This compact vocabulary maps concepts to their maintained definitions, proofs and execution owners. It is not another theory owner or research queue. Use the theory catalog and the authority hierarchy in AGENTS.md to resolve conflicts against explicit premises, mathematics and actual execution.
Canonical means a maintained definition or execution contract here; it does not mean uniquely derived or physically established. Fundamental names a primitive or an identity of a declared model, whose premises remain revisable. Emergence requires a dynamical result under stated assumptions. Computing a quantity, assigning a label or configuring a controller is not that result.
Each card separates its basis from its emergence claim. Primitive state, identities, constitutive premises, derived consequences, diagnostics, policies, auxiliary models and hypotheses have different roles. Maintained means the scoped declaration is maintained, not that nature has validated it. Candidate retains an unresolved proposal. Conditional emergence is reserved for derived dynamical results with explicit hypotheses. Exact identities, conditional proofs, represented arithmetic and finite numerical observations remain distinct evidence.
Dependencies are prerequisites of definitions or justifications, not the interaction edges of the dynamical system. Their acyclic declaration does not exclude coupled phase/form feedback. Related-reading links need not be dependencies.
The cards are the only editable concept catalog. Generate their index with
python scripts/check_documentation.py --write-generated.
| Concept | Basis | Emergence | Status |
|---|---|---|---|
| Form (EPI) | primitive | not-claimed | maintained |
| Reorganization capacity (nu_f) | primitive | not-claimed | maintained |
| Primitive phase (phi, theta) | primitive | not-claimed | maintained |
| Support, conductance and distance | primitive | not-claimed | maintained |
| Structural clock | primitive | not-claimed | maintained |
| Fractal-Resonant Node (NFR) | primitive | not-claimed | maintained |
| Structural pressure (DeltaNFR) | constitutive | not-claimed | maintained |
| Nodal equation and complete closure | identity | not-claimed | maintained |
| Conditional relational exchange law | constitutive | not-claimed | maintained |
| Conditional smooth-sine exchange law | constitutive | not-claimed | maintained |
| Relative resultant, phase metric and mobility | derived | not-claimed | maintained |
| Joint storage and signed exchange work | derived | not-claimed | maintained |
| Pure-EPI diffusion and relaxation | derived | conditional | maintained |
| Conditional pattern formation and recovery | derived | conditional | maintained |
| Conditional moving-pattern retention | derived | conditional | maintained |
| Conditional structural resonance | derived | conditional | maintained |
| Conditional autonomous nonlinear pulse | derived | conditional | maintained |
| Collective contact pulse and internal feedback | derived | not-claimed | maintained |
| Conditional parametric pulse instability | derived | conditional | maintained |
| Conditional nonlinear recurrence | derived | conditional | maintained |
| Derived form geometry | derived | not-claimed | maintained |
| Conditional dynamical scale inheritance | derived | conditional | maintained |
| Coarse closure and hidden-state obstruction | derived | not-claimed | maintained |
| Derived hidden-state memory | derived | not-claimed | maintained |
| Retained relational phase offset | derived | conditional | maintained |
| Supplied bridge interfaces | derived | not-claimed | maintained |
| Cycle winding | derived | not-claimed | maintained |
| Coherence read-out (C) | diagnostic | not-claimed | maintained |
| Pressure/rate equilibrium test | diagnostic | not-claimed | maintained |
| Sense Index (Si) | diagnostic | not-claimed | maintained |
| Structural-field tetrad | diagnostic | not-claimed | maintained |
| Structural potential (Phi_s) | diagnostic | not-claimed | maintained |
| Phase gradient magnitude | diagnostic | not-claimed | maintained |
| Circular phase curvature (K_phi) | diagnostic | not-claimed | maintained |
| Coherence range (xi_C) | diagnostic | not-claimed | maintained |
| Structural currents and balance diagnostic | diagnostic | not-claimed | maintained |
| Named structural operators | constitutive | not-claimed | maintained |
| Grammar and automatic selection | policy | not-claimed | maintained |
| Thresholds, gains and numerical tolerances | policy | not-claimed | maintained |
| Spectral pulse and modal rhythm | auxiliary | not-claimed | maintained |
| Auxiliary symplectic substrate | auxiliary | not-claimed | maintained |
| Arithmetic and Riemann constructions | auxiliary | not-claimed | maintained |
| Physical measurement bridge | constitutive | not-claimed | candidate |
| Physical constituents from TNFR | hypothesis | not-claimed | candidate |
- Status: maintained
- Basis: primitive
- Emergence: not-claimed
- Definition: Structural configuration x in a declared form space; the graph scalar chart is signed real.
- Domain: Declared form units X; finite real values or uniform-real BEPI for scalar-only consumers.
