Research construction: exact factor schedules save 26 R420 XORs (no new kappa)

[yzhouwang]

Change and mathematical scope

This finite bit-circuit construction reduces block 7 of the selected PR543 R420 word from 41 to 28 XORs. Its required literal reverse cleanup saves thirteen more, reducing complete native ADDs 26,916 → 26,890. No new κ is claimed.

An exact subset-state search certifies minima 14 + 14 for the two fixed twelve-wire integer factors, among schedules that finish each destination in one contiguous positive-addition batch. The verifier independently enumerates donor subsets using base-16 integer sums and checks every potential inequality: 8,192 states, 49,152 state/destination pairs, 43,520 feasible transitions. This is a scoped finite-class optimum, not unrestricted XOR optimality.

The forward integer map is identical and the reverse positive map is entrywise dominated. All arbitrary inputs, per-register frame paths, 420 helpers, nine copies, literal H1–H5 interface and paid rank mass 5,112 are preserved. The reverse prefix falls 2,270,064 → 2,205,308; the local payload allowance stays 100 bits. Every preparation, read and cleanup is charged. The paid recursive profile and selected κ remain unchanged.

Only research/r420-block7-exact-schedule/ is added: circuit, complete potentials, independent certificate replay, source pins, proof, native checks, validation and local claim. upstream/, selected sources and frontier are unchanged.

Validation

python3 -I -B research/r420-block7-exact-schedule/verify.py

Expected: PASS_R420_BLOCK7_EXACT_SCHEDULE factors=17+24->14+14 ADDs=26916->26890 states=8192 columns=660 controls=8 kappa=unchanged.

• All 4,096 block inputs and 660 dirty-input columns; exact E8/frame checks; eight mathematical/interface/accounting controls.
• Fresh unchanged C++17/Boost legality and 5/9/11-stage replay on both words: 900/1,380/1,620 columns and 96 bridge-omission controls. Exact native prefix bills agree with Python.
• Python 3.9.6 and 3.14.5, isolated optimized execution, byte-identical nomination, minimal relocated source tree, source/certificate/receipt corruption and output-preservation controls.
• Selected-record integrity and staged whitespace pass. A committed-files-only export replays and the patch applies cleanly. A bootstrap-created Python cache initially tripped the selected inventory; it was removed and bytecode writes are now suppressed. No selected source bytes changed.

Optional native command: python3 -I -B research/r420-block7-exact-schedule/native.py --out /absolute/fresh/directory.

No repository-wide suite, hosted-parent/invoice/outer assembly, selected cold replay, Linux CI, Lean or runtime result is claimed. All-size/compiler/common-label/mutable-basis/hosting/residual/precision/tape/exact-recovery/analytic obligations remain. Finite replay is not a proof of the full multiplication theorem.

Pins, overlap and attribution

Exact base: 66849e1. PR543: 2065fe4; consuming PR626: 660de89. Git confirms the original word's blob matches PR543. OS-random seed 17, bit-supplier track, selects block 7. No pinned coordination issue existed; the claim is local.

Credit eumemic's PR543/493, Dylan Crow's exporter/checker lineage, DreamingOfClouds, Zhihao Chen, chafreaky, DaysSky and retained predecessor notices. Concurrent #670/#674 change blocks 3/5, #691 changes quad 13, #681 integrates those circuits, and #754 synthesizes cleanup windows. Refresh through #786 found no block-7/fixed-factor schedule certificate; #774 forests and #782 lattice parity are distinct. No pending implementation is imported or assumed composable. Elementary dynamic programming is not claimed as a new technique.

Prepared by Yuzhou Wang (@yzhouwang) with substantial OpenAI Codex assistance in derivation, implementation, verification and writing. Apache-2.0. No delegated workers or independent human review.

[Mister-Meeseeks]

100-PR batch review at d1634f3b316f2c3a1bb5f93a6117c8ebab9ab011.

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

Reviewed scope: Block 7 two-factor restricted exact schedules save 26 native XORs; shortest-path potentials and complete arbitrary-input replay.

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.