From 52bc319675c2d77c894580059745f010a9fd2794 Mon Sep 17 00:00:00 2001 From: Ruge Lin Date: Mon, 5 Oct 2026 04:21:34 +0800 Subject: [PATCH 1/2] Expose uniform positive-minimum matching at a fixed margin below the crossover Add an author-side Gate C lemma chain: offset-independent central transfer including the forbidden region; a passive denominator that does not require Im(h)<=0; exact shifted negative-tail domination by the zero-minimum defect; and uniform endpoint/coefficient bookkeeping. No protected equation, observable, coefficient or claimed domain is changed. Add seven small symbolic/integral/ODE diagnostics, separate from the original 272 controls. All seven passed on the first local run. Preserve the original source/history inputs and comparison/workload policy, update navigation, and make Gate D the next bounded task. Manuscript and outreach remain on hold. Remote tree c30e3db132d4c9bfd8f482fb9d48e92dd1584fa5 matches the frozen local candidate exactly. The incoming original scientific sources passed the complete early local run byte-for-byte; its navigation-only overlap is recorded rather than called a frozen run. Full frozen candidate/base runs and actual hosted verification are checked separately before merge. --- .github/workflows/verify.yml | 3 + README.md | 2 + STATUS.md | 24 ++- provenance/GATE_C_2026-10-04.json | 85 ++++++++++ research/CLAIMS.md | 6 +- research/UNIFORM_MINIMUM.md | 242 +++++++++++++++++++++++++++ tools/test_uniform_minimum.py | 268 ++++++++++++++++++++++++++++++ work_orders/CURRENT.md | 98 +++++------ 8 files changed, 673 insertions(+), 55 deletions(-) create mode 100644 provenance/GATE_C_2026-10-04.json create mode 100644 research/UNIFORM_MINIMUM.md create mode 100644 tools/test_uniform_minimum.py diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml index 8b2512d..ec43540 100644 --- a/.github/workflows/verify.yml +++ b/.github/workflows/verify.yml @@ -44,6 +44,8 @@ jobs: run: python tools/test_amplitude_identification.py --output amplitude-evidence/REPORT.json - name: Check reflection matching separately run: python tools/test_reflection_matching.py --output reflection-evidence/REPORT.json + - name: Check uniform positive-minimum estimates separately + run: python tools/test_uniform_minimum.py --output uniform-minimum-evidence/REPORT.json - name: Check preserved inputs and document links run: python verify.py --integrity-only - name: Run every scientific suite and retain comparisons @@ -65,6 +67,7 @@ jobs: model-residual-evidence/ amplitude-evidence/ reflection-evidence/ + uniform-minimum-evidence/ tracked-source.zip if-no-files-found: warn retention-days: 14 diff --git a/README.md b/README.md index e96542d..0140be2 100644 --- a/README.md +++ b/README.md @@ -86,6 +86,8 @@ The [physical-amplitude lemma chain](research/AMPLITUDE_IDENTIFICATION.md) now s an author-side retarded reconstruction, channel normalization and uniform tail comparison. The [reflection-matching note](research/REFLECTION_MATCHING.md) expands Gate B: explicit endpoint cancellation and exact-lattice positive/negative outer control at zero minimum. +The [uniform-minimum note](research/UNIFORM_MINIMUM.md) expands Gate C: the full +positive-minimum domain, including its narrow turning region and shifted negative tail. [Source labels](research/SOURCES.md) map the preserved notes' local reference numbers. [Assumptions](literature/ASSUMPTIONS.md) distinguishes ideal model premises from a joint apparatus, with a [primary-source register](literature/PHYSICAL_PRECEDENTS.md) and diff --git a/STATUS.md b/STATUS.md index 99e6d31..ffd3617 100644 --- a/STATUS.md +++ b/STATUS.md @@ -12,7 +12,7 @@ and history inputs remain byte-preserved. | Inverse-square-logarithmic return | Author-side matched-asymptotic derivation | Fixed local trap and order of limits | | Energy reflection equals physical return | Explicit Gate A lemma chain | Not independent proof review | | Leading reflection and outer matching | Explicit Gate B endpoint and exact-lattice estimates | Zero minimum; not independent proof review | -| Positive-minimum joint law | Derived uniformly away from b=1 | No full crossover claim | +| Positive-minimum joint law | Explicit Gate C uniform lemma chain | Fixed margin below b=1; no crossover claim | | Finite-volume family | Sufficient bound and finite examples | Not an optimized size requirement | | Fixed positive hopping anisotropy | Scope corollary with checked hypotheses | Not uniform at zero transverse hopping | @@ -25,8 +25,12 @@ The new argument supplies that intermediate reasoning without changing the law. [Gate B](research/REFLECTION_MATCHING.md) now makes the endpoint-basis cancellation explicit, treats positive-side passivity without a chosen absorber, and bounds the entire negative tail with the exact positive spectral measure. No leading coefficient -correction was found. These are author-side arguments at zero minimum; Gates C and D -are not closed by this pass. The +correction was found. [Gate C](research/UNIFORM_MINIMUM.md) now treats the entire +positive-minimum domain at a fixed margin below b=1: its central perturbation is +offset-independent, its passive denominator does not require a sign of Im(h), and +its shifted exact negative-tail defect is dominated uniformly by the zero-minimum +integral. The coefficient and domain are preserved. These are author-side arguments; +Gate D remains separate. The [reader packet](research/READER_PACKET.md) remains a brief, not a received report. ## Prior art and physical premises @@ -55,8 +59,8 @@ Full crossover, optimal volume and experimental superiority remain unclaimed. The preserved scientific suites contain **5 suites, 28 groups and 272 controls**. Fourteen infrastructure tests, five predecessor checks, six operational checks, -seven model-residual checks, seven amplitude checks and six reflection checks are -counted separately. +seven model-residual checks, seven amplitude checks, six reflection checks and +seven uniform-minimum checks are counted separately. Execution, exact byte reproduction and independent scientific review are distinct. The Gate A base was `5167d02b9504596e1c1b071ed425dea63dec62c6`. Its downloaded main @@ -84,7 +88,13 @@ reclassify any previous failed, cancelled or non-byte-identical execution. ## Next bounded step -Follow [CURRENT](work_orders/CURRENT.md): challenge uniformity of the existing -positive-minimum law on the whole stated b domain, or record a concrete objection. +[Gate C provenance](provenance/GATE_C_2026-10-04.json) records the recovered current +main, source-tree identity and the new diagnostic evidence. The first seven-test +uniform-minimum run passed; no new failed scientific attempt is omitted. The early +base-source run overlapped addition of the new note, changing only its navigation +link count; a frozen candidate and actual hosted reports are separate evidence. + +Follow [CURRENT](work_orders/CURRENT.md): scrutinize the finite-volume initial-state, +periodic-seam and return-amplitude estimates without optimizing lattice size. Do not broaden the model to prolong development. A genuinely separate report remains absent. No manuscript, release or outside invitation is initiated here. diff --git a/provenance/GATE_C_2026-10-04.json b/provenance/GATE_C_2026-10-04.json new file mode 100644 index 0000000..88bd745 --- /dev/null +++ b/provenance/GATE_C_2026-10-04.json @@ -0,0 +1,85 @@ +{ + "date": "2026-10-04", + "repository": "GoGoKo699/Logarithmic-Threshold-Return", + "base_commit": "f00281f6fa9310091c7da402142f1f4e5560f272", + "base_tree": "db408710b9370ed31df0b397be6e294c19b938e1", + "scope": "Author-side Gate C: uniform positive-minimum matching at fixed delta>0; no changed law or independent review.", + "recovered_source": { + "run_id": 37229542484, + "artifact_id": 11313273793, + "sha256": "47f5b22eee51b0cbe192300e3cc855388bed7b35afb4fa2d1f0c82a1291d96b2", + "tracked_files": 57, + "source_tree_match": true, + "method": "Authenticated GitHub artifact after public clone failed DNS; prior local Gate B patch not applied because current upstream already has a different checked Gate B implementation." + }, + "early_local_base_source_run": { + "status": "PASS", + "suite_count": 5, + "group_count": 28, + "case_count": 272, + "all_reference_bytes_identical": true, + "report_sha256": "83da0543ff11ec7d5a5a664f536acc0a3b233f725525381cc88ba8a6fa3e09e8", + "before_integrity": { + "status": "PASS", + "preserved_files": 27, + "local_links": 83, + "suites": 5 + }, + "after_integrity": { + "status": "PASS", + "preserved_files": 27, + "local_links": 85, + "suites": 5 + }, + "boundary": "Original scientific inputs unchanged. Addition of the new note overlapped this run, changing navigation links only; it is not labeled a frozen whole-tree run." + }, + "existing_tests": { + "infrastructure": 14, + "predecessor": 5, + "operational": 6, + "model_residual": 7, + "amplitude_identification": 7, + "reflection_matching": 6, + "status": "PASS" + }, + "new_checks": { + "count": 7, + "first_run": "PASS", + "script_sha256": "02d7bc6223e585bd3e1762fee28751b3a5de5aec85fa600a8dfab709d87df681", + "report_sha256": "26f46c0806aed38d48ff200f1ee8c9b5f6ee590dac45dd17316118b4e198c314", + "original_272_members": false, + "sampled_sign_reversals": 169, + "scope": "Symbolic and finite integral/ODE diagnostics; not a supremum proof or long-time physical simulation." + }, + "preservation": { + "mapped_inputs": 27, + "protected_equations_changed": false, + "references_changed": false, + "comparison_or_workload_policy_changed": false + }, + "method_access": [ + { + "source": "NIST DLMF 19.12", + "url": "https://dlmf.nist.gov/19.12", + "depth": "HTML convergent elliptic series 19.12.1–3 and complementary modulus conventions", + "boundary": "Inherited local expansion, not new primary physics attribution." + }, + { + "source": "NIST DLMF 2.7(iii)", + "url": "https://dlmf.nist.gov/2.7#iii", + "depth": "HTML method context revisited", + "boundary": "No additional theorem imported; passive and shifted-defect bounds are derived explicitly." + } + ], + "operational_failures": [ + "Public git clone failed: Could not resolve host github.com. Source recovered by connector; no scientific run interrupted." + ], + "decision": { + "gate_c": "Explicit uniform author-side route; no coefficient/domain correction found.", + "gate_d": "Next bounded task.", + "separate_report": "Absent.", + "manuscript": "On hold.", + "outreach": "None." + }, + "candidate_and_hosted": "Inspect frozen candidate and actual PR/main reports separately. Their success is not inferred from this