Construction: five plane queries for selected P111 bit decoder (no new kappa)

[1337isnot1337]

Contribution

This adds an exact five-plane factorization of the selected PR589 P111 bit decoder. It acts on the full 111-port decoder boundary and uses an explicit 9-to-10 Parseval frame over F2. The frame transforms both the decoder's source and target factors, so the complete scatter map is preserved.

The selected nine line queries have exact rational B14 copy charge 63 (nine rank-7 terms). The five plane queries each have rank 8, for copy charge 40. The construction also charges ten basis-change ADDs. The verifier compares the original and plane decoder maps on all 661 formal input columns, including dirty targets and helpers, and checks the B0 identity on all 111-by-111 source-target pairs.

The candidate replacement law is paid mass = (64 - 2)W + 40, with W = 888/9 = 296/3. Its exact local profile has mass 5116 and idle mass 3124/3. Under the pinned R=42 guard, the favorable ceiling is a <= 8520849563/10^12; at a=1/99 the relaxation is already greater than one. The favorable profile omits physical plane routes, temporary cleanup, hosting and precision costs, so it is a mechanism-level screen only.

Provenance

• Track recursive-interfaces; seed ceccc7658dd89c833863007fb63ad7b2; task coverage-law-change; priority revision 3.
• Exact base 0b1cccf86e2f5132ed286a26ef0a681a495740ea.
• Selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Pinned bit word SHA-256 e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f.
• Claim and predecessor context: Discussion #1587, selected complex paired-plane PR #1825, merged bit word PRs Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589/Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555, and line-decoder package PR Research: bit E8 decoder witness and 9/17 pairing-cost floor #1084.

Reproduction and status

python3 -B research/bit-p111-parseval-plane-decoder-seedceccc765/verify.py
python3 scripts/research_package.py --package research/bit-p111-parseval-plane-decoder-seedceccc765 --check-only
python3.12 scripts/research_package.py --package research/bit-p111-parseval-plane-decoder-seedceccc765

Local evidence: PASS_BIT_P111_PARSEVAL_PLANE_DECODER on Python 3.14.7 and PASS_PACKAGE_METADATA_AND_PINS. This environment has no Python 3.12, so the registered Python 3.12 replay remains for CI.

This is not a physical bit supplier and does not establish a new selected bound or kappa. The selected result remains unchanged. Open obligations are plane-frame routes, streamed schedule and cleanup, owner hosting, precision/tape, and joint assembly with the complex side.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in construction, exact arithmetic, verification and writing. No independent human review is claimed. New work is Apache-2.0.

[Mister-Meeseeks]

Review follow-up for frozen head 9a891c9cb25b15f5a189bcad1d022198adeaf885.

The binary Parseval identity, rank-two factors and full dirty-column replay passed. The claimed 40-copy invoice and unpaid=2 rule require an additional block-copy/physical-plane interface, not just regrouping scalar factors by support-union rank. The independently replayed #1936 audit finds scalar minimum 73 over all 2,560 fixed-block term subsets, versus the union-rank total 40. Please label the proposed invoice as conditional on that missing interface or supply its complete operator/endpoint proof. The valid decoder identity is worth retaining separately.

Recorded scope, attribution and execution evidence. We are leaving this open with the outstanding work recorded; previously completed checks remain credited. Thank you for the contribution.