Equations and verification

Wave Confinement Theory Research Corpus

Start with the internal equation page, then move to the complete SymPy classification and Lean coverage pages. Repository files are secondary links inside those pages, so the website always has a clear return path.

142registered objects

68PASS

18CONDITIONAL

26DEFINITION

30OPEN

0FAIL

Visual orientation

Three recurring structures in the research program.

These illustrations are orientation aids for phase organization, topology, and curvature-feedback ideas. The canonical equations and verification records remain the source of truth.

Concept illustration of organized phase structure — **Phase organization**Concept illustration for global phase structure and phase-locking ideas.

Concept illustration of topology locking using a trefoil-knot geometry — **Topology locking**Closed-path topology as an explanatory visual for winding and locked-mode structure.

Concept illustration of entropy and curvature dynamics — **Curvature feedback**Visual orientation for the proposed balance between field organization, entropy, and curvature.

Boundary: concept illustrations are not simulation output, proof, or empirical validation.

01 · Canonical parent

All WCT equations

All 142 IDs, family structure, canonical registry links, and paths into SymPy and Lean.

Open equation page →02 · Executable audit

Complete SymPy audit

Every registered ID grouped by effective PASS, CONDITIONAL, DEFINITION, or OPEN status.

Open all 142 classifications →03 · Formal support

Complete Lean coverage

All 142 IDs accounted for, separating proofs, partial support, definitions, counterexamples, TODOs, and unmapped obligations.

Open Lean coverage →04 · Semantic graph

Research Command Center

Definitions, assumptions, derivations, equations, code, predictions, experiments, evidence, falsifiers, and chronology.

Open research graph ↗05 · Machine-readable

Corpus JSON

All 142 compiled objects with effective status, verification kind, assumptions, Lean mappings, empirical state, claims, and provenance.

Open JSON →06 · Archival record

Publication archive

Chronological Zenodo releases, DOI metadata, research-status labels, and citation exports.

Browse publications →

Status discipline: SymPy PASS is not a Lean proof or empirical validation. PROVED is reserved for declarations accepted by the Lean kernel under displayed hypotheses.

Registry provenance: schema 2.0.0; generated 2026-06-28T02:34:38+00:00. Open the compiled registry.