- Premises: Choose the state space and chart before specifying evolution.
- Dependencies: none
- Owner: Form foundations.
- Evidence: Types and implementation.
- Implementation: Scalar admission.
- Tests: EPI domain.
- Limits: Magnitude cannot substitute for the signed structure of richer BEPI; EPI is not automatically voltage, energy or matter.
- Status: maintained
- Basis: primitive
- Emergence: not-claimed
- Definition: Nonnegative multiplier of pressure in the nodal form rate, relative to the declared clock.
- Domain: Finite nonnegative rates in inverse structural-clock units; zero suppresses the unforced form row.
- Premises: Supply capacity or independently admit its evolution; Hz_str does not identify laboratory seconds.
- Dependencies: clock
- Owner: Capacity foundations.
- Evidence: Capacity-law admission.
- Implementation: Nodal arithmetic.
- Tests: Nodal contracts.
- Limits: Capacity is neither the actual form derivative nor angular frequency without another law; zero does not imply full equilibrium.
- Status: maintained
- Basis: primitive
- Emergence: not-claimed
- Definition: Circular synchronization coordinate in S¹, using a declared real lift where required.
- Domain: Finite represented angles in radians; wrapped differences require a branch convention.
- Premises: Phase evolution requires an independent supplied or derived row.
- Dependencies: none
- Owner: Parameter ledger.
- Evidence: Primitive phase closure.
- Implementation: Circular admission.
- Tests: Circular semantics.
- Limits: Phase is not itself a monotone clock or an angle derived from EPI contrasts.
- Status: maintained
- Basis: primitive
- Emergence: not-claimed
- Definition: Support names neighbors; conductance weights form transport; path distance supplies a separate observation geometry.
- Domain: The graph model declares direction, multiplicity, isolates and admissible weights.
- Premises: Initial support and any support evolution or intervention must be stated.
- Dependencies: none
- Owner: Relation foundations.
- Evidence: Zero-relation boundary; pressure contract.
- Implementation: Support transport.
- Tests: Regional cut.
- Limits: A zero-conductance edge can remain a phase neighbor. Normalized transport weight is not an absolute interaction rate; distance is separate. No autonomous relation-birth law is derived.
- Status: maintained
- Basis: primitive
- Emergence: not-claimed
- Definition: Declared parameter t relative to which continuous rates and timestamps are interpreted.
- Domain: Declared time units T and finite admitted intervals; Boolean durations and lost nonzero values are invalid.
- Premises: Clock changes transform the complete law, including capacity evolution.
- Dependencies: none
- Owner: Clock covariance.
- Evidence: Joint unit changes.
- Implementation: Time admission.
- Tests: Parameter covariance.
- Limits: Operator-word counts are not elapsed seconds; synchronization alone supplies no physical clock.
- Status: maintained
- Basis: primitive
- Emergence: not-claimed
- Definition: A supplied nodal unit; a collective NFR additionally needs a declared pattern identity, retained internal state and interaction model.
- Domain: A node or specified region; collective representations retain constituents unless a justified reduction removes information.
- Premises: Specify membership, identity/equivalence and consumed state before testing formation or persistence.
- Dependencies: epi, capacity, phase, support
- Owner: Substrate and scale.
- Evidence: Formation and identity obligations; retained pair state.
- Implementation: SDK observation, collective-state reader.
- Tests: Observation scope, realizable pair state.
- Limits: A node, nested child or named region is not proved autopoiesis or matter. Identity can persist while internal state changes; nesting alone proves neither predictive closure nor formation.
- Status: maintained
- Basis: constitutive
- Emergence: not-claimed
- Definition: Response p driving form change; its realization is selected independently of the written nodal product.
- Domain: Tangent response in the chosen form chart, with units [x]/([nu_f][t]).
- Premises: Supply the pressure law and its consumed state. The native form/phase/capacity/topology mixture is one specified realization.
- Dependencies: epi, capacity, phase, support, clock
- Owner: Pressure scope.
- Evidence: Specified relational map.
- Implementation: Native pressure.
- Tests: Pressure orientation.
- Limits: Stored and refreshed pressure differ. The full mixture is not generally a fixed-metric gradient; retrospective derivative reconstruction is not prediction.
- Status: maintained
- Basis: identity
- Emergence: not-claimed
- Definition: The unforced continuous form row is dx/dt = nu_f * p.
- Domain: An admitted form chart, pressure, capacity and clock.
- Premises: This model identity requires additional laws for all consumed state and events to determine a full evolution.
- Dependencies: epi, capacity, pressure, clock
- Owner: Nodal equation.
- Evidence: Integrated form.
- Implementation: Canonical derivative, integrators.
