVDARIANI_COMPARISON.md) and the [2014 construction comparison](literature/SOKOLOVSKI_PONS_MUGA_2014.md) give the attributions. -[Scope and evidence](STATUS.md) records the limits of those comparisons and internal review. +[Scope and evidence](STATUS.md) connects the result to its supporting records. ## Evidence and reproduction @@ -135,8 +135,8 @@ The five preserved scientific suites cover **28 groups and 272 finite controls** The **60 supplementary checks** are counted separately. The runner writes to a fresh directory, retains observed outputs and complete differences, and preserves saved references. [Verification policy](provenance/README.md) distinguishes assertions, numerical agreement -and exact bytes. Executable checks support the research record; they are not independent -proof review. Historical attempts and their evidence remain in the [archive](archive/README.md). +and exact bytes. Historical attempts and dated assessments are indexed in the +[archive](archive/README.md). ## Purpose and contact diff --git a/STATUS.md b/STATUS.md index e884cc5..eb714b1 100644 --- a/STATUS.md +++ b/STATUS.md @@ -1,128 +1,59 @@ -# Research status +# Scope and verification -**6 October 2026. Single-source tutorial selected and learning route integrated.** -Manuscript drafting and outreach remain on hold. +The result is logarithmically vanishing bound-state return for the specified +quadratic cycle of one attractive site on a square lattice. The +[proof map](research/PROOF_STATUS.md) states the exact uniform law and assembles +its four components. The [reading guide](docs/README.md) connects the selected +book to that argument. -The claim remains logarithmic bound-state return for one attractive square-lattice -site under the specified quadratic cycle, with the stated uniform residual-depth -and sufficient finite-volume limits. The Hamiltonian, observable and coefficient -are unchanged. All 27 protected scientific/history inputs are byte-preserved. +## Scope of the result -## Learning route - -The owner selected Demkov–Ostrovskii (1988) as the one external tutorial -foundation. [TUTORIAL](TUTORIAL.md) records the reading sequence, checkpoints -and exact access depth. [The project bridge](research/TUTORIAL_BRIDGE.md) -explains the lattice threshold, causal energy reduction, return normalization, -logarithmic matching and joint limits using the existing proof route. -It is an exposition update, with no new scientific claim, source-priority -clearance or independent review. Full chapter reading is not claimed from previews. - -## Scientific position after consolidated assessment - -| Part of the fixed claim | Author-side route | Retained boundary | +| Part of the argument | Derivation | Domain and interpretation | |---|---|---| -| Energy reflection equals physical return | [Gate A](research/AMPLITUDE_IDENTIFICATION.md) | Retarded norm reconstruction; remote time first; uniform finite-endpoint modulus estimate | -| Leading reflection and physical outer matching | [Gate B](research/REFLECTION_MATCHING.md) | Exact touching; both causal terms and exact-lattice tail estimates | -| Uniform positive-minimum return | [Gate C](research/UNIFORM_MINIMUM.md) | Fixed margin below b=1; full singular core and shifted negative tail | -| Finite periodic squares | [Gate D](research/FINITE_VOLUME.md) | Own normalized endpoint states; seam and midpoint comparison; sufficient, not optimal size | -| Fixed positive hopping anisotropy | [Scope check](research/SPECTRAL_SCOPE.md) | Not uniform at zero transverse hopping or a dimensional crossover | -| Fixed finite size even with varying residual depth | [Limits and accuracy](research/LIMITS_AND_ACCURACY.md) | Uniform recovery at each fixed size; constants need not be uniform as size grows | - -[PROOF_STATUS](research/PROOF_STATUS.md) assembles A-D. The -[critical assessment](research/CRITICAL_ASSESSMENT.md) found no required coefficient -or domain correction in its specific cross-gate checks. It composes amplitude errors -without identifying irrelevant phases or interchanging remote-time and slow limits. -This is author-side assessment, not a genuinely separate reader report; the -[reader packet](research/READER_PACKET.md) is still an unsent brief. - -The strongest originality objection is sharper: the local power-law tangent predicts -the full leading positive-minimum prefactor, not only the zero-minimum constant. -The contribution to assess is the controlled logarithmic physical limit and its -joint domain, not a new transform, midpoint identity or prefactor heuristic. The -assessment directly attributes the midpoint identity to Sokolovski-Pons 2016 Eq. (5). -All A-D proof files remain unchanged in this documentary pass. - -The [scientific preparation record](research/SCIENTIFIC_PREPARATION.md) integrates -the work authorized before writing. It proves the fixed-size recovery implication -uniformly in minimum depth, makes the power comparator's existing domain explicit, -and shows why the present remainder cannot certify a subleading logarithmic term. -These are bounded clarifications of the fixed account, not another central claim. - -The bounded significance follow-up in the assessment retains the strongest physical -point: vanishing return along the specified finite, strictly positive-minimum family. -Its gap-based corollary clarifies the leading relative factor but is already predicted -by the local tangent. A targeted Avron-Elgart hypothesis check does not subsume the -touching cycle; subsequent source readings are recorded below. No new conceptual claim, -priority clearance or reason to reopen routine internal development was established. - -## Prior art and implementation - -The [Devdariani construction comparison](literature/DEVDARIANI_COMPARISON.md) closes -the specified 1972 access gap at its recorded depth. The earlier unread label in -[PRIOR_ART](literature/PRIOR_ART.md) is historical. Exhaustive priority and broad -significance are not established by either this comparison or successful tests. -The local resolvent is logarithmic; the lower-edge density of states is finite. -The protected notes and [source map](research/SOURCES.md) retain the original routes. - -The new [scientific context](literature/SCIENTIFIC_CONTEXT.md) records exact static, -weak-binding, adiabatic and localization attributions. Tolstikhin 2008 is now checked -in public author-uploaded full text: its displayed turning-point/separation assumptions -do not directly supply this essential-binding limit. The -[Sokolovski-Pons-Muga 2014 comparison](literature/SOKOLOVSKI_PONS_MUGA_2014.md) -now records the supplied seven-page full text and visual checks of decisive pp. 2–6. -Its monotone linear delta-trap approach, normalized final-bound projection and -finite-box comparison strengthen inherited attribution. They do not supply the -two-leg quadratic logarithmic law or its required joint uniform estimate. The -identified source task is closed; exhaustive priority and separate review are not. - -[ASSUMPTIONS](literature/ASSUMPTIONS.md) remains a support/mismatch map. The -[primary register](literature/PHYSICAL_PRECEDENTS.md) has fifteen passage-level -records, one caption-limited, and one abstract-only comparator. P15 access is upgraded; -WE23 and CH25 complete the targeted motion/control background. The listed conventional -component collections now meet their five-to-ten range. Exact preparation, unconditional orbital readout, calibrated -generator and joint coherent operating window are not established as a device. -Broad generic collection remains paused. - +| Energy reflection and physical return | [A: physical amplitude](research/AMPLITUDE_IDENTIFICATION.md) | Retarded norm reconstruction, equal channel normalization and a uniform finite-endpoint amplitude-modulus estimate | +| Logarithmic reflection and outer matching | [B: reflection matching](research/REFLECTION_MATCHING.md) | Exact touching; both causal contributions and exact-lattice tail estimates | +| Shrinking positive minimum | [C: uniform minimum](research/UNIFORM_MINIMUM.md) | Fixed $`0<\delta\le1`$ and $`0\le b\le1-\delta`$ | +| Growing periodic squares | [D: finite volume](research/FINITE_VOLUME.md) | Each square's own endpoint orbital; sufficient side $`n(T)=2\lceil4.5T\rceil+1`$ in the same minimum-depth domain | +| Fixed size or fixed positive minimum | [Limits and accuracy](research/LIMITS_AND_ACCURACY.md) | Ultimate adiabatic return; constants can depend on size and gap | +| Fixed positive hopping anisotropy | [Spectral scope](research/SPECTRAL_SCOPE.md) | Supporting result with a nonuniform zero-transverse-hopping limit | + +The proof controls a leading asymptotic. Its remainder and resolution of +subleading logarithms are explained in [limits and accuracy](research/LIMITS_AND_ACCURACY.md). +The finite-size bound is sufficient rather than optimal. + +## Attribution and physical assumptions + +Static essential binding, threshold loss, the energy-domain method and localization +have established precedents. The local power-law tangent predicts the leading +prefactor; the controlled physical limit and joint domain are developed in the +proof notes. [Scientific context](literature/SCIENTIFIC_CONTEXT.md), the +[Devdariani comparison](literature/DEVDARIANI_COMPARISON.md) and the +[2014 construction comparison](literature/SOKOLOVSKI_PONS_MUGA_2014.md) record the +specific source statements and access depths. [The critical assessment](research/CRITICAL_ASSESSMENT.md) +contains the detailed tangent calculation and cross-component error composition. + +The model assumes pure endpoint preparation, closed coherent evolution and +unconditional projection onto the endpoint orbital. [Physical premises](literature/ASSUMPTIONS.md) +maps those conditions to component precedents and calibration requirements. [Preparation/readout](research/PREPARATION_READOUT.md) and -[model residuals](research/MODEL_RESIDUAL.md) give conditional error bounds, not -implemented protocols. Full crossover, optimal volume, arbitrary traps, many-body -extensions and application superiority are not claimed or automatically requested. - -## Verification record and preservation - -The [full sanity check](research/SANITY_CHECK_2026-10-05.md) records fresh -verification and a reconciled A-D reading of main `66a7d719`. No mathematical -correction was found in the inspected arguments. It repairs the separate-reader -packet's stale revision/reading route and makes the existing delta range explicit -in the proof summary. This remains internal scrutiny, not an external report. - -The preserved suite is **5 suites / 28 groups / 272 controls**. The supplementary -checks remain **60**: 14 infrastructure, five predecessor, six operational, seven -model-residual, seven amplitude, six reflection, seven uniform-minimum and eight -finite-volume tests. No new scientific suite or numerical campaign was added. -Three one-off exact algebra checks support the comparison in the critical assessment; -they are not additions to these counts or independent scientific review. - -[Assessment provenance](provenance/CRITICAL_ASSESSMENT_2026-10-05.json) pins the -assessed base, its recovered source artifact and completed fresh baseline. Candidate, -PR and post-merge results must be inspected separately. Raw comparisons and the -existing [workload review](provenance/HOSTED_IMPORT_REVIEW.json) distinguish scientific -agreement from exact byte equality. No saved reference, tolerance or policy changes. - -The full earlier records remain in [Gate A provenance](provenance/GATE_A_2026-10-04.json), -[Gate B provenance](provenance/GATE_B_2026-10-04.json), -[Gate C provenance](provenance/GATE_C_2026-10-04.json), and -[Gate D provenance](provenance/GATE_D_2026-10-05.json), with their failed attempts -under [archive](archive/README.md). This status condensation does not reclassify any -past failure, cancelled run or non-byte-identical result. - -## Stop boundary - -Follow [CURRENT](work_orders/CURRENT.md). The selected learning route is available -for self-directed study. The specific 2014 primary-source comparison -is complete at its recorded scope. Stop routine research unless an exact objection -or a genuinely separate reading supplies a concrete task. A separate report and a -device remain unestablished; neither is an extra hypothesis of the conditional -theorem. No outside contact, manuscript or -release is initiated. +[model residuals](research/MODEL_RESIDUAL.md) derive sufficient error bounds. + +## Verification and preserved evidence + +The five scientific suites cover **28 groups and 272 finite controls**. The +**60 supplementary checks** comprise 14 infrastructure, five predecessor, +six operational, seven model-residual, seven amplitude, six reflection, +seven uniform-minimum and eight finite-volume checks. + +The runner retains observed outputs and all differences in a fresh directory. +[Verification policy](provenance/README.md) distinguishes scientific assertions, +reference agreement under the recorded policy and exact byte identity. The +[hosted workload review](provenance/HOSTED_IMPORT_REVIEW.json) preserves the +source-derived interpretation of suite 07's ODE work counters. +Actual candidate and merged-revision runs are recorded in their pull requests +and workflow evidence. + +All **27 mapped scientific/history inputs** are preserved according to +[IMPORT_MAP](provenance/IMPORT_MAP.json). The dated A–D provenance, assessment +records and failed attempts are indexed in [the history guide](archive/README.md). +For fresh execution, use the [reproduction commands](README.md#evidence-and-reproduction). diff --git a/TUTORIAL.md b/TUTORIAL.md index a8b6c0e..46e2667 100644 --- a/TUTORIAL.md +++ b/TUTORIAL.md @@ -108,10 +108,8 @@ The source access for this selection was checked on 6 October 2026: | [Chapter 10 preview](https://page-one.springer.com/pdf/preview/10.1007/978-1-4684-5451-2_10) | Main text pp. 235–236 only | | Other assigned main-text pages | Located from contents; not read in this selection pass | -The publisher presents the full text as subscription content. No complete book -or chapter reading is claimed, and no third-party PDF is stored in this repository. -The available pages neither prove nor exclude the repository's specific theorem; -this pedagogical selection is not an exhaustive priority comparison. +The table distinguishes the inspected previews from the chapter assignments. +The publisher presents the full text as subscription content. The learning goal is the ability to reconstruct and question the fixed proof route, including its residual-depth and finite-size restrictions. For the diff --git a/WORKSPACE.md b/WORKSPACE.md index 78b1d1c..125ddf2 100644 --- a/WORKSPACE.md +++ b/WORKSPACE.md @@ -16,6 +16,9 @@ map in docs/README.md. llms.txt identifies relevant questions, search terms and authoritative reading paths. The README and LLM guide carry the owner's exact purpose/contact wording with a clickable email link. Keep maintenance instructions in this file and work_orders/CURRENT.md; preserve scientific scope and source access. +The owner requests a complete reader-facing account: use stable claims and reading +routes, with dated decisions and review templates indexed as historical records. +Avoid progress banners, obsolete next steps and repeated absence notices in exposition. Develop one defensible theoretical result: logarithmic slow return for the specified local lattice trap, with its stated finite-size and residual-depth domain. Preserve diff --git a/archive/README.md b/archive/README.md index 8f20469..768cc64 100644 --- a/archive/README.md +++ b/archive/README.md @@ -29,3 +29,21 @@ unchanged and their hashes are recorded. The five main research notes and five active scientific suites are ordinary browsable repository files. History is not an additional prerequisite for following the result. + +## Dated assessments and earlier presentation + +These records retain their assessed revisions and original conclusions: + +- [Critical assessment](../research/CRITICAL_ASSESSMENT.md): cross-component checks, + the local-power comparator and its bounded significance analysis. +- [5 October sanity check](../research/SANITY_CHECK_2026-10-05.md): mathematical + spot checks, execution evidence and documentary corrections at the recorded base. +- [Prepared reader brief](../research/READER_PACKET.md): the dated review route and + report template. +- [Provenance](../provenance/README.md): A–D records, source-access updates, + import preservation and hosted comparison policy. + +The earlier progress-oriented [status page](https://github.com/GoGoKo699/Logarithmic-Threshold-Return/blob/b09f51a36f176b4b663ca6282185e5db7a537c7d/STATUS.md) +and [proof summary](https://github.com/GoGoKo699/Logarithmic-Threshold-Return/blob/b09f51a36f176b4b663ca6282185e5db7a537c7d/research/PROOF_STATUS.md) +are preserved at that immutable revision. The current versions organize the same +result by scope, derivation and evidence. diff --git a/docs/README.md b/docs/README.md index 17871ef..8e53a6b 100644 --- a/docs/README.md +++ b/docs/README.md @@ -31,8 +31,7 @@ fixed margin below $`b=1`$. | Contour methods and quadratic time dependence | The two-dimensional logarithmic scaling and matched reflection coefficient | | Threshold-dynamics language | The uniform shrinking-minimum family and sufficient growing periodic squares | -This is a teaching map, not a novelty classification. Inherited methods keep the primary -attributions in the research and literature records. The book coverage is located from +Inherited methods keep the primary attributions in the research and literature records. The book coverage is located from publisher contents and checked at the preview depth recorded in [the access ledger](../TUTORIAL.md#access-ledger-and-stopping-point). @@ -53,14 +52,13 @@ publisher contents and checked at the preview depth recorded in | Inherited ingredients and exact source labels | [Scientific context](../literature/SCIENTIFIC_CONTEXT.md), [source map](../research/SOURCES.md) | | Closest inspected threshold constructions | [Prior art](../literature/PRIOR_ART.md), [Devdariani](../literature/DEVDARIANI_COMPARISON.md), [2014 construction](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) | | Physical premises, preparation, readout and generator errors | [Assumptions](../literature/ASSUMPTIONS.md), [primary precedents](../literature/PHYSICAL_PRECEDENTS.md), [preparation/readout](../research/PREPARATION_READOUT.md), [model residuals](../research/MODEL_RESIDUAL.md) | -| Internal scrutiny and the preparation record | [Critical assessment](../research/CRITICAL_ASSESSMENT.md), [scientific preparation](../research/SCIENTIFIC_PREPARATION.md), [reader packet](../research/READER_PACKET.md) | -| Verification evidence and preservation policy | [STATUS](../STATUS.md), [provenance](../provenance/README.md), [sanity-check record](../research/SANITY_CHECK_2026-10-05.md) | -| Historical attempts and retained failures | [Archive](../archive/README.md) | +| Detailed comparator and scope analysis | [Critical assessment](../research/CRITICAL_ASSESSMENT.md), [scientific preparation](../research/SCIENTIFIC_PREPARATION.md) | +| Verification evidence and preservation policy | [STATUS](../STATUS.md), [provenance](../provenance/README.md) | +| Historical attempts, dated assessments and retained failures | [Archive](../archive/README.md) | -The proof notes govern the mathematical claims. The five preserved scientific suites, -supplementary checks and dated audits serve different evidential roles; successful -execution does not supply an independent proof report. [STATUS](../STATUS.md) retains -the detailed scientific position and limits. +The proof notes give the mathematical argument. [STATUS](../STATUS.md) maps the +scientific suites and supplementary checks to their verification records and +preservation policy. For the repository's role and discussion details, see [Purpose and contact](../README.md#purpose-and-contact). diff --git a/literature/ASSUMPTIONS.md b/literature/ASSUMPTIONS.md index 20db592..b4ef8c3 100644 --- a/literature/ASSUMPTIONS.md +++ b/literature/ASSUMPTIONS.md @@ -1,42 +1,38 @@ -# Physical premises: evidence, mismatch and the remaining obligation +# Physical premises and calibration requirements -**5 October 2026. Scientific-background update; exact implementation remains unestablished.** The [primary-source register](PHYSICAL_PRECEDENTS.md) records fifteen passage-level primary comparisons (one caption-limited) and one abstract-only comparator. Source IDs below resolve there. -[The operational audit](../research/PREPARATION_READOUT.md) derives the distinction +[Preparation and readout](../research/PREPARATION_READOUT.md) derives the distinction between site occupation and the bound-state projector, and a sufficient error budget. -The [model-residual test](../research/MODEL_RESIDUAL.md) now makes the dynamical +The [model-residual bound](../research/MODEL_RESIDUAL.md) makes the dynamical comparison explicit, including basis motion, higher-band coupling and confinement. -The theorem remains about the fixed conditional Hamiltonian, not a completed device. +The calibration requirements below connect the component precedents to the fixed +Hamiltonian and bound-state projector. -## Preparation and readout: component support is not closure +## Preparation and readout -| Premise | Passage-level component precedents | Exact remaining obligation | +| Premise | Passage-level component precedents | Calibration requirement | |---|---|---| | Prepare the endpoint bound orbital | Y22, W11, K12, T12, N18, Z16: six distinct preparation-related records, including spectroscopy and site selection | Certify the actual extended $`b_4`$, its phases, contamination, yield and preparation cost. An occupied site and a tweezer ground state are not the declared lattice input. | | Measure unconditional bound-state return | Y22, W11, K12, T12, N18, S10, B22: seven distinct measurement/diagnostic records | Establish the effective orbital-sensitive effect and its errors for the output ensemble, including continuum admixtures. Position, sideband, internal-state and survival measurements are different observables. | -The five-to-ten target is met **only for these component collections**, not for six -or seven demonstrations of our exact state/projector. In the checked set, neither -exact model-specific implementation is established. Counting more ordinary microscope -papers cannot by itself repair that mismatch. Y22 is the closest jointly demonstrated -subset, rather than a collection of unrelated capabilities; its remaining differences -are recorded without treating it as our experiment. +These counts describe preparation and diagnostic components, rather than demonstrations +of the exact state/projector. Y22 is the closest jointly demonstrated subset; the +source register records its model-specific differences. -The new static check finds $`|\langle0|b_4\rangle|^2\simeq0.72404`$ at endpoint +The static calculation gives $`|\langle0|b_4\rangle|^2\simeq0.72404`$ at endpoint depth 4. A fixed spatial histogram does not determine its bound-state probability. -These facts sharpen the obligation; they do not change the asymptotic return law. Cooling or initial heralding can occur before the declared experiment with costs reported separately. Filtering on survival after that start changes its denominator. -## Other premises: what the targeted comparisons do and do not close +## Lattice dynamics and control -| Premise/resource | Checked basis and boundary | What remains | +| Premise/resource | Component evidence | Calibration requirement or scope | |---|---|---| -| Coherent single-particle lattice dynamics | Y22, W11, P15, WE23 and CH25: five passage-level motion records, including separately identified 1D and 2D walks | Conventional coherent lattice motion is supported; the finite coherent window for this protocol is unestablished. Position readout and survivor postselection are not unconditional orbital return. | -| Calibrated single attractive site, fixed quadratic schedule | Y22, W11, Z16, M17 and WE23: five addressing/shaping/control components with different signs, states or spatial profiles | The component count is met, not five realizations of a scalar attractive site. Certify all projected matrix elements and their time dependence, not just a central light shift or static occupation threshold. | -| Single-band and nearest-neighbor description | J98, W11, Y22, L13 and C18: five framework/diagnostic records, including a PRL reduction audit | A component-count target is met, not five validations of our reduction. Bound in-band errors, higher-band coupling and any moving-basis term. Small leakage alone does not certify phase accuracy. | -| Other confinement and coherent area/time | J98, Y22, S10, Z16, L13 and M17: six records exposing or controlling background potentials | These include idealizations and finite-region compensation, not six demonstrated coherent windows. Control the residual potential over the evolving state; a uniform density does not certify this. | +| Coherent single-particle lattice dynamics | Y22, W11, P15, WE23 and CH25: five passage-level motion records, including separately identified 1D and 2D walks | Establish the finite coherent window for this protocol. Position readout and survivor postselection are not unconditional orbital return. | +| Calibrated single attractive site, fixed quadratic schedule | Y22, W11, Z16, M17 and WE23: five addressing/shaping/control components with different signs, states or spatial profiles | Certify all projected matrix elements and their time dependence, not just a central light shift or static occupation threshold. | +| Single-band and nearest-neighbor description | J98, W11, Y22, L13 and C18: five framework/diagnostic records, including a PRL reduction audit | Bound in-band errors, higher-band coupling and any moving-basis term. Small leakage alone does not certify phase accuracy. | +| Other confinement and coherent area/time | J98, Y22, S10, Z16, L13 and M17: six records exposing or controlling background potentials | The sources include idealizations and finite-region compensation. Control the residual potential over the evolving state; a uniform density does not certify this. | | Positive-minimum limit | Preserved ROUNDING proof with $`b\le1-\delta`$ | A joint limit is not immunity to a fixed residual depth. Full crossover remains unclaimed. | | Fixed positive anisotropy | Preserved SPECTRAL_SCOPE proof and checks | Not uniform at zero transverse hopping; not evidence for arbitrary traps or extra bands. | | Closed evolution and no incoming continuum population | Conditional source model and the preparation/detection distinction | Certify contamination and environmental channels without relabeling continuum escape as environmental loss or discarding outcomes. | @@ -53,32 +49,15 @@ and higher-band couplings, not a consequence of the word addressing. J98 supplie the reduction framework; it does not justify applying its smooth-potential approximation to every focused beam. This is a calibration criterion, not a new model. -## Decision and bounded next step +## Sufficient error budgets -**Preserve the conditional theory; do not claim a calibrated experimental protocol.** -The generic operational probability bound remains valid. Under the additional pure-input, +The general operational probability bound applies to preparation, dynamics and readout. +Under the additional pure-input, unitary-evolution and rank-one-readout assumptions, MODEL_RESIDUAL proves the sharper bound $`|p-P|\le2\sqrt P\,d+d^2`$. A total vector error $`d=o(L^{-1})`$ is sufficient in the fixed joint domain; the generic absolute-error condition -$`o(L^{-2})`$ remains sufficient without that structure. Neither is a necessary -hardware tolerance or evidence that an apparatus attains it. - -The targeted update reaches the requested five-to-ten **component** range for the -listed preparation (six), readout/diagnostic (seven), motion (five), local-control -(five), single-band framework (five) and confinement/context (six) collections. -Those are different evidentiary roles, not six fulfilled implementation promises. -The explicit model-specific gaps remain in every implementation claim. More generic -papers cannot replace the required matrix elements, orbital identification, -phase/error bounds or coherent operating window. The pure input, closed evolution -and absence of incoming continuum define the conditional theory; they are not -assertions that a cited apparatus realizes it. Reopen a row only for a directly -relevant primary result or a concrete model-matched calibration. - -Exact endpoint preparation and unconditional readout are still unresolved in the -checked apparatus literature. The residual inequality does not construct them. -A genuinely separate proof report is absent. Neither that report nor a demonstrated -device is an already completed fact or an extra hypothesis of the conditional -Hamiltonian theorem. The [scientific preparation record](../research/SCIENTIFIC_PREPARATION.md) -records the bounded closure of the -[2014 source comparison](SOKOLOVSKI_PONS_MUGA_2014.md) and the stop boundary before writing. -Manuscript drafting and outreach remain on hold. +$`o(L^{-2})`$ remains sufficient without that structure. These are sufficient +analytical conditions, not necessary hardware tolerances. Applying them to an apparatus +requires calibrated orbital identification, matrix elements, phase/error bounds and a +coherent operating window. The pure input, closed evolution and absence of incoming +continuum specify the conditional model to which those calibrations must be compared. diff --git a/literature/DEVDARIANI_COMPARISON.md b/literature/DEVDARIANI_COMPARISON.md index 2735e9b..1c372ef 100644 --- a/literature/DEVDARIANI_COMPARISON.md +++ b/literature/DEVDARIANI_COMPARISON.md @@ -1,9 +1,8 @@ -# Devdariani comparison: the threshold, not the word logarithmic +# Devdariani: quadratic Robin trap and square-root threshold -**4 October 2026. Construction-level author-side comparison.