[1337isnot1337]

Gareth Davidson's retained PR952 R439 quad17 circuit already attains the exact minimum of 12 positive ADDs for its six-register integer transfer. This contribution certifies that minimum and proves its reverse positive envelope equals the entrywise absolute inverse, so it is the smallest valid endpoint envelope for every independent incoming coordinate budget. Scoped negative result; no new kappa or supplier adoption.

Two separately implemented complete searches remove gates from opposite ends. Each exhausts 9,739 states / 43,454 edges and counts 1,008,032 shortest ordered programs. Their independent row/column reverse censuses agree on all 57 matrices and multiplicities; the parent's matrix is the sole entrywise Pareto minimum, attained by 767,232 programs. The reverse-envelope floor also has a written algebraic proof covering all exact realizations of this fixed inverse.

Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. OS assignment seed 17, bit-supplier track. Actual input: PR952 head 11d24706f06e95271804c9438869546724c67aab, source-bound committed artifact, A[854:866], frame283, registers 312/355/412/429/434/490. Exact Git blob and SHA256 pins are in SOURCES.json. The selected result at the base is PR1094, conditional kappa 0.001672660197076918.

Reproduce from the repository root:

python3 -I -B research/r439-quad17-seed17/verify.py

Expected: PASS_R439_QUAD17 minimum=12 shortest_programs=1008032 reverse_endpoints=57 sharp_absolute_inverse controls=8 no_new_kappa.

Passed direct certificate replay, registered package metadata and replay, research baseline bindings, selected-record inventory/supplement checks, and diff whitespace checks. Eight controls reject gate deletion, noncommuting reorder, a Boolean-equivalent integer lift, a false minimum, an envelope below the inverse, both resource caps and a false path multiplicity. No complete supplier/native replay is claimed. A complete live overlap refresh covered 822 open PRs and 73 discussion/comment/reply records with no quad17/frame283 match; its coverage limits and the installed gh --slurp workaround are recorded in OVERLAP.json.

The gate minimum fixes the exact integer map, six labels and positive ADD alphabet; it excludes signed forward gates, other Boolean lifts, extra wires and free permutations. The envelope theorem fixes this inverse and independent coordinate budgets; it does not optimize full-word correlations or intermediate prefixes. The existing pair costs 12 forward plus 12 mandatory literal cleanup ADDs. Paid profiles, decoder costs, recursive children and the selected frontier are unchanged. All-size/compiler, realization, hosting, precision/tape, analytic and H1-H5 assumptions remain inherited.

Credit PR952/904 (Gareth Davidson), PR936/925 (Ross Richardson), frame272 PR1002 and frame281 (woklerx), earlier factorization/guard work, and the R439/PR589/selected construction lineage. This is new exact evidence about an existing construction, with none of its previous savings claimed anew. Prepared by Cinna Davis (@1337isnot1337) with substantial OpenAI Codex assistance; Apache-2.0; no independent human review claimed. The package includes concrete open next questions.

[Mister-Meeseeks]

100-PR batch review at becd4a2b6fad711914fe80f4344aef0008b30a28.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Exact twelve-positive-ADD minimum for the fixed six-register transfer, from complete acyclic row/column elimination graphs. Independent inverse-envelope optimum holds for that transfer and independent budgets; signed forward gates and altered lifts are outside scope.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.