baseline or stored prospectively here." +} diff --git a/research/CLAIMS.md b/research/CLAIMS.md index db1d3df..b0234de 100644 --- a/research/CLAIMS.md +++ b/research/CLAIMS.md @@ -13,7 +13,7 @@ positive-minimum and finite-volume domain are supporting parts of that statement |---|---|---|---| | 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 | Suite 08 joint-coefficient and finite-time checks | No formula through b=1 or every fixed residual depth | +| 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 | 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 | @@ -56,3 +56,7 @@ Full crossover, general trap universality, optimal volume, experimental superior 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. diff --git a/research/UNIFORM_MINIMUM.md b/research/UNIFORM_MINIMUM.md new file mode 100644 index 0000000..ffd7f9d --- /dev/null +++ b/research/UNIFORM_MINIMUM.md @@ -0,0 +1,242 @@ +# 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. + +## 1. Quantifiers and the physical parameters + +Fix $`0<\delta<1`$. All constants below may depend on this fixed margin but not on +$`b\in[0,1-\delta]`$. The case $`\delta=1`$ is just zero minimum. Parameterize the +whole family, rather than treating a sequence of fixed-$`b`$ examples: + +```math +\rho_0=\frac1{4\pi},\quad e_*=32e^{-L},\quad +u=\frac{b}{\rho_0L},\quad \alpha=\frac{e_*^2}{\rho_0L},\quad +T=\frac{\sqrt{(4-u)\rho_0L}}{e_*}. +``` + +For large $`L`$, uniformly $`0\le u\le u_*<4`$, and these definitions give exactly +$`\alpha=(4-u)/T^2`$ and the implicit logarithm equation in CORE. Remote time in +Gate A is still taken first at fixed $`\alpha,u`$. This parameterization does not +assert a new order of limits. Write + +```math +k=\sqrt{1-b}\in[\sqrt\delta,1],\qquad R=L^{1/4},\quad B=L^2, +\qquad F_b(x)=-\frac{\rho_0L}{g(e_*x)}-b,\quad +F_b^0(x)=\frac{L}{L-V(x)}-b, +\quad V=\ln|x|-i\pi\mathbf1_{x>0}. +``` + +The exact equation is $`y''+F_b y=0`$. The replacement error +$`\Delta=F_b-F_b^0`$ is **exactly independent of $`b`$**. Gate B Section 1 gives +its integrated central bound $`Ce_*R^2`$ and its outer derivative bounds +$`|\Delta^{(j)}|\le Ce_*|x|^{1-j}`$, $`j=0,1,2`$, on $`R\le|x|\le B`$. +Those bounds come from convergent elliptic series, not differentiation of an +unspecified remainder [C1]. The desired statement is uniform after an irrelevant +phase choice: + +```math +r_{L,b}=e^{i\theta_{L,b}}\left\{\frac{i\pi}{2L(1-b)} ++O_\delta\!\left(\frac1{LR}+\frac{R^2(1+\ln R)^2}{L^2}+e^{-cL}\right)\right\}. +``` + +The positive constant $`c`$ can be reduced to absorb polynomial factors. It does +not have to describe a sharp finite-$`L`$ error bar. + +## 2. Central transfer includes the forbidden region + +A second exact cancellation of the offset is decisive: + +```math +F_b-k^2=F_0-1,\qquad +F_b^0=k^2+\frac VL+\frac{V^2}{L(L-V)}. +``` + +The subscript $`0`$ on $`F_0`$ here means the exact zero-minimum coefficient. +For $`|x|<1`$, put $`t=-\ln|x|`$. The measure becomes $`e^{-t}dt`$ and +$`|L-V|\ge L`$. On $`1\le|x|\le R`$, $`\operatorname{Re}(L-V)\ge L/2`$ +eventually. Thus, without removing any neighborhood of zero, + +```math +F_b=k^2+V/L+\mathcal R,\qquad +\|\mathcal R\|_1\le C\frac{1+R(1+\ln R)^2}{L^2}+Ce_*R^2,\qquad +\|F_b-k^2\|_1\le C\frac{R(1+\ln R)}L+Ce_*R^2. +``` + +These constants are independent even of $`b`$ before conversion to wave amplitudes. +At zero $`F_b\to-b`$, so a uniform pointwise expansion would be false. For $`b>0`$ +there is one negative-energy turning point: $`W(\eta)=1/G(\eta)=u`$ with +$`G(\eta)=-g(-\eta)`$. Monotonicity of $`G`$ makes it unique. At +$`|x|=e^{-\delta L/2}`$, the exact unshifted coefficient is +$`(1+\delta/2)^{-1}+o(1)>1-\delta`$. Therefore the turning point lies at +$`|x_t|0`$ on the **whole** negative outer interval. It rules out +additional outer turning points without an approximation at deep energies. + +For the unit-mass positive spectral measure, +$`G'= -\int\rho(E)(E+\eta)^{-2}dE`$ and +$`G''=2\int\rho(E)(E+\eta)^{-3}dE`$. Cauchy–Schwarz gives +$`GG''\ge2G'^2`$, hence $`W'>0`$ and $`W''\le0`$. With derivatives now taken +in $`\eta`$, the exact physical-energy change of variables yields + +```math +\mathcal I_-(u)=\sqrt\alpha\int_a^\infty +\left[\frac{5W'^2}{16(W-u)^{5/2}}-\frac{W''}{4(W-u)^{3/2}}\right]d\eta. +``` + +Both displayed terms are nonnegative. Their powers of $`W-u`$ can therefore be +bounded separately, without losing a cancellation or differentiating an asymptotic: + +```math +\boxed{\mathcal I_-(u)\le(2/\delta)^{5/2}\mathcal I_-(0) +=O_\delta((LR)^{-1})+O_\delta(\sqrt\alpha).} +``` + +Here $`\mathcal I_-(0)`$ uses the same $`\alpha,a`$; it is the exact integral +already bounded in Gate B Section 3, not a second physical cycle. On this interval +$`q,h`$ are real and current passivity gives $`|r|\le1`$. The phase-adjusted +reflection changes by at most $`2\mathcal I_-(u)`$ on passage to the deep-bound +coefficients. The factor $`\sqrt\alpha`$ and the positive-margin inequality are +both essential. Copying the zero-minimum integral without shifting its denominators +would not establish the desired uniformity. + +## 5. Endpoint cancellation, coefficient and finite-time comparison + +At $`s=\pm R`$, let $`\mathsf P_k(s)`$ have columns +$`k^{-1/2}(1,\mp ik)^T e^{\mp iks}`$ and let $`\mathsf W_b(s)`$ have columns +$`q^{-1/2}(1,-h/2\mp iq)^T e^{\mp iks}`$. Direct inversion gives + +```math +\mathsf P_k(s)^{-1}\mathsf W_b(s) +=I-\frac{V(s)}{4Lk^2} +\begin{pmatrix}0&e^{2iks}\\e^{-2iks}&0\end{pmatrix} ++O_\delta\!