** This closes the -specified primary-access gap in the preserved [prior-art register](PRIOR_ART.md). -It does not certify exhaustive priority or independently validate our proof. -The scientific notes and saved numerical references remain unchanged. +Devdariani's quadratic boundary problem is a direct threshold-recapture +predecessor. Its square-root spectral dependence distinguishes it from the +logarithmic lattice threshold in the [prior-art comparison](PRIOR_ART.md). ## Primary source and access boundary @@ -17,8 +16,7 @@ Russian TMF **11**(2), 213–225, and its legitimate full-text download. The Russian original was checked visually at pp. 213–221 and 224–225, including Eqs. (1), (2), (8)–(11), (18), (20), (22), (32)–(34), and Appendix (P.5). Pages 222–223 did not render reliably and their interpolation is not used here. -No English full-text access, complete reproduction of the paper, or permission -to redistribute its PDF is claimed. The [access record](../provenance/CONTINUATION_2026-10-04.json) +The English full text was not accessed. The [access record](../provenance/CONTINUATION_2026-10-04.json) separates successful reading from failed retrievals. The source uses a free radial half-line equation with a time-dependent Robin @@ -100,21 +98,19 @@ must be carried into the physical scattering problem. The inverse-square term in the explicit bridge above illustrates precisely that obligation. Our binding law is essential rather than polynomial. Our rescaling retains -$`L`$ and $`b=\rho_0uL`$, so a uniform proof for $`b\le1-\delta`$ is still -needed. The formal small-power tangent discussed in [AUDIT Section 7](../research/AUDIT.md) -is not such a proof. The method and the existence of threshold loss are inherited; -the spectral matching estimate is the point to test. +$`L`$ and $`b=\rho_0uL`$. [Gate C](../research/UNIFORM_MINIMUM.md) supplies +uniform spectral matching for $`b\le1-\delta`$ at a fixed positive margin. The formal small-power tangent +discussed in [AUDIT Section 7](../research/AUDIT.md) predicts the leading +coefficient but does not supply this uniform estimate. The method and the +existence of threshold loss are inherited. -## Decision and remaining work +## Comparison and algebraic checks -**Core preserved; attribution narrowed.** This specific construction does not +This specific construction does not supply the logarithmic coefficient, the finite-endpoint estimate, or our -finite-periodic-volume joint law. That is a scoped comparison, not an assertion -that no predecessor could contain them. Do not advertise touching, detuning, -a scaled crossover parameter, or reflection-as-recapture as discoveries here. +finite-periodic-volume joint law. Touching, detuning, a scaled crossover parameter +and reflection-as-recapture are already present in the predecessor. -The next evidence is the [separate-reader packet](../research/READER_PACKET.md) -and the unfinished [physical-premise audit](ASSUMPTIONS.md), not a new model. The five algebra tests in `python tools/test_predecessor.py` check this bridge, -scaling, binding, probability labels and threshold ratios. They are not an -independent review or additional members of the preserved 272-control suite. +scaling, binding, probability labels and threshold ratios. They are separate +from the preserved 272-control suite. diff --git a/literature/PHYSICAL_PRECEDENTS.md b/literature/PHYSICAL_PRECEDENTS.md index bb69e11..fe99ee8 100644 --- a/literature/PHYSICAL_PRECEDENTS.md +++ b/literature/PHYSICAL_PRECEDENTS.md @@ -1,13 +1,11 @@ # Physical precedents: what each source actually supports -**5 October 2026. Primary-source audit for the fixed lattice model.** This register -supports [ASSUMPTIONS.md](ASSUMPTIONS.md); it does not select a new platform, tutorial -or detector. The older access labels in the preserved PRIOR_ART.md remain historical. -A component precedent is not evidence that our complete protocol has been implemented. -Only the passages specified below were checked; no paper's experimental data or full -supplement has been independently reproduced. +This register supports [ASSUMPTIONS.md](ASSUMPTIONS.md) by identifying the component +demonstrations, model differences and calibration requirements relevant to the fixed +lattice problem. Access is limited to the passages specified in each entry; +experimental data and full supplements were not independently reproduced. -## Y22 — closest joint subset, not the threshold experiment +## Y22 — coherent 2D motion and local attractive control A. W. Young et al., *Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice* (2022), [arXiv:2202.01204v1](https://arxiv.org/abs/2202.01204v1), @@ -24,7 +22,7 @@ walks and report curvature/inhomogeneity limitations. **Classification: jointly demonstrated subset.** It neither measures our bound-state projector nor establishes our quadratic cycle, residual-depth family, or coherent volume/time requirement. -**Control-pass access extension:** Methods I.2, I.3 and I.5, and Section II were +**Additional inspected passages:** Methods I.2, I.3 and I.5, and Section II were also checked. Alignment can change the effective oracle depth and address neighbors; the supplement describes intensity-control dynamic range, higher-band filtering, curvature, and a dynamical oracle-depth calibration. None supplies a uniform residual @@ -75,7 +73,7 @@ components.** Neither the tweezer eigenstate nor a temperature estimate establis the extended lattice state $`b_4`$. Pre-cycle cooling is not evidence for dissipation being harmless during the threshold cycle. -## T12 — radial cooling is not a three-dimensional fidelity certificate +## T12 — radial cooling and axial occupation J. D. Thompson et al., *Coherence and Raman sideband cooling of a single atom in an optical tweezer*, [arXiv:1209.3028v1](https://arxiv.org/abs/1209.3028v1) (2012); @@ -89,8 +87,7 @@ uses bias-field control with Raman sideband cooling. Its radial occupation is ne zero while its axial occupation is about eight; these are not near-unit joint 3D ground-state occupation. **Classification: preparation and spectroscopy components.** Internal-state coherence is not a measured coherence time for a freely spreading -lattice orbital. Keep the preprint's actual axial limitation rather than paraphrasing -its abstract as a stronger cooling result. +lattice orbital. ## N18 — strontium cooling and detection in one apparatus @@ -119,8 +116,9 @@ Holographic aberration control and atom-based calibration enable structured latt potentials and preparation of selected rows. The optical-bench intensity benchmark and the in-apparatus calibration are different measurements. The demonstrated microscope potentials are repulsive. **Classification: local-control and preparation -components.** Do not turn optical beam-profile precision into a measured residual -attractive on-site energy, or row preparation into preparation of $`b_4`$. +components.** The optical beam-profile benchmark measures a different quantity +from the residual attractive on-site energy; row preparation is distinct from +preparation of $`b_4`$. ## S10 — site fluorescence and background confinement @@ -136,7 +134,7 @@ particle sector parity reduces to occupation, but occupation is still not an orb projector. Imaging after pinning is not evidence for coherent, flat-lattice propagation throughout the same field of view. -## B22 — a phase-sensitive motional diagnostic, not our detector +## B22 — phase-sensitive motional diagnostics M. O. Brown et al., *Time-of-Flight Quantum Tomography of Single Atom Motion* (2022), [arXiv:2203.03053v2](https://arxiv.org/abs/2203.03053v2). @@ -148,7 +146,7 @@ reconstruction of single-atom motion. The demonstrated sequence includes prepara filtering and depends on a calibrated motional model. **Classification: phase-sensitive diagnostic component.** This shows why multiple controlled measurements contain more information than one position histogram; it is not a calibrated two-dimensional -lattice bound-state projector or an adopted replacement detector. +lattice bound-state projector. ## L13 — a moving basis changes the generator @@ -166,7 +164,7 @@ parity-symmetric single-band correction vanishes; higher-band couplings need not our local beam preserves a fixed band, nor supply an experimental error budget. The date printed inside a reformatted copy is not substituted for the 2013 record. -## C18 — lattice-depth spectroscopy is not local-defect calibration +## C18 — periodic-lattice depth calibration C. Cabrera-Gutiérrez et al., *Robust calibration of an optical-lattice depth based on a phase shift*, Physical Review A **97**, 043617 (2018), @@ -179,10 +177,9 @@ A phase shift populates Bloch bands; their energy differences determine dominant oscillation frequencies used to infer lattice depth. The analysis goes beyond a single-well Gaussian approximation. **Classification: band-spectrum calibration component.** Calibrating the periodic lattice does not calibrate the added attractive -site or certify negligible higher-band effects during another protocol. No benchmark -from this method is assigned to our device, and its quench is not adopted here. +site or certify negligible higher-band effects during another protocol. -## M17 — finite-region potential compensation, not an infinite flat lattice +## M17 — potential compensation over a finite interacting region A. Mazurenko et al., *A cold-atom Fermi–Hubbard antiferromagnet*, Nature **545**, 462–466 (2017), [DOI](https://doi.org/10.1038/nature22362). @@ -195,14 +192,13 @@ The captions specify a shaped field compensating gradients and central curvature with walls surrounding a finite subsystem. **Classification: confinement-control component in an interacting lattice.** Equilibrium density uniformity is not a bound on our single-particle phase error, propagation time, or residual generator. -No many-body result is imported into the threshold theorem. ## P15 — coherent motion and preparation shaping, with conditioned data P. M. Preiss et al., *Strongly Correlated Quantum Walks in Optical Lattices*, Science **347**, 1229–1233 (2015), [DOI](https://doi.org/10.1126/science.1260364), [arXiv:1409.3100v2](https://arxiv.org/abs/1409.3100v2). -**Access upgrade, 5 October:** [primary HTML](https://arxiv.org/html/1409.3100v2) +**Access, 5 October 2026:** [primary HTML](https://arxiv.org/html/1409.3100v2) and [PDF](https://arxiv.org/pdf/1409.3100) retrieved. Fig. 1, PDF p. 1; Eqs. (1)–(3), p. 2; Methods, p. 7; Table I, p. 8 checked in parsed text. Earlier access was limited to the abstract after failed PDF/HTML retrievals; those attempts are not reclassified. @@ -234,8 +230,6 @@ local-control components.** Blocking changes the accessible geometry; it is not attractive defect or its quadratic schedule. Hopping has measured anisotropy, and Appendix B2 conditions position data on one detected atom. Static occupation-threshold calibration does not certify all projected matrix elements during coherent evolution. -No demonstrated operating window or unconditional orbital measurement is transferred -to this model. ## CH25 — ordinary single-particle motion within a superlattice study @@ -266,28 +260,22 @@ Physical Review Letters **114**, 193001 (2015), Primary abstract checked; attempted full-text retrieval failed. It supplies a fermionic-site-imaging precedent, not detailed proof of our motional readout. -## Access and counting policy +## Source counts and evidentiary roles There are **fifteen passage-level primary records, including one caption-limited -record, and one abstract-only comparator (C15)** here. M17 remains limited to primary -extended-data captions. The 5 October additions are WE23 and CH25; P15 alone receives -the specified access upgrade. All other reading-depth limits remain as recorded. +record, and one abstract-only comparator (C15)** here. M17 is limited to primary +extended-data captions. Each entry records its specific reading depth. One article appearing under several applicable premises is still one article. Reformatted HTML dates are not publication dates; the cited preprint versions and bibliographic records determine those dates. Failed retrievals, reviews, unrelated search hits, and internal-spin-only addressing examples are not promoted to extra -motional-control evidence. Third-party PDFs are neither committed nor redistributed. +motional-control evidence. -For the six preparation-component and seven measurement/diagnostic-component records -used in the matrix, the five-to-ten *component* target remains met; those two -collections are unchanged. Motion now has five passage-level papers: Y22, W11, P15, -WE23 and CH25. The local-control collection has five: Y22, W11, Z16, M17 and WE23. +The [assumptions matrix](ASSUMPTIONS.md) uses six preparation-component and seven +measurement/diagnostic-component records. Motion has five passage-level papers: +Y22, W11, P15, WE23 and CH25. The local-control collection has five: +Y22, W11, Z16, M17 and WE23. These preserve their different signs, spatial profiles, states and calibrations; -they are not five calibrated attractive single-site implementations. P15's shaping -and CH25's alternating offsets are not needed to inflate that count. In particular, -the presence of a publication in Physical Review Letters does not erase its model -mismatch or prove the combined apparatus. Exact preparation/readout, generator -calibration and the joint coherent window remain unresolved in ASSUMPTIONS.md. -The [model-residual test](../research/MODEL_RESIDUAL.md) states what the remaining -model-specific calibration must establish. No further generic source expansion is -required merely to turn an unresolved implementation row into a larger citation count. +they are component precedents rather than five calibrated attractive single-site +implementations. The [model-residual bound](../research/MODEL_RESIDUAL.md) connects +model-specific orbital and generator calibration to the return-probability error. diff --git a/literature/SCIENTIFIC_CONTEXT.md b/literature/SCIENTIFIC_CONTEXT.md index a6cf40c..1f379be 100644 --- a/literature/SCIENTIFIC_CONTEXT.md +++ b/literature/SCIENTIFIC_CONTEXT.md @@ -1,15 +1,13 @@ # Scientific context and inherited ingredients -**5 October 2026. Internal research record, not a manuscript or independent review.