- Tests: Nodal equation, forcing scope.
- Limits: Declared Gamma adds an independent rate and can move form at zero capacity. Hybrid jumps are separate; the identity does not select their occurrence.
- Status: maintained
- Basis: constitutive
- Emergence: not-claimed
- Definition: Joint rows xdot = nu_f*(-eq/d + wg) and thetadot = (w/beta)nu_fq/H, where q_i=sum_neighbors(x_i-x_j) and d_i is the degree.
- Domain: Fixed connected simple reciprocal unit support with at least two nodes, held nonnegative capacities, e≥0, w,beta>0 and admitted phase chamber.
- Premises: Native pressure and joint storage plus the owner's capacity/locality premises and common-phase-clock convention.
- Dependencies: nodal-equation, phase-metric
- Owner: Capacity-separable law.
- Evidence: Conditional phase-row classification; storage/locality classification.
- Implementation: Relational engine.
- Tests: Exchange execution.
- Limits: This opt-in law differs from operator execution. The nodal identity does not select its coefficients or locality premises; compatible passive countermodels can change response while sharing equilibria.
- Status: maintained
- Basis: constitutive
- Emergence: not-claimed
- Definition: With K=diag(nu_i/d_i), unit graph Laplacian L and S_i=sum_neighbors sin(theta_j-theta_i), the baseline rows are xdot=-eKLx+(w/pi)KS and thetadot=(w/(betapi))KL*x.
- Domain: Fixed finite connected simple reciprocal unit support with at least two nodes, held nonnegative capacities, e>=0, w,beta>0 and finite signed form/circular phase.
- Premises: Select both rows, cosine storage and clock without forcing/events. Conservation, locality and phase-information assumptions remain conditional constitutive premises.
- Dependencies: nodal-equation, phase, capacity, support
- Owner: Complete smooth-law comparison.
- Evidence: Balance and continuation; constitutive nonselection.
- Implementation: Shared comparison/rates, admission.
- Tests: Complete-law controls, admission.
- Limits: This changes native form and phase rows, not merely phase admission. Storage, smoothness or a shared tangent does not uniquely select it. Individual theorems impose additional premises; detached readers do not replace Network.step_relational.
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: z_i = sum_j exp(i*(theta_j-theta_i)); g_i = Arg(z_i)/pi; H_i = pi*abs(z_i)*sinc(Arg(z_i)); phase mobility is nu_i/H_i.
- Domain: Reciprocal unit support without isolates, nonzero z_i and Arg(z_i) in (-pi,pi); H_i is positive on this regular chart. Acute edges suffice.
- Premises: Use the unweighted neighbor resultant and sinc(a)=sin(a)/a, continuously extended to 1 at zero.
- Dependencies: phase, support, capacity
- Owner: Relational geometry.
- Evidence: Phase-row derivation; regular-domain admission.
- Implementation: Captured relational field.
- Tests: Regular execution.
- Limits: Zero-resultant and branch boundaries are not successful zero values. A certified chart is not a trajectory/rate enclosure; unresolved represented states can reject.
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: For S = E_D + beta*V, with E_D = sum_edges (x_i-x_j)^2/2 and V = sum_edges [1-cos(theta_j-theta_i)], the ideal balances are Sdot=-sum D_i and E_D_dot=-sum D_i+sum J_i. Count unordered edges once.
- Domain: The selected native or baseline smooth-sine law on held unit support. With q=Lx, both have D_i=enu_iq_i^2/d_i; native exchange is J_i=wnu_iq_ig_i, while sine exchange is J_i=(w/pi)*(nu_i/d_i)q_iS_i.
- Premises: Use one complete unforced continuous law with held support; boundary inputs and support-event jumps require their separate balance terms.
- Dependencies: relational-law, sine-law
- Owner: Joint balances, sine channel work.
- Evidence: Native work identity; sine balance.
- Implementation: Native field work, sine rate/work kernel.
- Tests: Native work, sine complete-law controls.
- Limits: Storage is not physical or tetrad energy. Equal storage/loss need not give equal trajectories. Instantaneous power, accumulated work and endpoint storage differ; retain boundary work, signed remainders and numerical/event defects.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: Isolated form pressure is -L_rw*x; fixed positive capacities and reciprocal nonnegative conductance give consensus when the positive-conductance graph is connected.
- Domain: Source-free form channel, fixed conductance/support and held positive capacities; disconnected components and isolates have separate conclusions.
- Premises: Only EPI pressure, no forcing/events. The generator conserves the conductance-strength/capacity-weighted form total.
- Dependencies: nodal-equation, support
- Owner: Diffusion stability.
- Evidence: Ideal theorem.
- Implementation: Structural diffusion.
