Prove the exact pairing spectrum of every standard-coordinate Dn puncture

[ywz65]

For the standard-coordinate Gram decoder of any D_n root puncture, optimizing over every admissible binary pairing gives exact COPY cost 2e, where e is the number of represented coordinate edges. This answers PR #2272's pairing-minimization handoff (retained in #2518): all 1,023 D5 B0 ties stay optimal. The theorem also classifies every minimizer and gives the complete directed and symmetric cost generating functions.

The proof splits each coordinate support into singleton and opposite-sign 2x2 blocks; entries between disjoint edges are invisible to this fixed decoder. Arbitrary asymmetric pairings are included. Other factor bases, overcomplete decoders, physical compilation and the general T² law remain outside the claim. The predecessor B0 census and root model are credited to Aaron Wang and DreamingOfClouds, with exact source heads and hashes.

Validation: optimized CPython 3.12 registered replay passed, including all 117,648 relevant D4 pairing states; independent row-span rank checks; all 1,048,575 D5 B0 punctures; 360 varying directed pairings in D2–D10; assumption-breaking controls; Git-free unchanged export; receipt rejection and exclusive regeneration. Separate AI proof review found no actionable issue. No independent human review or CI result is claimed.

Base: current canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Original picker scope and justified handoff change are in TASK.json. Substantial OpenAI Codex assistance. No selected frontier or frozen evidence changed.