\left(\frac1{LR}+\frac{(1+\ln R)^2}{L^2}+e_*R\right). +``` + +The normalization removes the linear diagonal term for every permitted $`k`$. +Composing the right basis, backwards central transfer and inverse left basis, +then expanding the incident denominator, gives + +```math +r_c=-\frac{i}{2kL}\int_{-R}^RV e^{-2ikx}dx +-\frac{V(R)e^{-2ikR}-V(-R)e^{2ikR}}{4Lk^2}+O_\delta(\mathcal Q_L) +=\frac{i[2\operatorname{Si}(2kR)+\pi]}{4Lk^2}+O_\delta(\mathcal Q_L), +``` + +where $`\mathcal Q_L=(LR)^{-1}+R^2(1+\ln R)^2/L^2+e^{-cL}`$. +The identity uses both terms of +$`V'=\operatorname{PV}(1/x)-i\pi\delta(x)`$. The bound +$`|\operatorname{Si}(2kR)-\pi/2|\le1/(kR)`$ is uniform for +$`k\ge\sqrt\delta`$. Sections 3–4 give the claimed auxiliary amplitude in +Section 1, with remainder $`O_\delta(L^{-5/4})`$. + +Gate A's uniform $`O(T^{-1})`$ amplitude-modulus comparison applies because +$`u\le u_*<4`$ eventually. In this parameterization +$`T^{-1}=O(e^{-L}/\sqrt L)`$ uniformly. Squaring, and using +$`\pi/[2L(1-b)]\ge\pi/(2L)`$, proves the explicit uniform conclusion + +```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| +=O_\delta(L^{-1/4})\longrightarrow0. +``` + +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 + +**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. + +`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. + +[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. diff --git a/tools/test_uniform_minimum.py b/tools/test_uniform_minimum.py new file mode 100644 index 0000000..766f04e --- /dev/null +++ b/tools/test_uniform_minimum.py @@ -0,0 +1,268 @@ +#!/usr/bin/env python3 +"""Small Gate C diagnostics; finite sampling is not a uniformity proof. + +No original scientific script or saved result is rewritten. Optional JSON output +is exclusive-create. Run: python tools/test_uniform_minimum.py --output NEW.json +""" +from __future__ import annotations +import argparse +import json +from pathlib import Path +import unittest + +import mpmath as mp +import numpy as np +import sympy as sp +from scipy.integrate import quad, solve_ivp +from scipy.special import sici + +from test_reflection_matching import negative_green, complex_quad + +REPORT: dict[str, object] = {} +RHO = 1/(4*np.pi) + + +def local_data(x: float, L: float, b: float): + """F, q, h and Omega, only at nonzero x where this basis is used.""" + if x == 0: + raise ValueError('Wave data are undefined at the central turning point.') + D = complex(L-np.log(abs(x)), np.pi if x > 0 else 0.) + F = L/D-b + F1 = L/(x*D*D) + F2 = L*(2-D)/(x*x*D**3) + q = np.sqrt(F) + return F, q, F1/(2*F), 5*F1*F1/(16*F*F)-F2/(4*F) + + +def wave_matrix(x: float, L: float, b: float): + _, q, h, _ = local_data(x, L, b) + k = np.sqrt(1-b) + w = q**(-.5)*np.exp(np.array([-1j*k*x, 1j*k*x])) + return np.vstack((w, np.array([-h/2-1j*q, -h/2+1j*q])*w)) + + +def defect(eps: float, u: float): + """Exact shifted physical-energy defect before its sqrt(alpha) factor.""" + G, G1, G2 = negative_green(eps) + kappa = 1-u*G + if kappa <= 0: + raise ValueError('Negative-tail integration entered the forbidden region.') + term1 = 5*G1*G1/(16*G**1.5) + term2 = (G*G2-2*G1*G1)/(4*G**1.5) + return term1/kappa**2.5+term2/kappa**1.5 + + +class UniformMinimumTests(unittest.TestCase): + def test_symbolic_offset_frame_and_shifted_defect(self): + x, k = sp.symbols('x k', real=True, positive=True) + v, t = sp.symbols('v t', real=True) + q = sp.sqrt(k*k+t*v) + phase = sp.diag(sp.exp(-sp.I*k*x), sp.exp(sp.I*k*x)) + plane = sp.Matrix([[1, 1], [-sp.I*k, sp.I*k]])*phase/sp.sqrt(k) + wave = sp.Matrix([[1, 1], [-sp.I*q, sp.I*q]])*phase/sp.sqrt(q) + derivative = (plane.inv()*wave).diff(t).subs(t, 0) + target = -v/(4*k*k)*sp.Matrix([[0, sp.exp(2*sp.I*k*x)], + [sp.exp(-2*sp.I*k*x), 0]]) + self.assertEqual((derivative-target).applyfunc(sp.simplify), sp.zeros(2)) + F, b = sp.symbols('F b') + self.assertEqual(sp.expand((F-b)-(1-b)-(F-1)), 0) + G, G1, G2, u = sp.symbols('G G1 G2 u', real=True) + W1, W2 = -G1/G**2, (2*G1**2-G*G2)/G**3 + # Verify the polynomial numerators after multiplying out positive roots. + lhs = 5*W1**2*G**4/16-W2*G**3*(1-u*G)/4 + rhs = 5*G1**2/16+(G*G2-2*G1**2)*(1-u*G)/4 + self.assertEqual(sp.factor(lhs-rhs), 0) + REPORT['symbolic_identities'] = 'offset, endpoint frame, shifted defect numerator' + + def test_integrated_central_remainder_including_core(self): + rows = [] + for L in (16., 64., 256.): + R = L**.25 + # x=exp(-t): the full central core t in [0,infinity) is included. + small, outer = 0., 0. + for jump in (0., np.pi): + small += quad(lambda t: np.exp(-t)*abs(complex(-t, -jump)**2 + /(L*complex(L+t, jump))), 0., np.inf, + epsabs=2e-12, epsrel=2e-11)[0] + outer += quad(lambda x: abs(complex(np.log(x), -jump)**2 + /(L*complex(L-np.log(x), jump))), 1., R, + epsabs=2e-12, epsrel=2e-11)[0] + scale = (1+R*(1+np.log(R))**2)/L**2 + self.assertLess((small+outer)/scale, 20.) + for b in (0., .4, .8): + for x in (-.03, -.5, 1.2, R): + V = complex(np.log(abs(x)), np.pi*-float(x > 0)) + exact_remainder = (L/(L-V)-b)-(1-b)-V/L + self.assertLess(abs(exact_remainder-V*V/(L*(L-V))), 