- Tests: Diffusion controls.
- Limits: Other channels, directed support or changing capacities need separate proofs. Relaxation toward consensus does not establish NFR formation.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: Recovery restores a declared identity near it; formation reaches that identity from a preparation lacking it. Retention is an additional time-domain claim.
- Domain: Each native recovery/capture or sine formation theorem retains its own support, loss, capacity and initial/target domains.
- Premises: Match the complete law, environment, clock and uncertainty throughout entry and any retained interval.
- Dependencies: relational-law, sine-law, storage-work, winding, nfr
- Owner: Native recovery, sine formation/retention.
- Evidence: Native validated transit; conservative same-orbit theorem.
- Implementation: Native transit, sine formation certificate.
- Tests: Native transit, same-orbit formation.
- Limits: Sufficient storage is not entry. An existential source ball or a mapped-source prefix does not automatically supply an independent numerical preparation ball. Physical identity and source selection remain open.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: A declared geometric identity persists over a specified interval while the full state can evolve.
- Domain: Conservative unit sine C5 identities with full environment retained; moving-reference and energy-speed certificates have separate domains.
- Premises: Supplied initial identity, full-state uncertainty, positive chart margins and the selected storage/travel bound.
- Dependencies: sine-law, storage-work, winding, closure
- Owner: Moving-reference window, energy-speed retention.
- Evidence: Relative-storage bootstrap; whole-network travel bound.
- Implementation: Reference window, cycle retention.
- Tests: Full-row window controls, cycle retention.
- Limits: Maintenance is not attraction or first acquisition. Backward-valid windows constrain possible entry; regional storage alone cannot replace the full environmental budget.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: A positive finite-frequency maximum of a declared stable input/output gain.
- Domain: Normalized-sine tangent dynamics at a critical pattern, with positive capacity/loss/coupling and a positive-definite phase Hessian modulo the common origin.
- Premises: Specify probe and readout, retaining full support; collocated and remote-response theorems have different observation hypotheses.
- Dependencies: sine-law, phase, capacity, support, clock
- Owner: Resonance foundations.
- Evidence: Work-conjugate gain theorem; observation-dependent modes.
- Implementation: Sine resonance assessments.
- Tests: Independent tangent and response controls.
- Limits: A gain peak neither supplies its probe nor proves periodic motion, formation or physical resonance. RA execution and the auxiliary graph-wave model are separate mechanisms.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: Nonstationary periodic form/phase exchange under a complete autonomous law.
- Domain: Zero-loss sine law: isolated unit P2, nonnegative capacities of positive sum, 0<E<2beta; separately, the exact doubled-C5 family with common positive held capacity, 0<H<betacos(2*pi/5).
- Premises: Supplied support, nonzero preparation, positive beta/coupling and clock; replica internal coordinates obey the exact invariant-family conditions.
- Dependencies: sine-law, phase, capacity, support, clock
- Owner: Permanent-pulse admission.
- Evidence: P2 libration and dissipative obstruction, exact internal pulse and observation-dependent period.
- Implementation: P2 pulse, replica pulse.
- Tests: P2 controls, replica field/period.
- Limits: Exact continuous periods do not certify Euler orbits. Replica labeled/unordered periods differ by two; means stay fixed while constituents move. Sufficiently small nonzero replica pulses are transversely unstable. Conservation selects neither zero loss nor amplitude and cannot create motion from equilibrium.
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: Mean form contrast and lifted contact phase obey projected rows with feedback from unequal contacts.
- Domain: Conservative unit-capacity sine law on C5 with five private leaves, using declared continuous contact phase lifts and clock tau=t/pi.
- Premises: Retain actual nodal state and contact deviations; collective storage h_c and the signed remainder H-5h_c depend on the chosen lifts.
- Dependencies: sine-law, storage-work, phase, closure
- Owner: Actual mean-contact balance.
- Evidence: Projected feedback and storage identity.
- Implementation: Collective-pulse observer.
- Tests: Independent full-row/lift controls.
- Limits: The mean coordinates need not close or be periodic. A transfer sign or initial derivative proves neither winding acquisition, maintained identity, resonance nor a physical reservoir.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: Exponential transverse growth generated by periodic coefficients of a full autonomous variational law, established by an unstable return multiplier.
- Domain: Sufficiently small positive internal amplitude in the exact conservative doubled-C5 pulse family, with the full twenty real state directions retained.
- Premises: Use the pulse theorem's exact family, capacity and clock; retain collective feedback and the amplitude-dependent period.
- Dependencies: autonomous-pulse, storage-work
- Owner: Complete variation and symmetry-correct return.
- Evidence: Exact small-amplitude splitting and analytic remainder.
