Research: persist order-four boundary across two root echoes (no new kappa)

[1337isnot1337]

Status: scoped recursive-interface construction. No new kappa or selected-supplier change.

At exact base bce54fb3f895cbe5cd4c0eb477c3afeed100190f, OS seed 57 selected the recursive-interfaces track. For two identical five-child PR #1391 root echoes on the same source X, a joint ten-child dirty echo carries the order-four frame through the midpoint.

• Complete joint word: (1720 ADD, 184 NEG) = 1904 primitives.
• Two separate calls: (1840 ADD, 176 NEG) = 2016 primitives.
• Net: 112 fewer primitives and 232 fewer data reads; 8 more NEGs.
• Exact phase-path minimum: g(5)=140 and g(10)=248, with all 1,024 and 1,048,576 paths exhaustively checked.
• Both constructions implement (D,X,W) -> (D + 2 sum_i R_i X, X, W) for arbitrary dirty input vectors, checked on all 56 basis columns.
• Prefix row-L1 peak grows from 30 to 42; no precision benefit is claimed.

The standalone package is research/z4-persistent-pair-seed57/. Reproduce with:

python3 -I -O -B research/z4-persistent-pair-seed57/verify.py

Local verifier, focused tests, package metadata/source pins, and make selected-record-check pass on CPython 3.14.7. Python 3.12 is unavailable locally, so the registered Python 3.12 replay, hosted CI, and independent human review remain pending. VALIDATION.json records exact checks.

The predecessor certificate/verifier/README are byte-pinned to PR #1391 head 6ce8017e4c27c8b220b6c3a27a53bb18f138212a; inherited source pins are checked at the stated base. Credit PR #1391, Ross Richardson's PR #1287, and Sagar Thakrar's PR #1227. Prepared by Cinna Davis with substantial OpenAI Codex assistance; no proof-assistant formalization or human review is claimed. The result is restricted to the pinned family, same source, and declared order-four macro alphabet. Supplier admission, precision, routing/tape costs, recursive-profile transfer, and any new kappa remain open.

[Mister-Meeseeks]

100-PR batch review at 5b1c00b9f2770aabaa0085539405757f7818a14a.

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

Reviewed scope: Persistent order-four phase across two same-source echoes: complete ten-child word saves 112 primitives, with exhaustive 1,048,576-path comparison and all dirty columns. Increased prefix norm and absent physical supplier prevent precision/runtime or κ claims.

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.