1e-14) + delta = .2 + xc = np.exp(-delta*L/2) + e_star = 32*np.exp(-L) + exact_at_cut = RHO*L/negative_green(e_star*xc)[0] + self.assertGreater(exact_at_cut, 1-delta) + # Local turning points are never used as integration cutoffs. + for b in (.2, .5, .8): + log_xt = -L*(1/b-1) + value_at_turn = L/(L-log_xt)-b + self.assertLess(abs(value_at_turn), 1e-14) + self.assertLess(log_xt, -delta*L/2) + rows.append(dict(L=L, full_core_remainder=small, outer_remainder=outer, + integral_over_declared_scale=(small+outer)/scale, + exact_coefficient_at_uniform_core_cut=exact_at_cut)) + REPORT['central_integrals_no_deleted_core'] = rows + + def test_finite_central_transfers_with_varying_b(self): + rows = [] + for L in (64., 256., 1024.): + R = L**.25 + for label, b in (('zero', 0.), ('interior', .4), ('margin', .8), + ('varying', .8*(1-1/np.sqrt(L)))): + k = np.sqrt(1-b) + y = wave_matrix(R, L, b)[:, 0] + def rhs(x, state): + F = -b+0j if x == 0 else local_data(x, L, b)[0] + return np.array([state[1], -F*state[0]]) + for lo, hi in ((R, 0.), (0., -R)): + sol = solve_ivp(rhs, (lo, hi), y, method='DOP853', + rtol=2e-12, atol=2e-13) + self.assertTrue(sol.success, sol.message) + y = sol.y[:, -1] + coeff = np.linalg.solve(wave_matrix(-R, L, b), y) + r = coeff[1]/coeff[0] + leading = 1j*(2*sici(2*k*R)[0]+np.pi)/(4*L*k*k) + scale = 1/(L*R)+R*R*(1+np.log(R))**2/L**2 + scaled = abs(r-leading)/scale + self.assertLess(scaled, 4/(k**4)) + # Check the boundary cancellation without a distribution solver. + integral = (complex_quad(lambda x: np.log(-x)*np.exp(-2j*k*x), -R, 0.) + +complex_quad(lambda x: (np.log(x)-1j*np.pi)*np.exp(-2j*k*x), 0., R)) + boundary = (np.log(R)-1j*np.pi)*np.exp(-2j*k*R)-np.log(R)*np.exp(2j*k*R) + self.assertLess(abs(-1j*integral/(2*k*L)-boundary/(4*L*k*k)-leading), 2e-11) + rows.append(dict(L=L, b=b, family=label, reflection=[float(r.real), float(r.imag)], + finite_window_leading=[0., float(leading.imag)], + discrepancy_over_scale=float(scaled))) + REPORT['finite_transfer_not_exponential_time_simulation'] = rows + + def test_passive_bound_without_imaginary_h_sign(self): + rows, reversed_signs = [], 0 + L = 16. + R, B = L**.25, L*L + for b in (0., .6, .8): + grid = np.geomspace(R, B, 120) + data = [local_data(float(x), L, b) for x in grid] + reversed_signs += sum(h.imag > 0 for _, _, h, _ in data) + self.assertTrue(all(q.real > 0 and abs(h) <= q.real for _, q, h, _ in data)) + A = quad(lambda x: -local_data(x, L, b)[1].imag, R, B, epsabs=1e-10)[0] + I = quad(lambda x: abs(local_data(x, L, b)[3]/local_data(x, L, b)[1]), + R, B, epsabs=2e-12)[0] + bound = 7*np.exp(-2*A)+32*I + for label, m in (('real', 0j), ('passive', 2-3j), ('dirichlet', None)): + _, q, h, _ = local_data(B, L, b) + terminal = -1+0j if m is None else (m+h/2+1j*q)/(1j*q-m-h/2) + if m is not None: + self.assertGreaterEqual(abs(1j*q-m-h/2), q.real-abs(h)/2-1e-14) + self.assertLess(abs(terminal), 7.) + def rhs(x, z): + _, qx, _, omega = local_data(x, L, b) + return 2j*qx*z+1j*omega*(1+z)**2/(2*qx) + sol = solve_ivp(rhs, (B, R), np.array([terminal]), method='DOP853', + rtol=2e-10, atol=2e-12) + self.assertTrue(sol.success, sol.message) + r = abs(sol.y[0, -1]) + self.assertLess(r, bound+1e-8) + self.assertLess(np.max(abs(sol.y[0])), 7.) + rows.append(dict(L=L, b=b, termination=label, attenuation=A, + integrated_defect=I, passive_bound=bound, observed=float(r))) + self.assertGreater(reversed_signs, 0) + REPORT['positive_h_imaginary_part_samples'] = reversed_signs + REPORT['finite_passive_examples_not_physical_far_band'] = rows + + def test_exact_shifted_negative_tail_domination(self): + rows = [] + for L in (16., 32., 64.): + R = L**.25; e_star = 32*np.exp(-L) + root_alpha, a = e_star/np.sqrt(RHO*L), e_star*R + def integral(u): + middle = quad(lambda z: root_alpha*defect(a*np.exp(z), u)*a*np.exp(z), + 0., np.log(128/a), epsabs=2e-12, epsrel=2e-10, limit=200)[0] + far = root_alpha*quad(lambda eps: defect(eps, u), 128., np.inf, + epsabs=2e-10, epsrel=2e-10, limit=200)[0] + return middle+far + I0 = integral(0.) + for b in (0., .4, .8, .8*(1-1/L)): + u = b/(RHO*L); kappa = 1-u*negative_green(a)[0] + self.assertGreaterEqual(kappa, .1) + Ib = integral(u) + bound = kappa**(-2.5)*I0 + self.assertGreater(Ib, 0.) + self.assertLessEqual(Ib, bound+1e-11) + for eps in np.geomspace(a, 128., 25): + G, G1, G2 = negative_green(float(eps)) + self.assertGreaterEqual(1-u*G, kappa-1e-12) + self.assertGreaterEqual(G*G2-2*G1*G1, -1e-10*max(G*G2, 1.)) + rows.append(dict(L=L, b=b, margin_at_cutoff=kappa, defect_integral=Ib, + exact_margin_domination_bound=bound, + L_R_times_defect=L*R*Ib)) + REPORT['exact_shifted_negative_tail_integrals'] = rows + + def test_shifted_exact_lattice_root_and_derivative_control(self): + rows = [] + with mp.workdps(80): + for L0 in (16, 32): + L = mp.mpf(L0); e_star = 32*mp.exp(-L) + for x in (L**mp.mpf('.25'), L*L): + def unshifted(t): + E = e_star*t + a = (E-4)**2/16 + G = -(mp.ellipk(a)+1j*mp.ellipk(1-a))/(2*mp.pi) + return -L/(4*mp.pi*G) + exact0 = [mp.diff(unshifted, x, j) for j in range(3)] + D = L-mp.log(x)+1j*mp.pi + loc0 = [L/D, L/(x*D**2), L*(2-D)/(x*x*D**3)] + for b0 in (0, .4, .8): + b = mp.mpf(str(b0)) + def basis(dat): + F, F1, F2 = dat[0]-b, dat[1], dat[2] + q = mp.sqrt(F); h = F1/(2*F) + omega = 5*F1**2/(16*F**2)-F2/(4*F) + return