- Implementation: Detached variation and asymptotic splitting assessments.
- Tests: Full fine Jacobian, harmonic solvability and return-scope controls.
- Limits: Existence of a small-amplitude instability interval supplies no numeric threshold or chosen-amplitude verdict. Neutral shear is distinct from exponential growth; leaving a waveform need not destroy geometric identity.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: Full form/circular-phase state returns arbitrarily close to its initial state at unbounded positive times, without requiring a period.
- Domain: Conservative sine law on finite connected unit support with positive held capacities, a positive energy sublevel and a nonzero-width conserved-mean interval.
- Premises: Positive beta/coupling; no input, clipping or events. Use circular phases and the theorem's ambient volume measure.
- Dependencies: sine-law, phase, capacity, support, clock
- Owner: Full nonlinear recurrence.
- Evidence: Compactness, invariant volume and exceptions.
- Implementation: Family-level recurrence.
- Tests: Invariant/domain controls.
- Limits: The result is almost everywhere, not a verdict for one chosen state, grid or fixed-energy surface. It gives no return time or frequency. Winding protection needs an independent phase-sector barrier, not recurrence alone.
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: Regional EPI contrasts determine Cartesian/Gram observations and, away from zero contrast, an orientation angle.
- Domain: Supplied ordered regions, declared form chart and any independent held source used as an orientation reference.
- Premises: Project and differentiate the admitted fine law; retain source-relative information when a source distinguishes orientations.
- Dependencies: epi, nodal-equation
- Owner: Derived form phase.
- Evidence: Inherited observations, source-relative response.
- Implementation: Form geometry, source-relative form.
- Tests: Form geometry, source response.
- Limits: The derived angle is unavailable at zero contrast and is not automatically the primitive phase consumed by pressure.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: A fine-to-collective map intertwines the admitted evolution with a stated law family and explicit unit changes.
- Domain: The supplied synchronized replica submanifold of the native or separately declared sine law; retained internal coordinates are required away from synchronization.
- Premises: Fixed replicated support, fiber-compatible capacities/state and complete law; iterated maps must compose.
- Dependencies: relational-law, sine-law, support, capacity, phase, clock
- Owner: Scale inheritance.
- Evidence: Native exact replication, replica composition and constitutive freedom.
- Implementation: Native field, retained sine state.
- Tests: Complete replica rows, counterfamily inheritance.
- Limits: This does not derive generic fractality, a fractal dimension, spontaneous hierarchy or unique dynamics. Discarding internal coordinates requires closure or memory evidence; a repeated graph alone is insufficient.
Coarse closure and hidden-state obstruction
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: A retained state y=R(z) closes when DR(z)F(z) agrees on each fiber of R under the declared fine law.
- Domain: Each linear, native or sine reduction has its own realizable state/support domain; observed outputs need not constitute such a state.
- Premises: Specify law, observation, admissible fine states and discarded information. An autonomous subsystem must retain boundary dynamics or derived memory.
- Dependencies: nodal-equation, relational-law, sine-law
- Owner: Composition and closure, global pair state.
- Evidence: Instantaneous interface versus future state; exact pair realizability/closure.
- Implementation: Linear realization, retained pair state.
- Tests: Linear closure, global pair rows and realizability.
- Limits: Instantaneous interaction sufficiency, future closure and recovery from observations differ. On doubled C5, (X,Z) supplies currents but realized (X,Z,P,U,W) retains predictive internal information through cancellation. These are derived coordinates, not new constitutive parameters; tangent or snapshot agreement alone proves no nonlinear closure.
Derived hidden-state memory
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: Eliminating unobserved coordinates retains their propagated initialization and history-dependent influence in the visible equation.
- Domain: A complete fine law and fixed observation; diffusion and nonlinear relational results have different hypotheses.
- Premises: Retain hidden initialization and forcing; admit approximation error separately.
- Dependencies: closure
- Owner: EPI memory, relational memory.
- Evidence: Exact elimination; nonlinear forecast scope.
- Implementation: EPI memory, coordinate elimination.
- Tests: Linear memory, nonlinear controls.
- Limits: Memory selects no microscopic law. A signed remainder is not a sufficient hidden state; exact elimination does not imply forgetting, irreversible damping or a finite-history approximation.
- Status: maintained
- Basis: derived
- Emergence: conditional
- Definition: Recovery of the same internal twist can leave a preparation-dependent common phase relative to a retained reference.
- Domain: The ideal native isolated unit C5 law near an acute winding-one twist, with centered perturbations and a common phase frame.
- Premises: Positive homogeneous capacity/coefficient conditions, a declared reference/readout and the selected contact or isolation protocol.
- Dependencies: phase, relational-law, pattern-recovery
- Owner: Retained collective phase.
