# Verification and claim scope

The written proof covers all finite chains, not merely two-link paths.
The all-chain lower bound separates paths meeting the scalar stratum
from paths that never meet it. The explicit competitors attain the bound.
The orthogonal eigenline exception, scalar endpoints and equality cases
are included. The higher-dimensional statement is a sufficient criterion,
not a complete classification.

The originating researcher has accepted these specified theorems after
detailed self-audit. No independent reviewer or proof assistant is claimed.

The standard-library checker gives 40,222 passing conditions: 20,719 exact
rational checks and 19,503 binary64 regressions. Normal and optimized
execution produce identical JSON. Tests include the four endpoint lifts,
exact transition parameters, both scalar endpoint orders, the orthogonal
exception, reflection-leg identities, determinant splitting, nearest-wall
projections, a 75-vertex Floyd-Warshall graph and 12,000 seeded triangle
checks. These are bounded regression tests, not proofs over all inputs.

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