q, h, omega/q + exact, local = basis(exact0), basis(loc0) + ratios = [abs(exact[0]-local[0])/(e_star*x), + abs(exact[1]-local[1])/e_star, + abs(exact[2]-local[2])/(e_star/x+e_star**2)] + self.assertLess(max(ratios), 100.) + rows.append(dict(L=L0, x=float(x), b=b0, + scaled_root_h_defect_differences=[float(v) for v in ratios])) + REPORT['shifted_exact_lattice_derivative_diagnostics'] = rows + + def test_parameter_identity_and_uniform_endpoint_scale(self): + rows = [] + for L in (16., 64., 256.): + for b in (0., .4, .8, .8*(1-1/np.sqrt(L))): + u = b/(RHO*L) + log_T = .5*np.log((4-u)*RHO*L)-np.log(32)+L + implicit = log_T+np.log(32)-.5*np.log((4-u)*RHO) + self.assertLess(abs(implicit-L-.5*np.log(L)), 2e-13) + self.assertLess(u, 1.) + relative_tail_scale = L**1.25*np.exp(-log_T) + self.assertLess(relative_tail_scale, 1e-4) + rows.append(dict(L=L, b=b, u=u, log_T=log_T, + L_to_five_fourths_over_T=relative_tail_scale)) + REPORT['physical_parameter_and_endpoint_identities'] = rows + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output', type=Path) + args = parser.parse_args() + if args.output is not None and args.output.exists(): + parser.error('Output exists; choose a fresh path.') + result = unittest.TextTestRunner(verbosity=2).run( + unittest.defaultTestLoader.loadTestsFromTestCase(UniformMinimumTests)) + REPORT.update(status='PASS' if result.wasSuccessful() else 'FAIL', + tests_run=result.testsRun, failures=len(result.failures), errors=len(result.errors), + scope='Finite Gate C checks; not a uniform proof, device claim or original-suite extension.') + if args.output is not None: + args.output.parent.mkdir(parents=True, exist_ok=True) + with args.output.open('x', encoding='utf-8') as f: + json.dump(REPORT, f, indent=2, allow_nan=False); f.write('\n') + raise SystemExit(0 if result.wasSuccessful() else 1) diff --git a/work_orders/CURRENT.md b/work_orders/CURRENT.md index ca55ae0..40613da 100644 --- a/work_orders/CURRENT.md +++ b/work_orders/CURRENT.md @@ -1,55 +1,59 @@ -# Current work order: challenge uniform positive-minimum return +# Current work order: scrutinize the finite-volume comparison -**4 October 2026, after the reflection-matching pass.** Work only in +**4 October 2026, after the uniform-minimum pass.** Work only in `GoGoKo699/Logarithmic-Threshold-Return`. The fixed Hamiltonian, observable, coefficient and claimed domain are unchanged. Manuscript and outreach remain on hold. -## What Gate B supplied - -research/REFLECTION_MATCHING.md expands the zero-minimum proof. It displays the -central plane-wave transfer and both endpoint basis matrices, retaining the -principal-value and causal delta contributions. Positive-side control is based on -the actual retarded current, with a nonsingular reflection chart and an explicit -exact-lattice bound. The entire negative tail is controlled directly through the -positive spectral measure, with the energy-coordinate factor retained. - -The resulting phase-adjusted auxiliary amplitude is i*pi/(2L)+O(L^(-5/4)); Gate A -supplies the finite-endpoint amplitude-modulus comparison. This is author-side -reasoning, not independent review or a new physical result. No protected proof was -rewritten. Six small diagnostic tests remain separate from the original 272 controls. -The initial structural symbolic-zero failure and exact repair are archived. - -## Next bounded task: Gate C, not a crossover campaign - -Read READER_PACKET Gate C, ROUNDING Sections 2–4, and REFLECTION_MATCHING. Test -uniformity over every 0<=b<=1-delta for fixed delta>0, not merely each fixed b. - -Track the central transfer constants with q0=sqrt(1-b), including the exponentially -narrow turning region; no pointwise Taylor expansion or removal of that region is -permitted. Check the physical-to-local replacement and the passive denominator -without assuming the zero-minimum sign of Im(h). The direct negative-tail estimate -now involves W-u and must be justified uniformly, not copied from W alone. Keep the -uniform finite-endpoint estimate and the relation among u, alpha, L and T explicit. - -Produce either a concise uniform lemma chain with all amplitude errors o(1/L), -or a concrete objection naming the earlier passage and affected claim. Stop there. -Do not extend through b=1, solve the complete crossover, optimize lattice size, -change the cycle, or adopt another detector/platform. A required coefficient or -domain correction must be recorded and approved before any protected-file edit. -Gate D's finite-volume scrutiny remains a separate task. +## What Gate C supplied + +research/UNIFORM_MINIMUM.md exposes the supremum over every 0<=b<=1-delta for fixed +delta>0. Subtracting b from both the exact coefficient and its reference wave number +leaves the central perturbation independent of b. The full integrable singular core +and its exponentially narrow forbidden region are retained, not cut out. + +The passive denominator is controlled without assuming the zero-minimum sign of +Im(h). On the entire negative outer interval, W-u>=(delta/2)W, and positivity of +the two exact defect terms gives I_minus(u)<=(2/delta)^(5/2) I_minus(0), at the same +alpha and cutoff. This supplies a uniform author-side matching route and the old +coefficient pi^2/[4L^2(1-b)^2], without changing