Price address negations in uniform signed SWAP words

[ywz65]

In the uniform integer-address SWAP model, mod2 crossing cuts miss address signs. This package adds a separate determinant-sheet charge and proves the exact tariff for any mixture of signed anti-diagonal targets, with arbitrary free scalar mixing and restored dirty spectators:

r*(2*min(A,B)+max(A,B)) + t*C, where t targets have determinant -1, A/B price the two signed shear orientations, and C prices either address-coordinate NEG.

The mod2 ADD inequalities are inherited from PR2544 at 9fb1552f12ca4777ca660461a8b602e709285f99, which credits Aaron Wang's PR2444 handoff and Ross Richardson's PR1989/PR2415 crossing bound. The new obligation is n_NEG>=t; a two-sheet rank cut counts each target even when their overall determinant parity cancels. Exact integer three-shear words, with one NEG for each determinant-negative target, attain all charges together.

The proof is for complete formal F2[GL2(Z)] identities, equivalently fixed words on full integer streams or an unbounded family of moduli. It explicitly does not establish the lower bound for separately optimized words at one finite modulus: at M=2 three shears already swap coordinates. No native compiler, recursive supplier, physical tape cost or selected exponent is claimed.

Validation: native Python 3.12.7 registered replay and native 3.14.5 direct optimized replay pass. The verifier checks 930 rank-one factors, 1,364 full formal attaining endpoints, 42,625 rational tariffs and 720 mixed prefixes. Mathematical controls include a formal perturbation invisible to all quotient cuts, omitted signs, finite-modulus failure, negative-price loops and changed higher-rank units. Six export/evidence tests reject source and typed-receipt drift and verify read-only Git-free replay. A separate AI reviewer checks the proof and independent matrix calculations; the review receipt binds the submitted files.

Reproduce: python3 scripts/research_package.py --package research/integer-address-signed-swap. Current canonical main and source2544 remain unchanged at submission; recent open PR bodies/source comments were checked. The complete cached Discussion snapshot is older, as disclosed in TASK.json; overlap search is not proof of novelty. Advance claim.

Prepared by ywz65 with substantial OpenAI Codex assistance, including separate AI review. Predecessor attribution is retained. Hosted CI, human review and proof-assistant formalization are not asserted.