- Evidence: Skew-pairing derivation; finite contact and retained record.
- Implementation: Cycle memory, contact/retention.
- Tests: Independent mechanism, finite error budgets.
- Limits: Common phase is not an intrinsic isolated-ring label. A port signal alone is not a lasting receiver record; later interventions, nondestructive readout and physical identity need separate admission. These readers execute no contact.
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: A supplied bridge changes degree, form contrasts and phase resultants; both endpoint fields and the signed support-event cost are retained.
- Domain: Admitted simple unit native graphs before/after attachment or relocation, with unchanged nodal state and the owner's component/phase-domain conditions.
- Premises: Supply the candidate; retain internal state/relative frames and the same law. Passivity and recovery require additional premises.
- Dependencies: relational-law, phase-metric, storage-work
- Owner: Support-event interfaces.
- Evidence: Bridge identity; event nonselection.
- Implementation: Shared attachment and relocation observers.
- Tests: Static attachment, relocation and budget controls.
- Limits: A detached report neither changes support nor selects occurrence/time. Represented costs are not trigonometric enclosures; admission alone authenticates neither work nor subsequent recovery.
- Status: maintained
- Basis: derived
- Emergence: not-claimed
- Definition: Integer cycle count from consistently wrapped oriented phase gaps divided by 2*pi.
- Domain: A supplied oriented cycle and declared branch/availability conditions.
- Premises: Constancy along a path requires exclusion of relevant branch crossings and accounting for support changes.
- Dependencies: phase, support
- Owner: Native cycle boundary, conservative regional passage.
- Evidence: Native phase-domain invariant; sine whole-window passage.
- Implementation: Winding certificates.
- Tests: Winding admission.
- Limits: Winding, acute geometry and maintained identity differ. A principal-branch crossing need not be singular for the smooth sine law; an integer snapshot proves neither formation nor physical charge/spin.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Configured map C=1/(1+mean(abs(p))+mean(abs(xdot))) in declared pressure/rate scales.
- Domain: Admitted finite stored arguments; local and aggregate reductions have different scopes.
- Premises: The reciprocal observation is selected, not uniquely derived from the nodal equation.
- Dependencies: pressure, nodal-equation
- Owner: Telemetry scope.
- Evidence: Core metric definitions.
- Implementation: Shared kernel.
- Tests: Coherence reduction.
- Limits: High C proves neither complete equilibrium nor stability, identity or formation. Stored rates need not be fresh nodal predictions.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: A tolerance predicate on pressure and form-rate magnitudes, exposed by is_structural_equilibrium.
- Domain: Declared finite arguments and nonnegative tolerances.
- Premises: Supplied quantities and tolerances determine the diagnostic verdict.
- Dependencies: pressure, nodal-equation
- Owner: Diagnostic scope.
- Evidence: Equilibrium boundary.
- Implementation: Shared predicate.
- Tests: Equilibrium scope.
- Limits: A tolerated zero form rate is not a full phase/capacity/support fixed point, particularly at zero capacity or with forcing.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Configured clipped mixture of normalized capacity, phase dispersion and pressure magnitude.
- Domain: Admitted inputs and current normalization policy.
- Premises: Selected weights and reductions define the score; controllers may explicitly consume it.
- Dependencies: capacity, phase, pressure
- Owner: Si definition and consumers.
- Evidence: Diagnostic closure limits.
- Implementation: Sense Index.
- Tests: Study diagnostics.
- Limits: Controller use does not promote Si to an emergent law, complete state or proved stability margin.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Interface (Phi_s, abs(grad phi), K_phi, xi_C) observing pressure aggregation, local phase structure and coherence range.
- Domain: Each constituent retains its independent data and availability conditions.
- Premises: Four complementary questions motivate the interface; completeness is a separate mathematical obligation.
- Dependencies: potential, phase-gradient, phase-curvature, coherence-length
- Owner: Diagnostic degrees and reconstruction.
- Evidence: Dynamical non-reconstruction.
- Implementation: Shared fields.
- Tests: Read-out consistency.
- Limits: The tetrad does not reconstruct general form, capacity, support, history or future evolution; unavailable fields cannot certify a complete safety verdict.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Nonlocal aggregation Phi_s(i)=sum_j p_j/d(i,j)^2 over other nodes under the declared distance convention.
- Domain: Admitted pressure and lengths, with specified unreachable/zero-distance handling.
- Premises: The inverse-square aggregation is a selected observation kernel.
- Dependencies: pressure, support
- Owner: Structural fields.
- Evidence: Topology-dependent bounds.
- Implementation: Potential field.
- Tests: Field observations.