protected proof files or extending +through b=1. Seven small tests include varying-b examples but are not a proof by +sampling or additions to the original 272 controls. + +## Next bounded task: Gate D + +Read READER_PACKET Gate D and ROUNDING Section 6, with CORE's finite-size statement. +Reconstruct the endpoint-state comparison between the finite torus and infinite +lattice, including normalization, energy dependence and phase choice. Do not assume +that the initial vector is compactly supported or the finite and infinite states +are identical. + +Check the weighted hopping estimate on each geometry, the periodic seam residual +and the time-integrated comparison. Explain why the real, even-time Hamiltonian +makes the return amplitude the midpoint bilinear psi(0)^T psi(0), not its norm. +Propagate the midpoint state error to this amplitude uniformly in the stated b +family. Verify that mu=1/2 and n(T)=2 ceil(4.5T)+1 yield o(1/L) error, including +the endpoint localization condition and all size-independent constants. + +Produce a concise lemma chain or a concrete objection identifying the affected +passage. Do not optimize the lattice size, change boundaries or the cycle, solve +the residual-depth crossover, or adopt a different detector or platform. A required +coefficient/domain correction must be recorded and approved before editing protected +files. A completed author-side pass would still not be the absent separate report. ## Evidence, preservation and stopping rule Pin current main and read WORKSPACE.md, AGENTS.md and STATUS.md. Run integrity, -all existing supplementary tests and every preserved scientific suite in fresh -output paths. Include tools/test_reflection_matching.py, whose optional JSON -output is exclusive-create. Preserve raw failures, numerical differences and -exact reference bytes. Inspect actual candidate, PR and post-merge runs separately. -The source/workload policy and all 27 mapped inputs remain unchanged. - -provenance/GATE_B_2026-10-04.json records this pass's base and local evidence; -subsequent hosted results must be obtained from their reports, not inferred. -A fresh assistant pass is not the absent separate-reader report. No invitations -or other outside contact are authorized. Broad source collection remains paused; -reopen a physical premise only for model-matched evidence. Implementation and -priority limitations remain in the existing support/mismatch map. +all supplementary tests including tools/test_uniform_minimum.py, and all five +preserved scientific suites in fresh output paths. Keep raw failures and every +numerical difference; report byte equality separately from assertion success. +Inspect actual candidate, PR and post-merge reports, not only workflow badges. + +All 27 mapped inputs, original references, and comparison/workload policy remain +unchanged. provenance/GATE_C_2026-10-04.json pins the incoming source and local +scope; later hosted outcomes require their own evidence. Other repositories and +the earlier unmerged alternate Gate B package are not imported into this work. + +Broad source collection remains paused. Implementation and priority gaps remain +explicit in the support/mismatch map. No manuscript, release or outside invitation +is initiated. After the bounded proof scrutiny, consolidate rather than adding +new models to prolong development. From 05f5e474af881854daa9794386170efaf4855081 Mon Sep 17 00:00:00 2001 From: Ruge Lin Date: Mon, 5 Oct 2026 04:29:39 +0800 Subject: [PATCH 2/2] Keep the central diagnostic regular at an exact turning point An extra warning-as-error probe found unused singular wave-data evaluation in the otherwise regular central ODE coefficient. Add a coefficient-only evaluator and exact turning-point/origin assertions within the existing seven-test suite. Preserve the first passing candidate, raw failing probe and reversible arithmetic-path repair separately. No equation, reference, assertion tolerance, scientific source or comparison policy changed. The refined remote tree 478ba79d3f0a08c0b1e2563be25909e983148b39 matches the frozen local tree. The seven refined diagnostics pass and their report is byte-identical to the first passing report. Full frozen refined-candidate and hosted runs remain distinct evidence to inspect before merge. --- archive/GATE_C_DIAGNOSTIC_REFINEMENT.md | 56 +++++++++++++++++++++++++ provenance/GATE_C_2026-10-04.json | 9 ++-- tools/test_uniform_minimum.py | 13 +++++- 3 files changed, 74 insertions(+), 4 deletions(-) create mode 100644 archive/GATE_C_DIAGNOSTIC_REFINEMENT.md diff --git a/archive/GATE_C_DIAGNOSTIC_REFINEMENT.md b/archive/GATE_C_DIAGNOSTIC_REFINEMENT.md new file mode 100644 index 0000000..71b3301 --- /dev/null +++ b/archive/GATE_C_DIAGNOSTIC_REFINEMENT.md @@ -0,0 +1,56 @@ +# Gate C diagnostic refinement: keep the central equation off a singular wave chart + +**4 October 2026. Test implementation only; no physical equation or tolerance change.** +The first seven-test Gate C candidate passed. An additional exact-turning-point probe +then exposed an avoidable issue in its diagnostic RHS: it called `local_data(...)