** -This bounded source pass accompanies the fixed author-side result assessed at -`88b633f040bb075b6717c6306fe88d541c718924`. It updates access and attribution; -it does not change the model, coefficient, asymptotic domain or numerical policy. -The earlier comparisons remain in [PRIOR_ART](PRIOR_ART.md), with the later -[Devdariani construction reading](DEVDARIANI_COMPARISON.md) and -[critical assessment](../research/CRITICAL_ASSESSMENT.md) taking precedence where -they explicitly update historical access states. +The logarithmic return argument combines exact lattice identities with inherited +weak-binding, adiabatic and scattering methods. The table records the relevant +primary passages and the depth at which they were inspected. +[PRIOR_ART](PRIOR_ART.md), the [Devdariani comparison](DEVDARIANI_COMPARISON.md) +and the [critical assessment](../research/CRITICAL_ASSESSMENT.md) provide the +associated construction comparisons. -## 1. What is inherited, and what is actually established here +## 1. Inherited ingredients and their scope | Ingredient | Primary attribution and actual access | Use and boundary | |---|---|---| @@ -58,7 +56,7 @@ $`(\pi,0)`$ and $`(0,\pi)`$ instead lie at energy 4 and produce the middle-band density divergence. They are distinct singularities. The full retarded expansion and fixed-anisotropy checks remain in [SPECTRAL_SCOPE](../research/SPECTRAL_SCOPE.md). -## 3. Tolstikhin 2008: the scoped full-text comparison +## 3. Tolstikhin 2008: separated-zero approximations O. I. Tolstikhin, *Siegert-state expansion for nonstationary systems. III. Generalized Born-Fock equations and adiabatic approximation for transitions to @@ -68,7 +66,7 @@ the continuum*, Phys. Rev. A **77**, 032711 (2008): The host identifies an author upload on 30 July 2015. Parsed full text was read: Section II A, Eqs. (1)–(12); Section IV, Eqs. (42)–(43), (67); Section V, -Eqs. (76)–(87). PDF retrieval failed; no visual equation check is claimed. +Eqs. (76)–(87). Equation images were unavailable for a visual check. The half-line model has a free exterior and common remote endpoint potential. Its underbarrier analysis uses simple complex momentum zeros and separation; its overbarrier analysis uses separated real zeros and an antibound interval. @@ -78,19 +76,19 @@ Equation (86) includes initial-state survival, making this a recapture predecess $`\sqrt{\eta(s)}\sim\sqrt{32}\exp[-\pi/(2s^2)]`$, $`s=t/T`$, is flat to every finite power and cannot meet a simple-zero expansion. Those formulas therefore do not supply this lattice result by substitution, or its shrinking-minimum -uniformity. This does not exclude an extension of the method. The access gap is -closed for this scoped comparison, not for an independent audit of that paper. +uniformity. This comparison concerns the displayed approximations and does not +exclude an extension of the method. -## 4. The 2014 construction comparison: targeted gap closed +## 4. Sokolovski–Pons–Muga 2014: linear approach and finite confinement Sokolovski–Pons–Muga, *Adiabaticity near a continuum threshold: An exactly solvable model*, Phys. Rev. A **89**, 042125 (2014): [publisher](https://link.aps.org/doi/10.1103/PhysRevA.89.042125), [author-institution record](https://ekoizpen-zientifikoa.ehu.eus/documentos/5ed32bdf2999526aa7417480). -The user supplied the seven-page primary paper. Full text was read and decisive -pp. 2–6 were visually checked. The -[passage-level comparison](SOKOLOVSKI_PONS_MUGA_2014.md) supersedes the earlier -abstract-only status; failed retrievals remain historical evidence. +The supplied seven-page primary paper was read in full, with decisive pp. 2–6 +visually checked. The +[passage-level comparison](SOKOLOVSKI_PONS_MUGA_2014.md) provides the detailed +schedule, observable and asymptotic comparison. The protocol approaches a one-dimensional threshold monotonically with a linear delta attraction, starting at remote past and stopping below threshold. Equation (26) @@ -102,23 +100,16 @@ for high return probability; Eqs. (6), (32) are small-loss formulas. Section VII box analysis, Eqs. (36), (38)–(40), already supplies a finite-box/continuum contrast; its Sturmian pole $`\omega_1`$ is not the final perturbed energy $`E_1(t_f)`$. -**Comparison inference:** these results do not supply the two-leg quadratic -logarithmic return law or its required joint uniform estimate. The specific -source-access/comparison task is closed, with stronger inherited attribution and -no central coefficient, model, domain or proof correction. This is not exhaustive -novelty clearance or a separate expert review. No outside contact was made. +**Comparison inference:** these results establish method, observable and +finite-confinement precedents; they do not supply the two-leg quadratic logarithmic +return law or its required joint uniform estimate. -## 5. What this preparation does and does not settle +## 5. Power-tangent comparison and controlled limits The strongest local-power objection remains in [CRITICAL_ASSESSMENT](../research/CRITICAL_ASSESSMENT.md): the frozen tangent predicts the full leading coefficient, including its residual-depth -factor. Controlled physical matching and the joint domain remain the contribution -to assess. [LIMITS_AND_ACCURACY](../research/LIMITS_AND_ACCURACY.md) records the -fixed-size recovery, remainder limits and comparator domain without adding a model. - -Targeted searches through 5 October 2026 did not retrieve a directly matching -logarithmic-return theorem; irrelevant hits and failed searches have no exclusion -value. This record is not exhaustive priority clearance or a separate reader report. -It does not close the preparation, readout or apparatus gaps in -[ASSUMPTIONS](ASSUMPTIONS.md), and does not count mathematical citations as device -evidence. No third-party PDF, figure or full text is redistributed here. +factor. Controlled physical matching and the joint domain are the contribution +under comparison. [LIMITS_AND_ACCURACY](../research/LIMITS_AND_ACCURACY.md) gives +the fixed-size recovery result, the precision allowed by the matched remainder +and the power comparator's $`0<\sigma<1`$ domain. These distinguish the inherited +prediction from the uniform physical-return statement. diff --git a/literature/SOKOLOVSKI_PONS_MUGA_2014.md b/literature/SOKOLOVSKI_PONS_MUGA_2014.md index 8707461..ebb2bc2 100644 --- a/literature/SOKOLOVSKI_PONS_MUGA_2014.md +++ b/literature/SOKOLOVSKI_PONS_MUGA_2014.md @@ -1,29 +1,21 @@ # Sokolovski–Pons–Muga 2014: construction-level comparison -**5 October 2026. Internal primary-source comparison, not an independent report.** -Assessed repository base: `34ae43a4a8e8b596fe853995fd0d4c20de13b61c`, tree -`a64d3f293b547d764557d678f8a71709582cb9b4`. - Source: D. Sokolovski, M. Pons and J. G. Muga, *Adiabaticity near a continuum threshold: An exactly solvable model*, Phys. Rev. A **89**, 042125 (2014), -[DOI](https://doi.org/10.1103/PhysRevA.89.042125). The owner supplied the seven-page -published PDF. Its text, Sections I–VIII and Appendix, was read; the decisive +[DOI](https://doi.org/10.1103/PhysRevA.89.042125). The supplied seven-page +published PDF was read in full (Sections I–VIII and Appendix); the decisive equations on printed pp. 042125-2 through 042125-6 were visually checked. The file identity and reading scope are recorded in [provenance](../provenance/SOURCE_COMPARISON_2014_2026-10-05.json). -The PDF, page images and extracted full text are not redistributed in the repository. -## Disposition +## Method and physical comparison -**The specific previously open source-comparison task is closed.** The paper is -a direct predecessor for the outgoing energy/Sturmian method, normalized bound-state +The paper is a direct predecessor for the outgoing energy/Sturmian method, normalized bound-state population, and the contrast between finite confinement and a continuum threshold. It does not directly establish the present two-leg logarithmic return law or its -shrinking-minimum/growing-volume uniformity. No model, coefficient, domain or -proof correction follows from this reading. This is a construction comparison, -not exhaustive priority clearance or a significance upgrade. +shrinking-minimum/growing-volume uniformity. -## What the source actually solves +## Source model and asymptotic assumptions | Item | Primary passage | Exact scope | |---|---|---| @@ -88,19 +80,8 @@ supply uniformity for the present $`u(T)\to0`$ and increasing torus. The finite-box analysis is nevertheless a substantive predecessor. Ordinary finite-size recovery, squared-speed leakage near adiabaticity, outgoing -energy-domain reduction and stationary-phase normalization should remain inherited +energy-domain reduction and stationary-phase normalization are inherited ingredients. [LIMITS_AND_ACCURACY](../research/LIMITS_AND_ACCURACY.md) applies standard gapped reasoning to our fixed torus; it is not a new recovery mechanism. -The central contribution under assessment remains the controlled logarithmic -physical return and its stated joint domain, with the existing local-power -prediction fully acknowledged. - -## Closure and stop boundary - -The four requested checks—complete schedule, normalized observable, binding law, -and asymptotic hypotheses—are now recorded from the primary construction. -No additional scientific repair or new numerical campaign was identified. -Independent critical reading, exhaustive priority and exact experimental -implementation remain unestablished; closing this access gap does not establish -them. Manuscript drafting and outside contact remain on hold. - +The comparison concerns the controlled logarithmic physical return and its stated +joint domain, with the existing local-power prediction included. diff --git a/llms.txt b/llms.txt index 8c59b63..2929c9b 100644 --- a/llms.txt +++ b/llms.txt @@ -32,11 +32,11 @@ H(t)=H_0-[u+(4-u)(t/T)^2]|0\rangle\langle0|, The initial and final reference state is the normalized endpoint bound orbital b4. The observable is its unconditional return probability, not addressed-site occupation. -There is no bath, free waiting interval or postselection in the fixed model. +The fixed model is a closed, coherent weakening-and-restoration cycle. The lower-edge density is finite, rho0=1/(4*pi); the local resolvent is logarithmic. The middle-band van Hove singularity is a different spectral feature. -The recorded author-side asymptotic, as L tends to infinity, is +The uniform leading asymptotic, as L tends to infinity, is ```math \rho_0=\frac1{4\pi},\qquad @@ -53,7 +53,6 @@ P_infinity(T,0) is asymptotic to pi^2/(4*ln(T)^2) and tends to zero. Within the same domain, the law holds along the sufficient periodic-square sequence n(T)=2*ceil(4.5*T)+1, using each finite system's own endpoint bound state. Fixed positive u or fixed finite n instead gives ultimate adiabatic return. -The claim does not include b=1, a full crossover, or an optimal size bound. ## Reading order: authoritative repository text @@ -81,7 +80,7 @@ These raw URLs follow main. Resolve the consulted revision before citing it. The single external teaching foundation is Yu. N. Demkov and V. N. Ostrovskii, *Zero-Range Potentials and Their Applications in Atomic Physics* (1988): https://doi.org/10.1007/978-1-4684-5451-2 -Its selection does not certify a full reading or establish the repository's theorem. +TUTORIAL.md lists the chapter assignments and inspected preview pages. - [Source labels](https://raw.githubusercontent.com/GoGoKo699/Logarithmic-Threshold-Return/main/research/SOURCES.md): local reference numbering in preserved notes. - [Scientific context](https://raw.githubusercontent.com/GoGoKo699/Logarithmic-Threshold-Return/main/literature/SCIENTIFIC_CONTEXT.md): inherited ingredients and access depth. @@ -95,15 +94,16 @@ supersede only the older access labels they explicitly update. Cite the consulte repository file, relevant section and full commit SHA, preferably with an immutable GitHub blob URL. A repository summary is not a claim to have read its cited paper. -## Evidence limits +## Interpreting evidence -The proof route is author-side work; independent review, exhaustive priority and -an exact experimental implementation remain unestablished. Numerical controls, -byte integrity and proof review are distinct. The leading asymptotic does not -certify finite-time percentages or unresolved subleading coefficients. Consult -[current status](https://raw.githubusercontent.com/GoGoKo699/Logarithmic-Threshold-Return/main/STATUS.md) +The A–D notes give the mathematical argument. Numerical controls, reference +comparison and byte integrity have separate records. The leading asymptotic and +its remainder govern the formula's accuracy; use +[limits and accuracy](https://raw.githubusercontent.com/GoGoKo699/Logarithmic-Threshold-Return/main/research/LIMITS_AND_ACCURACY.md) +for finite-duration interpretation and subleading resolution. Consult +[scope and verification](https://raw.githubusercontent.com/GoGoKo699/Logarithmic-Threshold-Return/main/STATUS.md) and [verification policy](https://raw.githubusercontent.com/GoGoKo699/Logarithmic-Threshold-Return/main/provenance/README.md) -for the corresponding evidence records. +for execution and preservation evidence. ## Purpose and contact diff --git a/research/AMPLITUDE_IDENTIFICATION.md b/research/AMPLITUDE_IDENTIFICATION.md index a248235..00d5ca1 100644 --- a/research/AMPLITUDE_IDENTIFICATION.md +++ b/research/AMPLITUDE_IDENTIFICATION.md @@ -1,15 +1,14 @@ # Gate A: reconstructing the particle from the energy equation -**4 October 2026. Author-side lemma chain; not a separate-reader report.** -This fills in the physical-amplitude identification in ASYMPTOTIC Sections 2–3, -AUDIT Sections 2 and 5, and ROUNDING Section 2. Those protected files are unchanged. -The Hamiltonian, observable, logarithmic coefficient and joint domain are unchanged. -No new experiment, drive or detector is introduced. +This note identifies energy-domain reflection with physical bound-state return +and bounds the cost of removing the auxiliary temporal tails. It gives the detailed +construction behind [ASYMPTOTIC Sections 2–3](ASYMPTOTIC.md), +[AUDIT Sections 2 and 5](AUDIT.md), and [ROUNDING Section 2](ROUNDING.md). The energy representation and reflection interpretation are inherited from Sokolovski–Pons [A1]. The tail comparison uses the established adiabatic commutator -method [A2]. What needs checking here is their use for the exact lattice problem, -including its logarithmic spectral singularities and the order of limits. +method [A2]. The construction below applies these methods to the exact lattice +problem, including its logarithmic spectral singularities and the order of limits. ## 1. Statement and conventions @@ -272,22 +271,19 @@ made. Since $`T^{-1}=o(L^{-1})`$, the comparison is small enough for the recorde leading return amplitude. The compact-frequency argument need not itself have constants uniform in $`\alpha`$; the remote limit precedes this uniform tail bound. -## 6. Decision, tests and limits of this pass +## 6. Numerical diagnostics and attribution -**Gate A has an explicit author-side route, with no change to the claimed law.