- Limits: Potential is not universally bounded by pi, the relational storage or an independently derived physical interaction potential.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Mean absolute wrapped separation from the node's declared neighbors.
- Domain: Finite phases and supported neighbor conventions; circular bound pi.
- Premises: Mean separation is the selected local diagnostic.
- Dependencies: phase, support
- Owner: Structural fields.
- Evidence: Gradient scope.
- Implementation: Phase gradient.
- Tests: Field observations.
- Limits: A warning cut is not a derived instability threshold or a future-transition proof.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Wrapped displacement from the neighbor-resultant direction.
- Domain: Defined nonempty-neighborhood direction, with an explicit isolate convention; magnitude bounded by pi.
- Premises: Exactly joint-zero represented resultants are unavailable, not assigned an invented direction.
- Dependencies: phase, support
- Owner: Curvature contract.
- Evidence: Circular curvature scope.
- Implementation: Curvature observation.
- Tests: Resultant availability.
- Limits: Curvature alone proves neither confinement nor Mutation admission; Laplacian comparisons require additional small-spread hypotheses.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Distance-binned static coherence-product fit, with a separately tagged spectral fallback.
- Domain: Declared sampling, fit acceptance, graph and distance units.
- Premises: Pressure-derived products and fallback rules specify the observation.
- Dependencies: pressure, support
- Owner: Shared fit definition.
- Evidence: Correlation scope.
- Implementation: Estimator.
- Tests: Estimator provenance.
- Limits: An uncentered static fit is neither a temporal relaxation measurement nor proof of criticality; its fallback is a different observable.
- Status: maintained
- Basis: diagnostic
- Emergence: not-claimed
- Definition: Declared phase/pressure currents and density rho=Phi_s+K_phi supply a trajectory balance with measured residual.
- Domain: Matching captured support, positive finite intervals and the stated divergence convention.
- Premises: Temporal changes and both sector divergences come from actual captured evidence.
- Dependencies: potential, phase-curvature, clock
- Owner: Conservation diagnostics.
- Evidence: Measured balance.
- Implementation: Conservation observations.
- Tests: Observation admission.
- Limits: Single snapshots cannot establish temporal conservation. The field sum-of-squares energy is a Lyapunov candidate, distinct from relational storage.
- Status: maintained
- Basis: constitutive
- Emergence: not-claimed
- Definition: Thirteen registered transformations define declared jump contracts on nodal/graph state.
- Domain: The actual glyph, public operator, atomic stage or word-execution path.
- Premises: Identify primary and secondary writes and preserve their execution provenance.
- Dependencies: nodal-equation, phase, support
- Owner: Structural operators.
- Evidence: Execution contracts.
- Implementation: Operator registry.
- Tests: Operator contracts.
- Limits: A named jump is not a finite-duration nodal solution. Defining a transformation does not derive when it occurs or prove catalog completeness.
- Status: maintained
- Basis: policy
- Emergence: not-claimed
- Definition: U1-U5 impose word/live-state contracts; U6 monitors reference-relative potential drift. Automatic selection is a separate policy.
- Domain: Declared history, node state, grammar profile and execution path.
- Premises: Retain registered roles, configured choices, history and actual execution context; a supplied flag is not verified evidence.
- Dependencies: operators
- Owner: Unified grammar.
- Evidence: Premises and trajectories.
- Implementation: Grammar bases, selectors.
- Tests: Grammar bases.
- Limits: Admission is neither autonomous selection nor stability. U6 cannot be certified from a word. Mutation's observed signed growth evidence is distinct from the predicted nodal product.
- Status: maintained
- Basis: policy
- Emergence: not-claimed
- Definition: Settings used by named consumers to admit actions, label telemetry or control computation.
- Domain: Each value retains its units, normalization, consumer and overrides.
- Premises: Distinguish exact geometric bounds from policy cuts and arithmetic tolerances.
- Dependencies: clock, grammar
- Owner: Threshold ledger.
- Evidence: Assumption-explicit thresholds.
- Implementation: Defaults, compatibility constants.
- Tests: Threshold resolution.
- Limits: A CANONICAL name or pi-based formula does not prove universality. The exact radian wrap bound is a different claim.
- Status: maintained
- Basis: auxiliary
- Emergence: not-claimed
- Definition: A supplied graph-wave comparison assigns sqrt(lambda_k) frequencies; nodal pulse reports instead read stored capacity and phase.
- Domain: The declared graph operator, spectrum and supplied wave model.
- Premises: The wave law and units are additional choices, distinct from first-order diffusion.
- Dependencies: support, capacity, phase
- Owner: Wave correspondence.
- Evidence: Graph-mode calculation; generator distinction.
- Implementation: Pulse read-outs.
- Tests: Pulse scope.