[0]` +to obtain the regular scalar coefficient, but that helper also evaluated unused +wave-basis quantities proportional to inverse powers of the coefficient. At a zero +of the coefficient those unused quantities are singular. + +With NumPy floating-point warnings raised as exceptions, the actual probe was: + +```python +with np.errstate(all='raise'): + local_data(-np.exp(-16.), 16., .5)[0] +# FloatingPointError: divide by zero encountered in scalar divide +``` + +The central ODE coefficient itself is zero there and has no singularity. This is +not a failure of an original 272-control suite, not a defect of the integrated +central estimate, and not evidence for cutting out the turning region. + +The repair gives the central ODE a coefficient-only evaluator, including the exact +origin limit. Wave data remain confined to their outer-basis use. A new assertion +inside the existing central-remainder test checks both the exact turning point and +the origin with floating warnings promoted to errors. The seven-test count is +unchanged. No equation, integration tolerance, reference or protected source changed. + +The pre-refinement script, raw probe log and forward/reverse patch are retained in +the conversation evidence package. The original candidate is also Git commit +`52bc319675c2d77c894580059745f010a9fd2794`; its scientific report is not relabeled +as failed. The exact diagnostic code change is: + +```diff +--- a/tools/test_uniform_minimum.py ++++ b/tools/test_uniform_minimum.py +@@ -22,0 +23,8 @@ ++ ++ ++def local_coefficient(x: float, L: float, b: float): ++ """The central equation is regular even where a wave basis is singular.""" ++ if x == 0: ++ return complex(-b) ++ D = complex(L-np.log(abs(x)), np.pi if x > 0 else 0.) ++ return L/D-b +@@ -78,0 +87,3 @@ ++ with np.errstate(all='raise'): ++ self.assertEqual(local_coefficient(-np.exp(-16.), 16., .5), 0j) ++ self.assertEqual(local_coefficient(0., 16., .5), -.5+0j) +@@ -122 +133 @@ +- F = -b+0j if x == 0 else local_data(x, L, b)[0] ++ F = local_coefficient(x, L, b) +``` + +The refined frozen tree and hosted runs require their own completed reports. Do not +infer them from the initial pass or confuse this auxiliary probe with an interrupted +scientific verification. diff --git a/provenance/GATE_C_2026-10-04.json b/provenance/GATE_C_2026-10-04.json index 88bd745..67e8021 100644 --- a/provenance/GATE_C_2026-10-04.json +++ b/provenance/GATE_C_2026-10-04.json @@ -45,11 +45,13 @@ "new_checks": { "count": 7, "first_run": "PASS", - "script_sha256": "02d7bc6223e585bd3e1762fee28751b3a5de5aec85fa600a8dfab709d87df681", "report_sha256": "26f46c0806aed38d48ff200f1ee8c9b5f6ee590dac45dd17316118b4e198c314", "original_272_members": false, "sampled_sign_reversals": 169, - "scope": "Symbolic and finite integral/ODE diagnostics; not a supremum proof or long-time physical simulation." + "scope": "Symbolic and finite integral/ODE diagnostics; not a supremum proof or long-time physical simulation.", + "initial_script_sha256": "02d7bc6223e585bd3e1762fee28751b3a5de5aec85fa600a8dfab709d87df681", + "refined_script_sha256": "7703afd291d29eb03bde1b4be1359f645d1d3644cd448809acfad229b4df52b1", + "refinement": "An extra exact-turning-point probe exposed unused singular wave-data evaluation in the central RHS. Coefficient-only evaluation and an exact-point assertion repair it without an equation or tolerance change. See archive/GATE_C_DIAGNOSTIC_REFINEMENT.md; first passing script/log/probe/patch retained." }, "preservation": { "mapped_inputs": 27, @@ -72,7 +74,8 @@ } ], "operational_failures": [ - "Public git clone failed: Could not resolve host github.com. Source recovered by connector; no scientific run interrupted." + "Public git clone failed: Could not resolve host github.com. Source recovered by connector; no scientific run interrupted.", + "A clean-baseline launch selected its source directory as output and was rejected before any scientific suite. The corrected retry uses fresh baseline-frozen paths; rejected logs are retained." ], "decision": { "gate_c": "Explicit uniform author-side route; no coefficient/domain correction found.", diff --git a/tools/test_uniform_minimum.py b/tools/test_uniform_minimum.py index 766f04e..b3dda53 100644 --- a/tools/test_uniform_minimum.py +++ b/tools/test_uniform_minimum.py @@ -22,6 +22,14 @@ RHO = 1/(4*np.pi) +def local_coefficient(x: float, L: float, b: float): + """The central equation is regular even where a wave basis is singular.""" + if x == 0: + return complex(-b) + D = complex(L-np.log(abs(x)), np.pi if x > 0 else 0.) + return L/D-b + + def local_data(x: float, L: float, b: float): """F, q, h and Omega, only at nonzero x where this basis is used.""" if x == 0: @@ -76,6 +84,9 @@ def test_symbolic_offset_frame_and_shifted_defect(self): def test_integrated_central_remainder_including_core(self): rows = [] + with np.errstate(all='raise'): + self.assertEqual(local_coefficient(-np.exp(-16.), 16., .5), 0j) + self.assertEqual(local_coefficient(0., 16., .5), -.5+0j) for L in (16., 64., 256.): R = L**.25 # x=exp(-t): the full central core t in [0,infinity) is included. @@ -119,7 +130,7 @@ def test_finite_central_transfers_with_varying_b(self): k = np.sqrt(1-b) y = wave_matrix(R, L, b)[:, 0] def rhs(x, state): - F = -b+0j if x == 0 else local_data(x, L, b)[0] + F = local_coefficient(x, L, b) return np.array([state[1], -F*state[0]]) for lo, hi in ((R, 0.), (0., -R)): sol = solve_ivp(rhs, (lo, hi), y, method='DOP853',