** -The former normalization paragraph alone was not a norm-scattering construction; -Sections 2–4 now supply the extra source regularity, retarded reconstruction and -channel accounting. Section 5 supplies the tail estimate with its uniform domain. -These are the precise new passages for a separate reader to challenge. +Sections 2–4 establish source regularity, retarded reconstruction and channel +accounting. Section 5 gives the uniform tail estimate that connects the auxiliary +reflection coefficient to the finite-cycle return probability. `python tools/test_amplitude_identification.py --output NEW_PATH.json` checks seven small algebra/finite examples: normalization, an exact Airy benchmark, causal source reconstruction, lattice current accounting, reciprocal-log annuli, the tail -commutator/derivatives, and a finite tail propagator inequality. They do not prove -the all-time Fourier argument, the all-$`L`$ theorem or independent validation. +commutator/derivatives, and a finite tail propagator inequality. These finite +diagnostics do not prove the all-time Fourier argument or the all-$`L`$ theorem. The [initial diagnostic failure](../archive/GATE_A_DIAGNOSTIC_FAILURE.md) and its -exact repair are retained. No saved result or protected proof is rewritten. Gates B–D, exhaustive priority, -model-specific implementation and a separate report are not closed by this pass. +exact repair are retained. ### Primary attribution and reading boundary @@ -303,4 +299,3 @@ Commun. Math. Phys. **203**, 445–463 (1999), [author full text](https://arxiv.org/html/math-ph/9805022v4). Section 4, Lemma 1 and Eqs. (3)–(11), was re-read at passage level. Only the commutator comparison method is used on the gapped tails; no gapless theorem is applied at the touching instant. -No third-party PDF is redistributed. diff --git a/research/CLAIMS.md b/research/CLAIMS.md index 9a38c31..195354e 100644 --- a/research/CLAIMS.md +++ b/research/CLAIMS.md @@ -1,72 +1,51 @@ # Claim-to-proof map -**5 October 2026.** This is a navigation layer over the preserved source notes. It does -not strengthen a claim, remove a hypothesis, or replace the full derivations. +For the specified quadratic local-trap cycle, the logarithmic lower-edge resolvent +produces vanishing slow-cycle return to the endpoint bound orbital. Its uniform +shrinking-minimum and sufficient growing-volume domains form one central result. +[The proof map](PROOF_STATUS.md) states its exact quantifiers and error composition. -## The single central statement +## Claims and derivations -For the stated quadratic local-trap cycle, a logarithmic lower-edge resolvent gives -vanishing slow-cycle recapture with a calculated inverse-square-logarithmic law. Its -positive-minimum and finite-volume domain are supporting parts of that statement. - -| Claim | Exact route | Numerical controls | What is not inferred | +| Claim | Derivation | Numerical controls | Scope | |---|---|---|---| -| Local unitary source and bound-state return | CORE, model; ASYMPTOTIC Sections 2–4 | Suite 05 coordinate/spectral comparison, suite 06 time/energy comparison | Site occupation is not the return projector | -| Leading logarithmic law and coefficient | ASYMPTOTIC Sections 5–7, read together with AUDIT | Suites 06–07 scalar formulations, physical-band and boundary checks | Numerical convergence is not the matching proof | -| Positive-minimum law for b below one | ROUNDING Sections 2–4; UNIFORM_MINIMUM | Suite 08 joint-coefficient and finite-time checks | No formula through b=1 or every fixed residual depth | -| A finite-system family with the same limit | ROUNDING Section 6; FINITE_VOLUME | Suite 08 finite torus/coordinate and locality controls | Sufficient size is not necessary or optimized size | -| Fixed positive unequal hoppings | SPECTRAL_SCOPE Sections 2–4 | Suite 09 resolvent, causality and scalar checks | Not uniform as transverse hopping vanishes | - -Read [CORE.md](CORE.md) first, then [ASYMPTOTIC.md](ASYMPTOTIC.md), -[AUDIT.md](AUDIT.md), [ROUNDING.md](ROUNDING.md), and -[SPECTRAL_SCOPE.md](SPECTRAL_SCOPE.md). The local source labels differ between the -preserved notes; [SOURCES.md](SOURCES.md) resolves them. - -## Four proof obligations for a separate reader - -1. Does the retarded Fourier equation and its stationary-phase normalization identify - auxiliary reflection with the physical bound-to-bound amplitude, with the finite - gapped tails controlled at the stated order? -2. Do the integrated central expansion, branch discontinuity and outer current bound - control all matching errors, including the van Hove region without an artificial sink? -3. Is the positive-minimum estimate uniform on the stated b domain, without extrapolating - its apparent pole into the unresolved crossover? -4. Does the finite-volume estimate include the initial-state difference and periodic - seam, making the stated order of limits sufficient without asserting an optimal size? - -These are questions for the exact argument, not a claim that the software has proved it. -The earlier audit answers are author-side answers. A separate report is not yet present. - -[Gate A](AMPLITUDE_IDENTIFICATION.md) now expands the physical-channel identification. -[Gate B](REFLECTION_MATCHING.md) expands the endpoint cancellation and exact-lattice -outer estimates for zero minimum. [Gate C](UNIFORM_MINIMUM.md) supplies the uniform -positive-minimum expansion and [Gate D](FINITE_VOLUME.md) the finite-volume chain. -The [consolidated proof status](PROOF_STATUS.md) records the dependencies and remaining -obligations. All four are author-side arguments; no separate report is present. - -[Limits and accuracy](LIMITS_AND_ACCURACY.md) now makes fixed-size recovery uniform -in minimum depth and states the resolution limit of the existing remainder. The -[scientific preparation record](SCIENTIFIC_PREPARATION.md) connects these clarifications -to the updated primary-source context and the completed -[2014 construction comparison](../literature/SOKOLOVSKI_PONS_MUGA_2014.md). - -## What is inherited and what remains open - -The static resolvent, essential weak binding, threshold-loss problem, energy-domain -method, gapped recovery and locality tools are established ingredients. Read -[PRIOR_ART.md](../literature/PRIOR_ART.md) before framing originality. -The 2014 comparison also makes explicit that a finite-box/continuum contrast is -inherited; the controlled logarithmic law and stated joint domain remain the claim. - -The [Devdariani construction comparison](../literature/DEVDARIANI_COMPARISON.md) -now closes the specifically recorded primary-access gap while preserving the narrow -core and strengthening attribution. Exact physical implementation and a separate -reader report remain open; the [reader packet](READER_PACKET.md) is preparation only. -Full crossover, general trap universality, optimal volume, experimental superiority -and a joint apparatus are not claimed. The known terminology -correction is in SPECTRAL_SCOPE: the lower-edge density is finite; the Green function -is logarithmic. The original older wording is preserved, not silently rewritten. - -[Gate C](UNIFORM_MINIMUM.md) makes the positive-minimum quantifiers and shifted -negative-tail domination explicit. Its seven finite diagnostics are separate from -the preserved scientific suites and do not constitute an independent report. +| Local unitary source and bound-orbital return | [CORE](CORE.md); [A: physical amplitude](AMPLITUDE_IDENTIFICATION.md) | Suite 05 coordinate/spectral and suite 06 time/energy comparisons | Unconditional endpoint orbital projection | +| Leading logarithmic law and coefficient | [B: reflection matching](REFLECTION_MATCHING.md); [ASYMPTOTIC](ASYMPTOTIC.md), Sections 5–7; [AUDIT](AUDIT.md) | Suites 06–07 scalar formulations, physical band and causal boundaries | Exact touching; controlled leading matching | +| Uniform shrinking-minimum law | [C: uniform minimum](UNIFORM_MINIMUM.md); [ROUNDING](ROUNDING.md), Sections 2–4 | Suite 08 joint-coefficient and finite-time checks | Fixed $`0<\delta\le1`$, $`0\le b\le1-\delta`$ | +| Growing finite squares with the same law | [D: finite volume](FINITE_VOLUME.md); [ROUNDING](ROUNDING.md), Section 6 | Suite 08 torus/coordinate and locality controls | Sufficient $`n(T)=2\lceil4.5T\rceil+1`$; each square's own endpoint state | +| Fixed positive unequal hoppings | [SPECTRAL_SCOPE](SPECTRAL_SCOPE.md), Sections 2–4 | Suite 09 resolvent, causality and scalar checks | Supporting result; nonuniform at zero transverse hopping | + +The original derivations are [CORE](CORE.md), [ASYMPTOTIC](ASYMPTOTIC.md), +[AUDIT](AUDIT.md) and [ROUNDING](ROUNDING.md). Their local source labels are +resolved in [SOURCES](SOURCES.md). + +## Four proof components + +1. [A](AMPLITUDE_IDENTIFICATION.md) reconstructs the retarded solution, identifies + equal bound-channel normalization and controls the finite temporal endpoints. + The endpoint estimate compares **amplitude moduli** at order $`O(T^{-1})`$. +2. [B](REFLECTION_MATCHING.md) controls the integrated central expansion, causal + jump and exact-lattice outer matching, including the full physical band. +3. [C](UNIFORM_MINIMUM.md) makes those estimates uniform on the fixed-margin + residual-depth domain. +4. [D](FINITE_VOLUME.md) bounds the finite/infinite initial-state difference, + periodic seam and propagated error for the sufficient growing family. + +[Limits and accuracy](LIMITS_AND_ACCURACY.md) treats fixed-size recovery, +the leading remainder and the power comparator's domain. [Preparation/readout](PREPARATION_READOUT.md) +and [model residuals](MODEL_RESIDUAL.md) state sufficient operational error conditions. + +## Inherited ingredients and contribution + +The static resolvent, essential weak binding, threshold-loss phenomenon, +energy-domain method, gapped recovery and localization tools have established +precedents. The local power-law tangent also predicts the leading prefactor. +The proof route controls the logarithmic physical limit and its stated joint domain. + +[Scientific context](../literature/SCIENTIFIC_CONTEXT.md), the +[Devdariani construction comparison](../literature/DEVDARIANI_COMPARISON.md) and +[2014 comparison](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) supply precise +attributions and inspected-source boundaries. The detailed comparator algebra is +in [the critical assessment](CRITICAL_ASSESSMENT.md). The lower-edge density is +finite; the logarithm belongs to the local Green function, as explained in +[spectral scope](SPECTRAL_SCOPE.md). diff --git a/research/FINITE_VOLUME.md b/research/FINITE_VOLUME.md index c59d175..db4f371 100644 --- a/research/FINITE_VOLUME.md +++ b/research/FINITE_VOLUME.md @@ -1,11 +1,10 @@ # Gate D: finite volume without replacing the initial state -**5 October 2026. Author-side lemma chain; not a separate-reader report.** -This expands [ROUNDING Section 6](ROUNDING.md) for the same periodic squares and -quadratic cycle. The protected proof, observable, leading coefficient and sufficient -size family are unchanged. No smaller necessary size, new boundary condition, or -experimental implementation is claimed. [The proof map](PROOF_STATUS.md) collects -the four author-side gates after this pass. +This note derives finite-volume error bounds for the periodic squares and quadratic +cycle of [ROUNDING Section 6](ROUNDING.md). It compares the normalized finite and +infinite endpoint states, controls propagation across the periodic seam, and gives +a sufficient size family that preserves the logarithmic return law. +[The proof map](PROOF_STATUS.md) connects Gates A–D. ## 1. Statement, embeddings and constants @@ -209,7 +208,7 @@ The second inequality retains the small amplitude: a state error $`o(1/L)`$ is sufficient for a relative probability error $`o(1)`$ when $`P_\infty\asymp_\delta L^{-2}`$. Using only the norm conservation $`\psi^\dagger\psi=1`$ would not measure return. -## 6. The already claimed family is sufficient, uniformly +## 6. A sufficient family, uniformly in the minimum depth At $`\mu=1/2`$, $`a_\mu<13/25<4/57/5`$. Similarly, $`\sinh(1/2)\le1/2+1/48+(1/3840)/(1-1/168)<209/400`$. Thus no rounded numerical root is needed for either margin. -Choose exactly the preserved family +Choose the family ```math R(T)=\lceil4.5T\rceil,\quad n(T)=2R(T)+1,\qquad @@ -257,7 +256,7 @@ The relative error added by finite volume is $`O_\delta(L\mathcal B+L^2\mathcal B^2)`$ and is negligible beside Gate C's conservative remainder. This does not exchange fixed-volume and slow-time limits. -## 7. Tests, attribution and decision +## 7. Numerical diagnostics and attribution `python tools/test_finite_volume.py --output NEW.json` supplies eight small algebra/matrix/short-cycle diagnostics. Large finite grids used to check a static @@ -266,18 +265,11 @@ finite geometries test the seam/Duhamel identity, not an infinite-lattice simula These diagnostics are separate from the original 272 controls and cannot prove the uniform all-size statement by sampling. -Exponential localization is established methodology, not a discovery of this pass. +Exponential localization is established methodology. For attribution only, the primary publisher abstract and metadata of J. M. Combes and L. Thomas, *Asymptotic behaviour of eigenfunctions for multiparticle Schrodinger operators*, Commun. Math. Phys. **34**, 251-270 (1973), [DOI 10.1007/BF01646473](https://doi.org/10.1007/BF01646473), were checked on 5 October 2026. Its full construction was not read or imported. All lattice weight, seam and normalization estimates needed here are derived above; no continuum -hypothesis is silently transferred. This is not an additional experimental-precedent -record or a reopening of broad source collection. - -**Decision:** Gate D has an explicit author-side route preserving the finite family -and original law. All four specified gates now have author-side expansions. A separate -critical report, exhaustive priority, and model-specific implementation remain absent. -The next step is consolidated critical assessment, not another model or an automatic -Gate E. Protected notes, saved references and the original archive remain unchanged. +hypothesis is silently transferred. diff --git a/research/LIMITS_AND_ACCURACY.md b/research/LIMITS_AND_ACCURACY.md index a106286..87f633e 100644 --- a/research/LIMITS_AND_ACCURACY.md +++ b/research/LIMITS_AND_ACCURACY.md @@ -1,9 +1,7 @@ # Limits and accuracy of the fixed return law -**5 October 2026. Author-side clarification, not a new central result.