- Limits: A modal readout is not a maintained wave or physical clock. The unit sine consensus tangent has frequency lambda in tau=t/pi, not sqrt(lambda). Same-law periodic motion uses the separate autonomous-pulse theorem.
- Status: maintained
- Basis: auxiliary
- Emergence: not-claimed
- Definition: An ambient model assigns canonical pairs to selected graph read-outs and a declared quadratic Hamiltonian.
- Domain: That auxiliary phase space, not arbitrary complete nodal execution.
- Premises: Canonical brackets, conjugate partners and Hamiltonian are supplied construction choices.
- Dependencies: tetrad, balance-diagnostic
- Owner: Auxiliary substrate.
- Evidence: Nodal correspondence boundary.
- Implementation: Symplectic substrate.
- Tests: Auxiliary model, graph realizability.
- Limits: Its harmonic flow and classical U(2) constructions do not establish quantum states, particle emergence or a Hamiltonian full-engine law.
- Status: maintained
- Basis: auxiliary
- Emergence: not-claimed
- Definition: Supplied arithmetic encodings and finite spectral constructions support scoped identities, diagnostics and comparisons.
- Domain: The particular inputs, graph family, cutoff and numerical evaluator.
- Premises: Prime/divisor data, logarithmic frequencies and known-zero targets remain identified when supplied.
- Dependencies: support
- Owner: Number theory, Riemann scope.
- Evidence: Construction inventory.
- Implementation: Arithmetic model, finite pulse.
- Tests: Arithmetic contracts, finite pulse.
- Limits: Shared telemetry does not identify arithmetic and physical dynamics. Finite scans or assigned spectra establish no RH proof or unproved asymptotic limit.
- Status: candidate
- Basis: constitutive
- Emergence: not-claimed
- Definition: Independently justified map from model state or collective observations to measurements, preparation and laboratory time.
- Domain: A named terrestrial system with declared data/instruments, uncertainty, calibration and reserved evaluation.
- Premises: Specify observables and pressure inputs before observing the response; latent primitive coordinates need not each have a direct sensor.
- Dependencies: epi, capacity, phase, clock, pressure
- Owner: Measurement admission.
- Evidence: Physical atlas status.
- Implementation: none: protocol-specific evaluators do not establish an admitted general physical bridge.
- Tests: none: no general physical identification has passed independent measurement admission.
- Limits: Retrospective pressure reconstruction is circular. Compatibility with known physics need not distinguish a unique explanatory mechanism.
- Status: candidate
- Basis: hypothesis
- Emergence: not-claimed
- Definition: Hypothesis that justified nodal structure and dynamics generate patterns explaining physical constituents and collective properties.
- Domain: A future identified model with independent observable predictions and terrestrial evidence.
- Premises: Admit complete state, constitutive laws, support/capacity evolution and the physical measurement bridge.
- Dependencies: nfr, nodal-equation, measurement-bridge
- Owner: Research strategy.
- Evidence: Foundation origin ledger.
- Implementation: none: the engine implements scoped models, not an established physical ontology.
- Tests: none: model tests cannot replace independent physical validation.
- Limits: Conditional formation, winding, symmetry and memory results do not themselves derive matter, spin, quantum mechanics or substrate creation from nothing.
Revise a card and its responsible owner together, retaining a stable lowercase
ID. Use the exact field order below and replace instructional values with scoped
statements or references. Dependencies contains existing comma-separated card IDs
or none; it is a declared prerequisite graph, not a mathematical proof.
<a id="new-concept"></a>
### Concept title
- **Status:** maintained or candidate
- **Basis:** primitive, identity, constitutive, derived, diagnostic, policy, auxiliary or hypothesis
- **Emergence:** not-claimed or conditional
- **Definition:** State what the concept means.
- **Domain:** State where it is defined and executable.
- **Premises:** Name supplied assumptions and choices.
- **Dependencies:** existing-id, another-id
- **Owner:** Link the maintained theory/docs definition owner.
- **Evidence:** Link the evidence; a derived concept needs a theory derivation anchor.
- **Implementation:** Link its src owner, or write none: followed by a reason.
- **Tests:** Link relevant test files, or write none: followed by a reason.
- **Limits:** State what does not follow from the declaration.The glossary checker validates card structure, labels, local references, declared dependencies and index freshness. A maintained implemented concept needs linked tests; derived claims need a derivation section and declared dependencies; hypotheses retain candidate status. These checks cannot verify a proof, test adequacy or physical truth, and never promote a concept automatically.
Reproducibility also requires fixed source, configuration, inputs, ordering, precision and execution path; a seed alone is insufficient. Use TESTING.md for validation and the sole execution plan for the next research task.