BCODR-LUC: the bidirectional circular-overlap method applied to root 6217
BCODR-LUC-04 · Tangent decomposition of the overlap germ
Neo.K / Aletheia
True Overlap Germ Tangent Decomposition: Normal–Tangent Separation and Second-Order Isolation of Root 127's Earliest Common Overlap Point — From a Three-Dimensional Critical Tangent Space to a Zero-Dimensional Birth Germ
A normal–tangent decomposition of root 127's earliest common overlap point: the active gradients of the two distance fields, the KKT relation (rank 2) and a three-dimensional critical tangent space, then a "combined germ stiffness" κ_germ = the minimum over unit critical tangent vectors of max(vᵀH₊v, vᵀH₋v) ≈ 0.4543 > 0 built from the two reduced Hessians, on which a second-order isolation theorem is claimed: the overlap has no tangent extent until the kernel radius exceeds T* (birth dimension 0), together with a growth law after birth. The paper lists CERT-04A to 04C as still needed for formal certification (interval enclosures, an interval proof of the active-set pattern, and a strict lower bound on κ).
Under the paper's own definition of combined stiffness, root 127's earliest common overlap point is isolated at second order (birth dimension 0); the interval certificates CERT-04A to 04C needed for formalization have not been done.
Layer two (RUN-066) reproduced, at 50 digits, the meeting point, the KKT relation, the rank and the critical tangent space, D₊, H± and Q±, the stiffness as §14 defines it, and the isolation of the birth germ; not as stated is that stiffness as the overlap's second-order law, and the growth law built on it (§16–19, §22): the overlap's second-order law is the Lagrangian αH₊ + (1 − α)H₋, softest 0.2366, not the straight-line 0.4543, so the lens grows to 1.036 √ε, not 0.748 √ε. The isolation of the germ itself stands. The package's verifier was re-run here and passes (it only checks the rank, the dimension, the symmetry and κ > 0.4 recorded in the ledger).