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csv
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Tags:
mathematics
homogenization
spectral-theory
variational-methods
matrix-analysis
scientific-computing
| { | |
| "release": "EVE-QELTHA final 4.0", | |
| "date": "2026-10-20", | |
| "scope": "Specified passive linear reduced variational transport models; assumptions and complete proofs in manuscript.", | |
| "proved_within_stated_assumptions": [ | |
| { | |
| "claim": "Coherence-dependent two-history determinant and rank classification", | |
| "source": "origins_and_capacity.tex" | |
| }, | |
| { | |
| "claim": "Exact Bessel impedance, including original angular exponent 15/8 and logarithmic endpoint", | |
| "source": "origins_and_capacity.tex" | |
| }, | |
| { | |
| "claim": "Common transported drainage kernel characterizes zero capacity; quantitative lower bound", | |
| "source": "origins_and_capacity.tex" | |
| }, | |
| { | |
| "claim": "Weak-twist horn capacity k0*epsilon^gamma for s>(a+1)/2", | |
| "source": "baseline_twist.tex" | |
| }, | |
| { | |
| "claim": "Equal-diagonal, globally isospectral compact kernels can yield different critical impedance fate", | |
| "source": "theorem_nexus.tex" | |
| }, | |
| { | |
| "claim": "Balanced fixed finite-rank compact L1 ports preserve leading capacity uniformly for all strengths, including a hard constraint", | |
| "source": "theorem_nexus_uniform.tex" | |
| }, | |
| { | |
| "claim": "Anchored weak-port joint asymptotic kappa=k0*epsilon^gamma+lambda*norm(L e2)^2+o(epsilon^gamma+lambda)", | |
| "source": "theorem_nexus_uniform.tex" | |
| }, | |
| { | |
| "claim": "Log-periodic capacity, explicit small-amplitude nonconstancy, finite-band local inverse synthesis", | |
| "source": "theorem_logperiodic.tex" | |
| }, | |
| { | |
| "claim": "Exact matrix connection/potential frame realization and sharp worst-case ambient dimension 2k", | |
| "source": "theorems_geometry.tex" | |
| }, | |
| { | |
| "claim": "Sharp first-order finite-penalty inlet correction W/rho", | |
| "source": "theorems_geometry.tex" | |
| }, | |
| { | |
| "claim": "One-bright microstructure realization in dimension k+1 with endpoint quantitative bounds", | |
| "source": "theorem_microstructure.tex" | |
| }, | |
| { | |
| "claim": "Complete periodic critical scale-ratio variational limit V_tau=T^dagger D_tau T, tau in [0,infinity], assuming rho_n tends to infinity", | |
| "source": "theorem_critical.tex" | |
| }, | |
| { | |
| "claim": "Critical inlet matrix-norm convergence and convergence of every fixed Dirichlet eigenvalue with multiplicity", | |
| "source": "theorem_critical.tex" | |
| }, | |
| { | |
| "claim": "Critical compensation realizes any stated nonnegative target with C1 square root at every fixed positive ratio", | |
| "source": "theorem_critical.tex" | |
| } | |
| ], | |
| "computed": { | |
| "verification_suites": 10, | |
| "passed": 10, | |
| "pass_percentage": 100.0, | |
| "summary": "results/verification_summary.json", | |
| "interpretation": "Percentage refers only to successful shipped programs; not proof confidence, novelty probability, or physical validation." | |
| }, | |
| "not_established": [ | |
| "Literature-first priority, field-defining significance, or a certified major scientific breakthrough", | |
| "Formal proof-assistant certification", | |
| "Full fluid PDE derivation, physical higher-dimensional fluid, ordinary hydraulic-network realization, or experiments", | |
| "Arbitrary physical loop holonomy or curvature from a connection on an interval", | |
| "Critical convergence rate, critical norm-resolvent bound, or optimality of the old rho^(-1/3) achievable bound", | |
| "Uniform critical compensation resource bounds as tau approaches zero", | |
| "Aperiodic or arbitrary-frequency microstructure, infinite-rank/noncompact ports, inlet atoms, or escaping port supports", | |
| "Weak-twist threshold s=(a+1)/2 or its subcritical side", | |
| "Negative target potentials, nonlinear fluid laws, molecular reaction predictions, or universal computation" | |
| ], | |
| "prior_art_boundary": "Connections, dark-state geometric potentials, energy-form traces, oscillatory-constraint homogenization, and multiple scale-ratio regimes have established predecessors; exact novelty of the combined results is unverified.", | |
| "review": "Proofs audited within this collaboration; external specialist review remains needed." | |
| } | |