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Kernel-checked formal layer
Complete WCT Lean Coverage Lean coverage is generated from the same registry used by the equation and SymPy pages. The symbolic outcome remains separate from kernel-checked declarations.
142 canonical objects
62 mapped definitions or declarations
80 unmapped or incomplete
Boundary: mapped does not mean equal proof strength. Dimensional lemmas, algebraic support, definitions, partial theorems, counterexamples, and TODOs remain distinct.
Registry v2.0.0 · generated 2026-06-29T23:28:10+00:00 · machine-readable registry
M1 Curvature-locking functional PROVED · PARTIAL SUPPORT M2 Nonsingular curvature operator and Lyapunov candidate PROVED · PARTIAL SUPPORT M3 Finite-band spectral selector PROVED · PARTIAL SUPPORT M4 Dimensional stability threshold PROVED · PARTIAL SUPPORT M5 Curvature-bounded computation PROVED · PARTIAL SUPPORT M6A Unified linear operator DEFINITION M6B Nonlinear curvature operator PROVED · ALGEBRAIC SUPPORT M7 Full curvature-wavefield equation PROVED · PARTIAL SUPPORT M8 Curvature-acoustic cosmology system UNMAPPED E1A Curvature-rate density PROVED · DIMENSIONAL SUPPORT E1B Curvature spectral rate PROVED · DIMENSIONAL SUPPORT E2 Weighted loop average PROVED · ALGEBRAIC SUPPORT E3 Loop-locking action PROVED · ALGEBRAIC SUPPORT E4 Covariant locking solution PROVED · PARTIAL SUPPORT E5 Effective-wavenumber chain PROVED · ALGEBRAIC SUPPORT E6 Mass-curvature law PROVED · DIMENSIONAL SUPPORT E7 Solenoidal mass law PROVED · DIMENSIONAL SUPPORT E8 Corrected weighted-lock identity PROVED · PARTIAL SUPPORT E9 Phase-flux constitutive relation PROVED · ALGEBRAIC SUPPORT E10 Radial shell quantization PROVED · ALGEBRAIC SUPPORT E11 Phase winding PROVED · ALGEBRAIC SUPPORT E12 Finite-band dispersion rail PROVED · ALGEBRAIC SUPPORT E13 Band-pass amplitude evolution PROVED · PARTIAL SUPPORT E14 Band-pass Lyapunov functional PROVED · PARTIAL SUPPORT E15 Modal growth bound UNMAPPED E16 Linear spectral concentration UNMAPPED E17 Nonsingular curvature-feedback operator PROVED · PARTIAL SUPPORT E18 WCT Lyapunov candidate PROVED · PARTIAL SUPPORT E19 Gap-curvature scaling UNMAPPED E20 Higher-order cavity quadratic sector PROVED · PARTIAL SUPPORT E21 Second-derivative Euler-Lagrange equation UNMAPPED E22 Effective metric ansatz UNMAPPED E23 Enthalpic curvature relation UNMAPPED E24 Sobolev embedding threshold PROVED · PARTIAL SUPPORT E25 Critical Sobolev exponent DEFINITION E26 Corrected curvature $L^2$ bound DEFINITION E27 Finite-energy confinement DEFINITION E28 Corrected alpha-drop exponent PROVED · ALGEBRAIC SUPPORT E29 Entropy-drop pruning PROVED · ALGEBRAIC SUPPORT E30 Spectral entropy UNMAPPED E31 Conditional entropy-production bound UNMAPPED E32 Subexponential exploration condition UNMAPPED E33 Corrected support-entropy relation PROVED · ALGEBRAIC SUPPORT E34 Energy-entropy conversion UNMAPPED E35 Curvature-locked fixed point UNMAPPED E36 Discrete WCC update PROVED · PARTIAL SUPPORT E37 Bandlimit from energy UNMAPPED E38 Spatial channel capacity UNMAPPED E39 Polynomial update bound UNMAPPED E40 WCC complexity identification UNMAPPED E41 Curvature-bounded configuration count UNMAPPED E42 Theta-information relation UNMAPPED E43 Curvature-entropy tradeoff UNMAPPED E44 Theta eigenmode problem UNMAPPED E45 Corrected quality factor PROVED · ALGEBRAIC SUPPORT E46 Plasma-cavity curvature match UNMAPPED E47 Corrected power balance PROVED · ALGEBRAIC SUPPORT E48 Curvature-gap stability criterion UNMAPPED E49 Corrected effective-mass gap law PROVED · ALGEBRAIC SUPPORT E50 Phase-coherence functional UNMAPPED E51 Curvature-gradient commutator PROVED · ALGEBRAIC SUPPORT E52 Curvature