[thakrarsagar]

PR3147's centre block-repair argument uses a false triangle lower bound: on a genuine nine-point C4-free cubic incidence graph it gives 30 triangles, while the graph has 27. This package binds the exact offending expression, supplies the counterexample, and replaces the affected argument with a sharp local path-counting theorem.

The repaired result is stronger: a nonzero common-kernel perturbation in the inherited selected PR1094 calls 0/4 observation model needs at least 15 source owners. Every repair block of at most 14 owners therefore still needs exactly 104|B| scalar linear observations for the whole later-query field. The abstract graph floor of 15 is attained by the duad/perfect-matching incidence, without claiming a physical route labeling.

The proof uses |B| >= 5*degree(d) - six_cycles_through(d), the actual braid capacities, and a cubic divisibility obstruction at 14. It replaces the faulty degree-partition triangle argument. The native interpretation retains the predecessor's common-frame, constant-endpoint and source-adapter assumptions.

Validation: registered CPython 3.12.15 replay; exact census of 1,379,952 reduced route triples; all 227,920 scalar column triples (896 dependent, braid histogram 846/50); independent literal-walk checker; seven behavioral groups including 1,096 small graphs, missing graph hypotheses, malformed relators, and scientific/excerpt source corruption. Metadata, source pins, whitespace and all 14 committed publication/input files pass. The source prose's reported 229,936 port triples is also corrected to C(112,3)=227,920.

This answers the released PR3168 handoff; canonical claim and result. Credit dcharb78/PR3147, Gonzalo Mier/PR3097, Sudarsh3301/PR3168, Ross Richardson/PR3071, Aaron Wang/navinor, ywz65 and the retained selected-source lineage. Developed with substantial OpenAI Codex assistance.

No selected-frontier or frozen-source change. Physical 15-owner realization, changed/nonlinear observation interfaces, complete supplier costs, native adapter refinement and the selected cold replay remain outside this proof. Open next questions are in the package. Canonical main and fork were synchronized; the branch is rebased on 463113d675af7410ac91d53a4fed51ec6494eb9a.