** -This note makes two implications of the existing argument precise before prose is -built around them. It leaves the Hamiltonian, observable and main asymptotic domain -in [PROOF_STATUS](PROOF_STATUS.md) unchanged. +This note derives fixed-size recovery, interprets the leading remainder and states +the power comparator's domain. The uniform return law is in [PROOF_STATUS](PROOF_STATUS.md). ## 1. Fixed finite size restores return uniformly in the minimum depth diff --git a/research/MODEL_RESIDUAL.md b/research/MODEL_RESIDUAL.md index 25c366f..7569f9e 100644 --- a/research/MODEL_RESIDUAL.md +++ b/research/MODEL_RESIDUAL.md @@ -1,10 +1,10 @@ # From microscopic control to the fixed Hamiltonian: a residual test -**4 October 2026. Author-side calibration argument, not a new threshold law.** -The Hamiltonian, endpoint orbital and observable in [CORE](CORE.md) are unchanged. -This note supplies an explicit way to bound the dynamical error left abstract in -[PREPARATION_READOUT](PREPARATION_READOUT.md). It neither specifies hardware nor -claims that any cited experiment meets the bound. All norms below use $`\hbar=J=1`$. +This note bounds the dynamical error in [PREPARATION_READOUT](PREPARATION_READOUT.md) +by comparing a physical generator with the fixed Hamiltonian in [CORE](CORE.md). +Applying the bound requires a common-space orbital identification, in-band residual +matrix elements, out-of-subspace coupling or an error-controlled effective generator, +and the background potential over the occupied region. All norms below use $`\hbar=J=1`$. ## 1. Compare generators, not just populations or light profiles @@ -101,8 +101,8 @@ image or a nearly uniform equilibrium density is not this dynamical certificate. ## 3. Small higher-band population does not certify the ideal return -The following elementary three-level example tests a purported calibration -criterion; it is not a new physical model for this project. Let $`N\ge2`$ be an integer, +The following elementary three-level counterexample tests a calibration +criterion. Let $`N\ge2`$ be an integer, $`\Omega=N/(N-1)`$, $`g=\tfrac12\sqrt{\Omega^2-1}`$, and use ```math @@ -161,17 +161,12 @@ Mixed preparation, unknown detector effects, dissipative evolution and additive false positives still require the general error contract. For example, a fraction $`r`$ of perfectly accepted incoherent contamination changes a signal $`P`$ to $`(1-r)P+r`$. Small coherent-amplitude errors and small additive probabilities are -different guarantees. No detector, ramp, platform or postselection is introduced. +different guarantees. -## Evidence and stop boundary +## Numerical diagnostics `python tools/test_model_residual.py --output NEW_PATH.json` checks seven small identities/inequalities, including a short 5-by-5 fixed-cycle Duhamel check and the -analytic three-level counterexample. It does not perform an asymptotic campaign, -validate a microscopic apparatus or add members to the preserved 272 controls. - -The missing experimental evidence is now specific: a common-space orbital -identification, in-band residual matrix elements, out-of-subspace coupling or an -error-controlled effective generator, and the background potential on the occupied -region. No checked source supplies those together for this exact protocol. The -conditional logarithmic claim and the separate-reader obligations are unchanged. +analytic three-level counterexample. These finite diagnostics are separate from +the preserved 272 controls; they do not perform an asymptotic campaign or validate +a microscopic apparatus. diff --git a/research/PREPARATION_READOUT.md b/research/PREPARATION_READOUT.md index 59f3686..92605d4 100644 --- a/research/PREPARATION_READOUT.md +++ b/research/PREPARATION_READOUT.md @@ -1,10 +1,9 @@ -# Preparation and readout: an operational boundary for the fixed claim +# Preparation and readout of bound-state return -**4 October 2026. Author-side audit, not a new dynamical result or detector design.** -The [core](CORE.md), its bound-state projector and all preserved proofs are unchanged. -[Physical precedents](../literature/PHYSICAL_PRECEDENTS.md) supply components, not a -calibrated implementation of the entire threshold cycle. This note states what such -an implementation would have to certify. +This note derives calibration requirements for the bound-state projector in +[CORE](CORE.md). The [physical precedents](../literature/PHYSICAL_PRECEDENTS.md) +support individual components; applying them to the complete threshold cycle +requires the preparation, dynamics and readout bounds below. ## 1. An occupied site is not the endpoint bound orbital @@ -27,7 +26,7 @@ I_2=-\frac{dI_1}{d\eta}=\frac{2E(16/z^2)}{\pi(z^2-16)}. ``` Here $`K`$ and $`E`$ use the parameter, not the elliptic modulus, convention. -The new static diagnostic gives +The static calculation gives ```math \eta_4\simeq1.045878167,\qquad w\simeq0.724043782,\qquad @@ -104,7 +103,7 @@ A fixed absolute error budget alone cannot certify an indefinitely shrinking sig a finite experiment instead needs a stated signal-to-uncertainty window. No physical coherence time, attainable error budget or laboratory size follows from this inequality. -## 3. What is to be certified, without changing the observable +## 3. Orbital calibration and the ensemble denominator Preparation must certify the extended $`b_4`$ of the actual endpoint Hamiltonian, including relative phases, contamination and its own yield. Cooling before the @@ -123,7 +122,6 @@ Thus a certified calibration on $`b_4`$ can bound this readout error under those structural assumptions. Without them, a high response on one input does not determine a general effect: $`M=I`$ accepts $`b_4`$ perfectly but also accepts every orthogonal state. Reversing a parameter schedule alone does not establish the required mapping. -No new readout protocol or loading ramp is proposed here. The ensemble denominator must be fixed at the declared start. Initial heralding can define that ensemble, with loading cost reported separately. Later survival filtering @@ -132,7 +130,7 @@ $`p_{\rm raw}=(1-q)p_{\rm conditional}`$. Escape into the lattice continuum is n loss to an unobserved environment. Site pinning, fluorescence and motional spectroscopy must each be assigned to preparation, evolution or detection rather than conflated. -## Verification and decision +## Numerical diagnostics `python tools/test_operational_contract.py --output NEW_PATH.json` performs six small checks: elliptic/integral agreement, finite static endpoint states, projector distance, @@ -140,8 +138,3 @@ the equal-histogram counterexample, the trace-distance inequality, and ensemble/ conventions. It checks 17-, 33- and 65-site-side periodic **static** states; it does not propagate a threshold cycle or extend the original 28-group / 272-control suite. The values above are numerical diagnostics, not interval-certified constants. - -**Decision:** preserve the conditional logarithmic theorem and its declared observable. -The component literature does not yet close endpoint preparation and readout for this -protocol. That is a specific implementation obligation, not a counterexample to the -Hamiltonian claim, and not permission to substitute site occupation or survival return. diff --git a/research/PROOF_STATUS.md b/research/PROOF_STATUS.md index 317cbf7..1cf2011 100644 --- a/research/PROOF_STATUS.md +++ b/research/PROOF_STATUS.md @@ -1,13 +1,12 @@ -# Consolidated proof status: one claim, four author-side gates +# Return law and proof map -**5 October 2026. Internal research map, not a manuscript or independent report.** Read [CORE](CORE.md) for the physical question and [CLAIMS](CLAIMS.md) for the -original-source routes. This map records what the bounded A-D scrutiny supplied, -what it did not establish, and where further work should stop. +claim-to-derivation routes. The four components below establish the uniform +return law and its sufficient finite-volume realization. ## The fixed statement and its quantifiers -The protocol remains one particle, a nearest-neighbor square lattice, attraction +The protocol uses one particle, a nearest-neighbor square lattice, attraction $`U(t)=u+(4-u)(t/T)^2`$ for $`-T\le t\le T`$, and unconditional return to the endpoint bound orbital. For fixed $`0<\delta\le1`$, let @@ -16,23 +15,23 @@ endpoint bound orbital. For fixed $`0<\delta\le1`$, let T(L,b)=\frac{e^L}{32}\sqrt{(4-u(L,b))\rho_0L},\quad 0\le b\le1-\delta. ``` -The author-side claim is the uniform law +The uniform law is ```math \sup_{0\le b\le1-\delta} \left|\frac{4L^2(1-b)^2}{\pi^2}P_\infty(T(L,b),u(L,b))-1\right|\to0. ``` -The same limit holds for $`P_{n(T)}`$ with the already specified sufficient +The same limit holds for $`P_{n(T)}`$ with the sufficient $`n(T)=2\lceil4.5T\rceil+1`$. Each finite observable uses its own endpoint bound vector, not an assumed copy of the infinite one. At $`u=0`$ this yields $`P\sim\pi^2/(4\ln^2T)`$. Fixed positive depth and fixed volume are different orders of limits and ultimately have adiabatic return. The margin below $`b=1`$ -must stay fixed; no full crossover is claimed. +must stay fixed. ## Dependency chain and error scale -| Gate | Author-side expansion | What it supplies | Error or normalization boundary | +| Component | Derivation | What it supplies | Error or normalization boundary | |---|---|---|---| | A | [Physical amplitude](AMPLITUDE_IDENTIFICATION.md) | Retarded norm reconstruction, no incoming continuum, equal bound-leg normalization, finite endpoints | Remote time first at fixed parameters; endpoint modulus error $`O(T^{-1})`$ uniformly for small $`u`$ | | B | [Reflection matching](REFLECTION_MATCHING.md) | Both causal contributions, explicit endpoint cancellation, exact-lattice passive and negative-tail matching | Zero minimum; phase-adjusted amplitude $`i\pi/(2L)+O(L^{-5/4})`$ | @@ -51,68 +50,17 @@ so the small instantaneous gap does not enter that comparison. The additional relative probability error is $`O_\delta(L\mathcal B+L^2\mathcal B^2)`$. This is negligible compared with the existing conservative matched remainder. -The original protected notes remain byte-preserved. The four expansions add -explicit arguments; they do not erase their earlier wording or certify every -sentence in the historical source. No coefficient, Hamiltonian or domain -correction was found in these bounded author-side passes. This is an author-side -assessment, not evidence of an independent reader's agreement. +## Attribution and accuracy -## Consolidated author-side assessment +The local power-law tangent in [AUDIT Section 7](AUDIT.md) predicts the full leading +positive-minimum prefactor. [The critical assessment](CRITICAL_ASSESSMENT.md) +works out that comparison and composes the A–D errors. The controlled logarithmic +physical limit and its joint domain are the result supplied by the proof route. +The same assessment attributes the midpoint identity to Sokolovski–Pons (2016), +Eq. (5). -[CRITICAL_ASSESSMENT](CRITICAL_ASSESSMENT.md) checks the A-D interfaces and combines -their amplitude errors explicitly. No coefficient or domain correction was found in -those checks. It also sharpens the originality objection: the local power-law tangent -predicts the full positive-minimum prefactor, not only the zero-minimum constant. -The controlled physical limit, not those prefactors in isolation, is the contribution -under assessment. The assessment adds direct attribution of the midpoint identity to the 2016 -predecessor. No independent reader rating is supplied by this pass. - -The later [scientific preparation](SCIENTIFIC_PREPARATION.md) adds bounded scope -clarifications in [LIMITS_AND_ACCURACY](LIMITS_AND_ACCURACY.md): fixed-size recovery -is uniform in residual depth, and the current remainder does not resolve subleading -logarithmic coefficients. The inherited power comparator is explicitly restricted -to its existing $`0<\sigma<1`$ domain. The A-D derivations remain unchanged. - -## What remains genuinely unresolved - -**Separate critical reading.** All four reader gates remain unrated by an external -reader. [READER_PACKET](READER_PACKET.md) is still a brief, not a received report. -An assessor must specify the revision, passages checked, reasoning, and the effect -of any objection on the central claim. Another assistant session does not establish -independence merely by repeating the calculation. - -**Priority and significance.** [The scoped comparison](../literature/DEVDARIANI_COMPARISON.md) -resolves the identified predecessor construction but is not exhaustive priority. -The static logarithm, threshold-loss phenomenon, energy-domain method, power-law -connection formula and localization tools are inherited. The contribution under -assessment is this controlled logarithmic return law and its finite joint domain, -not the number of auxiliary lemmas or successful tests. The familiar small-power -tangent in [AUDIT Section 7](AUDIT.md) remains a serious comparator, not a result to -hide or automatically equate with a proof of the present limit. - -**Implementation.