← BCODR-LUC: the bidirectional circular-overlap method applied to root 6217 / BCODR-LUC-03 · True common-point overlap

BCODR-LUC: the bidirectional circular-overlap method applied to root 6217 BCODR-LUC-03 · True common-point overlap Neo.K / Aletheia

True Common-Point Overlap and Provenance Resolution: the True Intersection Time of the Root-6217 Bidirectional Kernel Fields, the Container-Separation Gap, and the Low-Dimensional Overlap Germ of Root 127

Corrects coarse box contact into a field intersection at one point: it proves that the true intersection time is at least the box distance (T∩true ≥ T_box) and defines the container-separation gap G_sep = T∩true − T_box. On the selected frontier, root 131's zero-radius nexus is false (T∩true ≈ 0.04733, the meeting point being the midpoint of the analytic ray's nearest point and pruned box 155's nearest point); root 127 is a near-true balanced overlap germ (T_box = 0.125 → T∩true ≈ 0.126954, earliest inward provenance 155, 0.0420 ahead of the runner-up 144), and its five-dimensional minimax problem reduces analytically to a one-dimensional scalar problem.

"BOTH by arrival" is not "balanced true overlap": on the selected frontier only 127 and 131 are balanced common-point germs, and 127's five-dimensional problem reduces analytically (numerical equality is taken within 2×10⁻⁹). Layer two (RUN-065) reproduced the theorem, every true overlap time and gap, the modes, 131's midpoint, and 127's value, provenance and reduction; not as stated is the provenance of 101, 103 and 104, where four pruned boxes tie exactly and there is no single provenance. Noted: the seven outward-limited gaps are exactly zero, and the ledger's negative ones come from LUC-01's ray grid, not the optimizers; the printed r* and λ* are right only to about 10⁻¹¹; at 127 the provenance 155 is right, but no flip led to it. The package's verifier was re-run here and passes (it only checks the ledger's own inequalities and flags).

Connections · Connections

Layer twoRUN-065 · 懸衡's recompute: the true overlap times reproduce; 101, 103 and 104 have no single provenance (NOT AS STATED · PASS)
PreviousBCODR-LUC-02 · Atomic cut and structural recomposition · Atomic Cut and Structural Recomposition: the First Cut, Separation and Recomposition of the Root-6217 Bidirectional Information Field — From Coarse Arrival Cells to a Seven-Class Bidirectional Interaction Spine
NextBCODR-LUC-04 · Tangent decomposition of the overlap germ · 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

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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