Research: fixed-port two-projection connector with 10 frame XORs

[1337isnot1337]

Result

This adds research/two-projection-connector-seed51a5/, an exact fixed-port construction for the universal five-source F2 connector. It keeps every inherited B_j and A_m child call at physical helper row z0, adds one arbitrary dirty helper row, and permits paid transitions among invertible two-row frames.

Use source word [0,1,0,1,2,3,4,2,4,3]. Sources 0, 1, 2 and 4 inject along logical direction (1,0); source 3 injects along (1,1). Readouts use covectors (1,0) and (1,1). The corresponding prefix difference sets have sizes 26 and 16, and their union covers all 32 masks. EXPECTED.json gives one pair of readout boundaries for each of the 31 nonzero masks.

The complete-call lower bound in this interface is 10 source calls plus 62 output readouts, or 72 calls. The schedule meets it. The exact 945-by-32 word/direction census finds 175 covers using only these two projections. An exact six-frame dynamic program finds a 10-full-row-XOR schedule for the pinned readout pairs. This is not a minimization over alternative boundary-pair tables.

Charged budget

The pinned one-row certificate prices B0..B4 at [1,4,10,16,28] rank-one children and each output readout at one. The new schedule uses each B twice and each A twice, for 180 children. The current one-row five_extra_output schedule uses 10 B and 64 A calls for 182 children. Open PR #1770 reports 182 as the exact weighted optimum in the one-row alphabet.

The frame schedule adds 10 full-row XORs, or 10*L bitwise XORs on length-L rows, and one extra length-L dirty helper. Independently conjugating each framed call would cost 28 row XORs; the global schedule reuses frames. If a rank-one child costs P(L) and a full-row XOR costs X(L), the local difference is -2*P(L) + 10*X(L), plus the helper row. This is a conditional interface result; no finite-size runtime gain, selected-supplier occurrence, or new kappa is claimed.

Scope and overlap

Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; accepted seed: 51a5e88d2c6fe1d9dc43f025b20473e1; track recursive-interfaces, priority revision 3; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

The accepted maintainer-reviewed conditional finite construction remains complex-binding at 836330098538459/500000000000000000. Its review, source manifest and assembly certificate are pinned as provenance; none is changed.

A final cached overlap refresh covered 541 open PRs (fetched 2026-10-14T13:19:48Z) and 524 Discussion records (fetched 13:18:04Z), with complete pagination. Exact two-projection/fixed-port terms found no remote match; the cache warns live state may have changed. Immediately refreshed heads of nearby open work remain distinct: #1531 adds DUO and obtains 72 dispatches at 74 toggle-adds; #1770 optimizes the one-row weighted cost; #1812 obtains 72 calls with eight one-way transfers while allowing B/A calls to select either root. This PR keeps all B/A calls at physical z0 and uses both paid shear directions in a persistent frame. The contracts differ, and no cost dominance over the port-selectable construction is claimed without a port-access and row-XOR tariff.

Verification

• python3 -I -O -B research/two-projection-connector-seed51a5/verify.py — passes the 945-by-32 census, all 31 arbitrary-dirty output maps, helper restoration, shortest fixed-boundary frame schedule, 180-child invoice, and four negative controls.
• python3 -B scripts/research_package.py --package research/two-projection-connector-seed51a5 --check-only — PASS_PACKAGE_METADATA_AND_PINS.
• CPython 3.14.7 was used locally. The registered runner requires Python 3.12, which is unavailable here; the Python 3.12 replay and repository-wide CI were not run. The selected-result reproduction was not rerun because the selected assembly is unchanged.

Attribution

The fixed one-row connector predecessor is Ross Richardson's PR #943. PRs #1531, #1770, #1811 and #1812 are credited for the nearby but different mechanisms above. This package adds no predecessor code. Prepared by Cinna Davis with substantial OpenAI Codex assistance; new work is Apache-2.0 under the repository license.

Coordination claim: Discussion #1167 comment.

[Mister-Meeseeks]

Batch review at 025d4fcd87f1b6ea01aa1c52721f8f46389aacce.

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

Reviewed scope: Fixed-port two-helper construction uses72 complete map calls,180 inherited rank-one children and10 paid row XORs. Literal dirty-state replay,30240 bounded candidates and fixed-boundary GL2 shortest-path schedule checked. Two-child advantage is conditional on additional helper/frame tariff and selected placement remains open.

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.