** [ASSUMPTIONS](../literature/ASSUMPTIONS.md) records component -support and exact-model mismatches. The endpoint preparation, unconditional orbital -projector, calibrated generator and joint coherent operating window are not -established as a device. The error inequalities in [PREPARATION_READOUT](PREPARATION_READOUT.md) -and [MODEL_RESIDUAL](MODEL_RESIDUAL.md) are sufficient conditional guarantees, not -achieved specifications. The targeted conventional component collections now reach -their five-to-ten range; they remain different from exact implementation evidence. - -The full residual-depth crossover, optimal lattice size, arbitrary trap universality, -many-body extensions, dimensional crossover and application superiority are outside -the claim. They are not required repairs unless a concrete objection makes one -necessary. Fixed positive anisotropy remains a supporting scope check, not a fifth -central proof gate or a substitute for significance. - -## Completion boundary for this phase - -The bounded author-side A-D expansion is complete as a route for critical reading. -Do not start an automatic Gate E or another numerical campaign. The consolidated author-side assessment is now recorded. Further work must -respond to an exact objection, a directly matching predecessor, or a genuinely -separate critical reading; routine internal proof expansion stops here. Reopen a physical premise only for directly model-matched evidence. -Manuscript drafting, release and all outside contact remain on hold. - -Numerical execution, byte reproduction, symbolic diagnostics and scientific proof -review remain distinct. The original suite is still 5 suites / 28 groups / 272 -controls; the eight D diagnostics are supplementary. Actual verification outcomes -belong in their retained reports and PR comments, not in claims inferred from badges. +[Limits and accuracy](LIMITS_AND_ACCURACY.md) derives uniform recovery at each +fixed finite size and explains the resolution of the leading remainder. The +inherited power comparator uses its stated $`0<\sigma<1`$ domain. +[Scientific context](../literature/SCIENTIFIC_CONTEXT.md) records primary +attributions; [scope and verification](../STATUS.md) maps the executable evidence. diff --git a/research/REFLECTION_MATCHING.md b/research/REFLECTION_MATCHING.md index 65f4e11..2f1d036 100644 --- a/research/REFLECTION_MATCHING.md +++ b/research/REFLECTION_MATCHING.md @@ -1,16 +1,16 @@ # Gate B: the leading reflection and its physical outer matching -**4 October 2026. Author-side lemma chain, not a separate-reader report.** -This expands ASYMPTOTIC Sections 4–7 and AUDIT Sections 3–5 without changing their -protected bytes. The fixed cycle, bound-state observable and leading coefficient -are unchanged. This pass treats exact touching, $`u=0`$; the uniform positive-minimum -and finite-volume arguments remain separate Gates C and D. +This note derives the leading reflection coefficient at exact touching, $`u=0`$, +with physical outer matching and explicit remainder estimates. It develops +[ASYMPTOTIC Sections 4–7](ASYMPTOTIC.md) and [AUDIT Sections 3–5](AUDIT.md). +The positive-minimum and finite-volume extensions are in +[Gate C](UNIFORM_MINIMUM.md) and [Gate D](FINITE_VOLUME.md). The energy-to-time identification and finite-endpoint comparison are supplied by [Gate A](AMPLITUDE_IDENTIFICATION.md). The argument below starts from its nonzero physical recessive energy solution. WKB residual estimates and elliptic logarithms -are inherited tools, not new methods [B1–B2]. The specific endpoint cancellation -and exact-lattice error bookkeeping below are the author-side calculations to check. +are inherited tools [B1–B2]. The endpoint cancellation and exact-lattice error +estimates are derived below. ## 1. Exact coefficient, local replacement and the target error @@ -290,27 +290,24 @@ $`O(T^{-1})`$ as in Gate A. Since $`T^{-1}=o(L^{-5/4})`$, that comparison does n change the probability statement. No phase observable or sharp finite-time error bar is asserted. -## 6. Decision and evidence boundary +## 6. Numerical diagnostics and the positive-minimum extension -**Gate B has an explicit author-side route; no coefficient correction was found.** -The substantive additions are the endpoint matrices, the exact-lattice version of -the passive bound, and an exact spectral-measure estimate for the entire negative -tail. They replace compressed steps, not the fixed claim. A separate reader should -check these passages together with Gate A; no independent report exists. +The endpoint matrices, exact-lattice passive bound and spectral-measure estimate +for the entire negative tail connect the central reflection calculation to the +physical channels of Gate A. `python tools/test_reflection_matching.py --output NEW_PATH.json` runs six small checks: the basis/Riccati algebra, distributional cancellation, finite central transfers, passive terminal examples including a zero of $`y`$, exact negative-tail -integrals, and high-precision local coefficient derivatives. They are not a proof -by sampling, new time-domain threshold simulations, or additional members of the -original 272 controls. The initial structural symbolic-zero assertion failure and -its canonicalization repair are retained in [the failure record](../archive/GATE_B_DIAGNOSTIC_FAILURE.md). -No numerical tolerance, equation or protected source was changed. +integrals, and high-precision local coefficient derivatives. These finite checks +are separate from the original 272 controls; they do not prove the asymptotic +bounds by sampling or simulate time-domain threshold dynamics. The initial +structural symbolic-zero assertion failure and its canonicalization repair are +retained in [the failure record](../archive/GATE_B_DIAGNOSTIC_FAILURE.md). -Next: challenge the already stated positive-minimum uniformity (Gate C). A result -for every fixed minimum parameter below the boundary is not automatically a uniform -result along varying parameter sequences. Gate D remains separate. Broad literature -collection, new models, manuscript drafting and outside contact remain on hold. +[Gate C](UNIFORM_MINIMUM.md) establishes uniformity for the positive-minimum +family. A result for every fixed minimum parameter below the boundary alone +would not establish a uniform result along varying parameter sequences. ### Method sources and actual access @@ -322,5 +319,4 @@ explicitly for this problem. The underlying book was not newly read. [B2] NIST Digital Library of Mathematical Functions, [Section 19.12](https://dlmf.nist.gov/19.12), Eqs. 19.12.1–3: HTML convergent elliptic series and modulus conventions checked. -This supports the local derivative expansion, not a dynamical priority claim or -a newly selected tutorial. No third-party PDF is redistributed. +These series support the local derivative expansion. diff --git a/research/SCIENTIFIC_PREPARATION.md b/research/SCIENTIFIC_PREPARATION.md index c7e6a6c..4ab9eec 100644 --- a/research/SCIENTIFIC_PREPARATION.md +++ b/research/SCIENTIFIC_PREPARATION.md @@ -1,95 +1,56 @@ -# Scientific preparation for the fixed theoretical claim +# Scientific support for logarithmic return -**5 October 2026. Research record, not manuscript text or a readiness certificate.** -Assessed base: `88b633f040bb075b6717c6306fe88d541c718924`, tree -`a5d7328e17cd6a291b16475d80e8089823a93d1c`. The owner authorized this targeted -prewriting research and repository integration. The model, observable and leading -law remain those in [PROOF_STATUS](PROOF_STATUS.md). - -## Present disposition - -The accessible author-side work identified in this pass is integrated: a precise -fixed-size recovery corollary, accuracy and comparator-domain clarification, -updated predecessor reading, and the missing conventional motion/control support. -The owner subsequently supplied the missing Sokolovski-Pons-Muga 2014 paper. -The [construction-level comparison](../literature/SOKOLOVSKI_PONS_MUGA_2014.md), -assessed at base `34ae43a4a8e8b596fe853995fd0d4c20de13b61c`, closes that -specific access and comparison task. The identified bounded author-side research -tasks are now recorded; this does not certify exhaustive novelty or independent -review. - -The central physical contribution remains the controlled logarithmic return for -the specified cycle and its stated joint domain. The local power tangent predicts -the full leading prefactor. Technical control establishes that prediction as the -declared physical return; its significance remains a reasoned judgment. +The result is controlled logarithmic bound-state return for the specified quadratic +cycle, with the residual-depth and finite-volume domain stated in +[PROOF_STATUS](PROOF_STATUS.md). This map connects the physical observable, +asymptotic estimates and source comparisons. ## Claim and support map -| Item needed for the fixed account | Exact support now available | Disposition | +| Claim or ingredient | Supporting argument | Scope | |---|---|---| -| Physical bound-to-bound observable and normalization | [Gate A](AMPLITUDE_IDENTIFICATION.md); CORE and ASYMPTOTIC | Author-side route supplied; no incoming continuum and unconditional endpoint projector remain explicit | +| Physical bound-to-bound observable and normalization | [Gate A](AMPLITUDE_IDENTIFICATION.md); [CORE](CORE.md) and [ASYMPTOTIC](ASYMPTOTIC.md) | No incoming continuum; unconditional endpoint projector | | Leading logarithmic return and uniform positive minimum | [Gates B](REFLECTION_MATCHING.md) and [C](UNIFORM_MINIMUM.md); [assessment](CRITICAL_ASSESSMENT.md) | Fixed margin below $`b=1`$; power comparator restricted to $`0<\sigma<1`$ | -| A sufficient increasing finite family | [Gate D](FINITE_VOLUME.md) | Own endpoint states and seam errors controlled; no optimal-size claim | -| Fixed finite geometry, including $`u=u(T)\to0`$ | [Limits and accuracy, Section 1](LIMITS_AND_ACCURACY.md) | Uniform recovery proved with an $`n`$-dependent bound; no substitution of growing $`n`$ | -| Meaning of implicit $`L`$ and the current remainder | [Limits and accuracy, Section 2](LIMITS_AND_ACCURACY.md) | Leading coefficient only; no certified subleading log coefficient, finite-time precision or eventual monotonicity | +| A sufficient increasing finite family | [Gate D](FINITE_VOLUME.md) | Own endpoint states and seam estimates; sufficient rather than optimal size | +| Fixed finite geometry, including $`u=u(T)\to0`$ | [Limits and accuracy, Section 1](LIMITS_AND_ACCURACY.md) | Uniform recovery with an $`n`$-dependent bound; growing $`n`$ requires a separate comparison | +| Meaning of implicit $`L`$ and the matched remainder | [Limits and accuracy, Section 2](LIMITS_AND_ACCURACY.md) | Leading coefficient controlled; subleading logarithmic coefficients, finite-time precision and eventual monotonicity are not resolved by this remainder | | Static logarithm, essential binding, adiabatic and localization tools | [Scientific context](../literature/SCIENTIFIC_CONTEXT.md); [source map](SOURCES.md) | Inherited ingredients attributed; exact lattice conventions separated from continuum analogies | -| Closest threshold-dynamics constructions | [Prior art](../literature/PRIOR_ART.md), [Devdariani](../literature/DEVDARIANI_COMPARISON.md), [context](../literature/SCIENTIFIC_CONTEXT.md), [2014 construction](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) | Targeted source comparisons recorded; no direct subsumption found, without exhaustive priority clearance | -| Physical model conventions | [Physical precedents](../literature/PHYSICAL_PRECEDENTS.md) and [assumptions](../literature/ASSUMPTIONS.md) | Listed component collections reach five-to-ten records with source-specific mismatches; no joint device inferred | -| Possible implementation errors | [Preparation/readout](PREPARATION_READOUT.md), [generator residual](MODEL_RESIDUAL.md) | Sufficient conditional inequalities, not attained specifications | - -The existing fixed-positive-anisotropy result remains a supporting scope check. -No arbitrary-trap, dimensional-crossover, many-body, application-advantage or -complete residual-depth-crossover assertion is needed for the present claim. - -## The supplied primary text closes the identified task - -The 2014 paper was read in full, with its decisive equations visually checked. -It solves a monotone linear approach stopped below threshold, measures the final -normalized bound-state population, and has algebraic binding. Its exact integral -and fixed-final-energy slow limit do not supply the two-leg logarithmic return -or the required joint uniform estimates. Its energy method and finite-box contrast -strengthen the inherited attribution; no central correction was identified. - -The [comparison](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) records all four -requested items: schedule/endpoints, observable, binding law and asymptotic -hypotheses. [Follow-up provenance](../provenance/SOURCE_COMPARISON_2014_2026-10-05.json) -records the supplied PDF hash and supersedes the earlier open access status. -The historical failed-access record is retained. No third-party PDF is committed. - -## What is unresolved but is not an added theorem hypothesis +| Threshold-dynamics constructions | [Prior art](../literature/PRIOR_ART.md), [Devdariani](../literature/DEVDARIANI_COMPARISON.md), [context](../literature/SCIENTIFIC_CONTEXT.md), [2014 construction](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) | Comparisons track the schedule, observable, binding law and asymptotic hypotheses | +| Physical model conventions | [Physical precedents](../literature/PHYSICAL_PRECEDENTS.md) and [assumptions](../literature/ASSUMPTIONS.md) | Source-specific support and model differences for local trapping, motion and control | +| Preparation, readout and generator errors | [Preparation/readout](PREPARATION_READOUT.md), [generator residual](MODEL_RESIDUAL.md) | Sufficient conditional bounds on changes to the declared return probability | -**Separate critical reading:** no independent report has been received. The -[reader packet](READER_PACKET.md) stays unrated. The additional internal readings -in this pass are not independent scientific review. +Uniformity requires $`0\le b\le1-\delta`$ with fixed $`0<\delta\le1`$. +The fixed-positive-anisotropy check in [SPECTRAL_SCOPE](SPECTRAL_SCOPE.md) +is likewise restricted to positive transverse hopping; it is not uniform in +the dimensional-crossover limit. -**Experimental realization:** exact endpoint preparation, unconditional orbital -readout, a calibrated time-dependent generator and the joint coherent operating -window remain unestablished. A conditional Hamiltonian theorem need not assert a -device. Any later experimental claim must discharge those actual obligations; -component counts do not do so. +## Power-tangent comparison -**Priority and significance:** the bounded comparisons support a carefully scoped -contribution, not exhaustive novelty or an external endorsement. The inherited -threshold-loss phenomenon and local-power prediction remain visible. +The local power tangent predicts the full leading prefactor, including its +residual-depth factor. The [critical assessment](CRITICAL_ASSESSMENT.md) compares +this prediction with the controlled logarithmic limit. The contribution is the +identification and uniform control of the declared physical return, including +finite endpoints and a sufficient growing-volume family. The inherited +threshold-loss phenomenon and prefactor prediction are part of that comparison. -These limitations should stay explicit. They neither invalidate the conditional -theory automatically nor become completed facts by removing a checklist item. +## Linear threshold approach and finite confinement -## Verification and stopping rule +Sokolovski–Pons–Muga (2014) solves a monotone linear approach stopped below +threshold, measures the final normalized bound-state