gain and gradient loss UNMAPPED E53 Curvature pressure density PROVED · ALGEBRAIC SUPPORT E54 Resonance-lock condition UNMAPPED E55 Curvature-induced effective potential UNMAPPED E56 Phase-wall criterion UNMAPPED E57 Swift-Hohenberg shell operator PROVED · PARTIAL SUPPORT E58 Band-selective Green kernel PROVED · ALGEBRAIC SUPPORT E59 Projection onto a dominant annulus PROVED · ALGEBRAIC SUPPORT E60 Center-manifold amplitude equation UNMAPPED E61 Pattern-formation threshold PROVED · ALGEBRAIC SUPPORT E62 Spectral energy concentration PROVED · ALGEBRAIC SUPPORT E63 Entropic mode selection UNMAPPED E64 Corrected selected wavelength PROVED · PARTIAL SUPPORT E65 Critical Sobolev exponent DEFINITION E66 Gagliardo-Nirenberg interpolation DEFINITION E67 Failure of $H^2 o L^\infty$ above three dimensions PROVED · PARTIAL SUPPORT E68 Localized energy estimate DEFINITION E69 Corrected high-regularity curvature bound DEFINITION E70 Dimensional stability criterion PROVED · PARTIAL SUPPORT E71 Physical computation resource bound UNMAPPED E72 Curvature-pruned search space UNMAPPED E73 Polynomial verification UNMAPPED E74 Curvature separation conjecture UNMAPPED E75 Physical-oracle impossibility UNMAPPED E76 WCC complexity equivalence UNMAPPED E77 Mutual-information decay UNMAPPED E78 Fisher-information curvature bound TODO E79 Entropy-production rate UNMAPPED E80 Landauer-type bound UNMAPPED E81 Corrected coherence length DEFINITION E82 Information-geometry tensor UNMAPPED CLE1 Curvature-locking functional UNMAPPED CLE2 Corrected curvature-lock Euler-Lagrange equation UNMAPPED CLE3 Curvature-locking condition UNMAPPED CLE4 Locked-field equation UNMAPPED CLE5 Thin/product-torus Laplacian UNMAPPED CLE6 Separation ansatz UNMAPPED CLE7 Periodic angular mode family UNMAPPED CLE8 Selected torus eigenmode UNMAPPED CLE9 Electron radius from curvature UNMAPPED CLE10 Curvature scalar chain UNMAPPED G1 Log-periodic ghost modulation PROVED · ALGEBRAIC SUPPORT EX Logarithmic field representation PROVED · ALGEBRAIC SUPPORT EY Log-curvature evolution PROVED · ALGEBRAIC SUPPORT EZ Cole-Hopf reduction PROVED · ALGEBRAIC SUPPORT FA Filament-localization condition PROVED · ALGEBRAIC SUPPORT CM1 Fundamental field evolution UNMAPPED CM2 Curvature-spectral tilt UNMAPPED CM3 Potential from curvature UNMAPPED CM4 Horizon-entry potential decay UNMAPPED CM5 Curvature-acoustic oscillators UNMAPPED CM6 Sound speed from curvature feedback UNMAPPED CM7 Curvature diffusion UNMAPPED CM8 Initial conditions UNMAPPED CM9 First-order mode system PROVED · ALGEBRAIC SUPPORT CM10 Tight-coupling drag UNMAPPED CM11 Curvature damping envelope UNMAPPED CM12 Dimensionless power spectrum DEFINITION CM13 Peak metrics DEFINITION CM14 Peak-response interpretation UNMAPPED CM15 WCT angular scaling UNMAPPED CM16 Acoustic horizon DEFINITION CM17 Curvature-energy closure UNMAPPED CM18 Minimal cosmology closure set UNMAPPED CM19 Acoustic speed from curvature equation of state UNMAPPED CM20 Theta-based expansion ansatz UNMAPPED TOP1 Closed spectral-loop representation UNMAPPED TOP2 WCT loop-energy functional UNMAPPED TOP3 Irreversible gradient flow UNMAPPED TOP4 Emergent-topology criterion UNMAPPED TOP5 WCT dynamical codimension UNMAPPED TOP6 Spectral topology bands UNMAPPED TOP7 Topological mass proxy UNMAPPED TOP8 Holonomy non-invariance UNMAPPED TOP9 Protein-particle structural correspondence UNMAPPED CORR1 Full Lyapunov candidate UNMAPPED CORR2 Mean-amplitude spectral closure UNMAPPED CORR3 Spectral-weight notation UNMAPPED CORR4 Macro-micro control parameter UNMAPPED CORR5 Entropy-curvature coupling UNMAPPED CORR6 Isoelectronic-flow alignment UNMAPPED
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