Manuscript VIII-B@3 · VIII-B-v3.tex · section · 3aa6baa1
Dependencies and verification status
Dependencies and verification status · lines 2754–2814
| Result | Mathematical inputs |
|---|---|
| Accessible-current criterion | Finite-dimensional adjoints and spectral separation |
| Cone dictionary | Interval, rays, seam, spinless affine packet |
| Persistence | Oblique metric, retuning, exact graph decomposition, lengths, areas, and localization |
| Matching certificate | Realized polygons, fixed affine extensions, overlap components, winding marks, and primitive meridians |
| Source constructor | Fixed named Hermitian matrix and scalar substitution |
| Spectator invariance | Partial trace; controller conclusion additionally uses Assumption ass:control |
| Finite realization | Algebraic table, exact reports, source promise, canonical codes, retained history, and gate synthesis |
| Recovery comparisons | Kraus identities, complete complements, and a Bell test |
All proofs used for the new constructor are present in this file. Companion citations identify related interfaces and scope distinctions, not hidden hypotheses.
The main symbolic audits are:
constant physical gradient norms (eq:gradient-identities);
exact cap and loop clearances (eq:bounds)–(eq:loop-clearance);
complete finite lengths and areas (eq:edge-metric), Table tab:lengths, and (eq:areas);
active-cell positivity and the unique event;
Lorentz membership and adapted face times (eq:boost)–(eq:chart-table);
canonical affine transitions and three- and six-factor words;
the reference specialization;
rational-tangent table identities;
bit and gate totals (eq:total-bits)–(eq:gate-bound);
the distinction between fixed-token correctness, branchwise ensembles, and nonlinear unconditional semantics.
Numerical sampling would be diagnostic, not a substitute for the interval proof. Useful independent checks include polygon intersection tests, area signs, adapted chart equations, seam orientation, algebraic report floors, and the reversible word action.