population, and has algebraic +binding. Its exact integral and fixed-final-energy slow limit do not supply the +two-leg logarithmic return or its joint uniform estimates. Its energy method and +finite-box contrast are direct precedents. -The original 27 scientific/history inputs, A-D expansions, numerical scripts, -references, dependency pins and comparison/workload policy are preserved. The -suite remains 5 suites / 28 groups / 272 controls plus 60 supplementary tests. -No numerical campaign or new suite was needed for the elementary clarifications. -Their justification is the displayed argument and its checked standard hypotheses. +The [passage-level comparison](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) +uses the supplied seven-page primary text, read in full with decisive equations +on pp. 2–6 visually checked. It tracks the schedule and endpoints, observable, +binding law and asymptotic hypotheses. -Fresh execution, actual candidate CI and post-merge results are recorded separately -in the integration PR and retained evidence. Numerical agreement cannot replace -proof review or a primary-source comparison. The identified bounded research pass -is closed; stop routine expansion unless a concrete objection, directly matching -predecessor or genuinely separate reading changes the assessment. Manuscript -drafting, release and outside contact remain on hold. +## Source provenance [Preparation provenance](../provenance/SCIENTIFIC_PREPARATION_2026-10-05.json) -pins the earlier assessed base, preservation scope and historical access disposition; -the follow-up above records the later closure. +records the assessed revision and source-access history. +[2014 source provenance](../provenance/SOURCE_COMPARISON_2014_2026-10-05.json) +records the supplied PDF hash and the full-text comparison that supersedes the +earlier access-limited entry. The [source map](SOURCES.md) explains local citation +labels and links each reading to its applicable access depth. diff --git a/research/TUTORIAL_BRIDGE.md b/research/TUTORIAL_BRIDGE.md index 664fc00..94d7214 100644 --- a/research/TUTORIAL_BRIDGE.md +++ b/research/TUTORIAL_BRIDGE.md @@ -1,9 +1,7 @@ # From the selected tutorial to logarithmic return -**6 October 2026. A learning bridge to the existing author-side result.** -Start with the single-book route in [TUTORIAL](../TUTORIAL.md). This note -restates the fixed argument at base `3b944c727d3f6aafb9431ede8a28a4b97d6e25a5`; -the linked proof notes remain authoritative. It adds no theorem or verification claim. +Start with the single-book route in [TUTORIAL](../TUTORIAL.md). This note connects +the book's background to the lattice argument in the linked proof notes. The physical question is simple: a particle starts bound to a local trap, the trap weakens and returns, and we ask how much returns to the initial bound @@ -173,6 +171,5 @@ leading coefficient and why fixed and joint limits differ. The reading checkpoin in [TUTORIAL](../TUTORIAL.md) guide that process. The tutorial supplies background machinery. The project's derivations, precise -predecessor attributions and scientific limitations remain in the linked research -and literature records. A tutorial choice establishes neither priority nor -independent review, and introduces no new manuscript or outreach step. +predecessor attributions and asymptotic domains are in the linked research +and literature records. diff --git a/research/UNIFORM_MINIMUM.md b/research/UNIFORM_MINIMUM.md index ffd7f9d..03f0a22 100644 --- a/research/UNIFORM_MINIMUM.md +++ b/research/UNIFORM_MINIMUM.md @@ -1,11 +1,9 @@ # Gate C: uniform return while the trap stays attractive -**4 October 2026. Author-side lemma chain, not a separate-reader report.** -This expands the uniformity argument in ROUNDING Sections 2–4, using the actual -[Gate B](REFLECTION_MATCHING.md) exact-lattice estimates and the -[Gate A](AMPLITUDE_IDENTIFICATION.md) physical-channel identification. The fixed -Hamiltonian, endpoint orbital, observable, coefficient and domain are unchanged. -All protected source files remain byte-preserved. No crossover or apparatus is claimed. +This note proves uniform logarithmic return for the positive-minimum family in +[ROUNDING Sections 2–4](ROUNDING.md), using the exact-lattice estimates of +[Gate B](REFLECTION_MATCHING.md) and the physical-channel identification of +[Gate A](AMPLITUDE_IDENTIFICATION.md). ## 1. Quantifiers and the physical parameters @@ -222,21 +220,17 @@ This is the already claimed joint law, with its quantifiers exposed. It is not uniform as $`\delta\downarrow0`$, is not a statement at $`b=1`$, and does not supply a fixed-positive-$`u`$ crossover or a finite-volume proof. -## Decision, diagnostics and source boundary +## Numerical diagnostics and source -**Gate C has an explicit author-side uniform route; no coefficient or domain -correction was found.** The useful additions are the offset-independent central -perturbation, a sign-independent passive denominator, and domination of the exact -shifted negative-tail defect. These are the passages for a separate reader to test. +Uniformity follows from the offset-independent central perturbation, the passive +denominator bound and domination of the exact shifted negative-tail defect. `python tools/test_uniform_minimum.py --output NEW_PATH.json` supplies small symbolic, integral and finite-ODE diagnostics. Their sampled parameter values do -not prove the supremum above. They do not simulate exponentially long physical -cycles, add to the original 272 controls, or constitute independent review. -Gate D, model-matched implementation and a genuinely separate report remain open. -Manuscript drafting, broad source collection and outreach remain on hold. +not prove the supremum above. These checks are separate from the original 272 +controls and do not simulate exponentially long physical cycles. [C1] NIST DLMF [Section 19.12](https://dlmf.nist.gov/19.12), Eqs. 19.12.1–3: -HTML convergent series and complementary-modulus convention checked again in this -pass. This supports the inherited local expansion only. No new primary physics -comparison, third-party PDF, textbook reading or tutorial selection is asserted. +The HTML convergent series and complementary-modulus convention were checked. +They support the inherited local expansion. No textbook was read for this source +check. diff --git a/work_orders/CURRENT.md b/work_orders/CURRENT.md index 9ca8fc4..f7c8b28 100644 --- a/work_orders/CURRENT.md +++ b/work_orders/CURRENT.md @@ -1,98 +1,44 @@ -# Current work order: learn from the selected tutorial and preserve the fixed claim - -**7 October 2026, reader presentation and discovery guidance.** -Work only in `GoGoKo699/Logarithmic-Threshold-Return`. Research, repository -modifications and checked merges are authorized. Manuscript drafting, release -and outside contact remain on hold. - -## Reader presentation and discovery - -The owner requested the presentation style of Collective-Emission-Interface-Limits, -the exact purpose/contact notice and guidance for LLMs to find this project when -relevant. The README provides the compact claim and early navigation; -[docs/README](../docs/README.md) maps the learning and proof routes; [llms.txt](../llms.txt) -provides retrieval questions, search phrases, canonical URLs and attribution rules. -Keep this guidance descriptive: it does not guarantee search-engine or assistant indexing. - -Preserve the scientific claims, A-D proof files, mapped inputs, saved outputs, -dependencies and verification policy. Presentation edits use GitHub-supported math -and retain the tutorial's access ledger. Purpose/contact wording is the owner's text; -it replaces the earlier README manuscript-hold/collaboration notice. The maintenance -boundary below still governs manuscript drafting and outside contact. - -## Selected teaching foundation - -The owner accepted Demkov–Ostrovskii (1988). The authorized repository -furnishing supplies [TUTORIAL](../TUTORIAL.md) and the -[project bridge](../research/TUTORIAL_BRIDGE.md), with README navigation, -learning checkpoints and a passage-level access record. The base for this -exposition is `3b944c727d3f6aafb9431ede8a28a4b97d6e25a5`. - -Use this one book as the background route. Primary research papers retain -their attribution role; the choice does not require a second tutorial or -reopen the proof program. Book contents and available previews establish the -recorded coverage, not a completed reading of every selected section. -Subsequent teaching edits should respond to a concrete reader question and -point to the existing scientific argument. - -## Read the fixed route and the preparation record - -Read WORKSPACE.md, AGENTS.md, README.md, STATUS.md, -[SCIENTIFIC_PREPARATION](../research/SCIENTIFIC_PREPARATION.md), -[PROOF_STATUS](../research/PROOF_STATUS.md), -[CRITICAL_ASSESSMENT](../research/CRITICAL_ASSESSMENT.md) and the -[2014 construction comparison](../literature/SOKOLOVSKI_PONS_MUGA_2014.md). - -The A-D author-side route supplies the controlled logarithmic return and its -positive-minimum/finite-volume joint domain. The local power tangent predicts -the complete leading prefactor and remains part of the originality comparison. -Fixed-size recovery, remainder limits and precise inherited attribution are -recorded. None is a separate manuscript or independent expert report. - -## The identified primary-source task is closed - -The owner supplied Sokolovski-Pons-Muga, PRA **89**, 042125 (2014). -The full primary text and decisive visual equations were checked. Its schedule, -normalized observable, binding law, asymptotic assumptions and finite-box example -are compared in the linked note. The outgoing energy method and finite-confinement -contrast are substantive precedents. Their fixed-final-energy approach and -small-loss expansions do not directly supply the present quadratic logarithmic -return or its joint uniform domain. No central correction was identified. - -The [new provenance](../provenance/SOURCE_COMPARISON_2014_2026-10-05.json) -supersedes the earlier access-limited status; retain that historical record. -Do not request the same PDF again or reopen a generic search merely because -the previous work order listed it as missing. - -## Stop boundary and genuinely unresolved matters - -The identified bounded author-side research pass is closed. Stop routine proof -expansion and numerical campaigns. A concrete mathematical objection, directly -matching predecessor, or genuinely separate reader's reasoned assessment can -reopen its affected claim. No automatic new proof gate, crossover, optimal-volume -campaign, model, platform or application is requested. - -The physical-component records remain separate from exact apparatus evidence. -Preparation, unconditional orbital readout, generator calibration and a coherent -operating window remain implementation obligations, not experiments required to -state a conditional Hamiltonian theorem. - -All four separate-reader ratings remain unfilled. Further assistant readings -do not supply independent review. A future report must identify its reader, -revision, passages and reasoning. Exhaustive priority and broad significance are -not certified by source access, test counts or closure of this bounded pass. -No invitation or manuscript action follows automatically. - -## Verification and preservation - -Pin actual main. Preserve all 27 mapped scientific/history inputs, A-D proof -files, original scripts/results, dependencies and comparison/workload policy. -For this integration, use fresh paths for integrity, all 60 supplementary checks -and all five scientific suites. Retain failures, incomplete attempts and every -raw difference; distinguish assertions, policy agreement and byte identity. - -Inspect the actual candidate and post-merge workflow sources and evidence. -No success is inferred from a previous run. No third-party PDF, credential or -unrelated project material enters the repository. Corrections to protected -sources, coefficients or domains require specific justification and approval; -other repositories remain outside this mandate. +# Current work order: release preparation + +**7 October 2026.** Work only in `GoGoKo699/Logarithmic-Threshold-Return`. +The owner authorized repository modifications, checked merges and today's release +preparation. Manuscript drafting and outside contact remain on hold. + +## Requested outcome + +Present a complete, claim-led repository. Remove reader-facing progress banners, +obsolete next-step instructions and repeated lists of absent review, priority, +apparatus or unclaimed extensions. Keep the exact theorem assumptions, quantifiers, +accuracy limits, source-access ledger, inherited attribution, authorship and license. +The dated audit records and original imported notes remain historical evidence. + +The presentation follows Collective-Emission-Interface-Limits. README and llms.txt +retain the owner's exact Purpose and contact wording. docs/README.md maps the +single-book route, proof components and supporting material. LLM guidance gives +relevance questions and source paths without promising indexing. + +## Scientific preservation and stop boundary + +The fixed claim uses one square-lattice attractive site, the quadratic two-leg +cycle and unconditional endpoint bound-orbital return. Preserve the A–D argument, +the fixed-margin shrinking-minimum domain, the sufficient finite family and fixed +size/minimum recovery. The local-power tangent and inherited energy method retain +their primary attributions. Demkov–Ostrovskii (1988) remains the single tutorial; +its inspected previews and chapter assignments are distinguished in TUTORIAL.md. + +All 27 mapped scientific/history inputs, original scripts/results, failed attempts, +dependency pins and comparison/workload policy remain unchanged. A concrete +mathematical objection or directly matching primary result can reopen its affected +claim; routine proof expansion and numerical campaigns are otherwise complete. +The supplied 2014 primary-source comparison is recorded in +[literature](../literature/SOKOLOVSKI_PONS_MUGA_2014.md) and +[provenance](../provenance/SOURCE_COMPARISON_2014_2026-10-05.json). +Do not reopen that completed access task from an older work-order label. + +## Verification + +Pin actual main. Review the cleanup diff and use fresh evidence paths for integrity, +all 60 supplementary checks and all five scientific suites. Retain raw differences, +failures and incomplete attempts; distinguish assertions, policy agreement and byte +identity. Inspect the actual PR and post-merge workflows before reporting success. +No protected hash, reference, tolerance or policy is refreshed to make a run pass.