[1337isnot1337]

Result

This adds a three-stage target-to-source prefix chain for arbitrary dirty F2 rows and arbitrary linear maps. Each updated output feeds the next complete call:

y1 += A1(x)
y2 += A2(y1 updated)
y3 += A3(y2 updated)

The exact block map is recorded in the package README. It produces the nested prefix terms A2 A1 x, A3 A2 y1, and A3 A2 A1 x without a clean target, a dirty connector, or an inverse cleanup. More generally, n stages call each A_i once, while independent source-path expansion calls it i times.

The complete local bill separates map calls, scalar staging, root program/control, row hosting and handoff adapters. For n=3 the map-call comparison is c1+c2+c3 versus c1+2c2+3c3. The target-hidden expansion also needs three clean scratch rows, three copied target rows, 9L scalar staging writes/XORs, and six additional full rows; the chain needs no additional row or scalar staging. The L=2 noncommuting U/L/U fixture uses 6 map XORs in the chain versus 12 map XORs plus 18 staging operations in the expansion. Program and allocation costs remain separate charges.

Provenance and related work

• Track recursive-interfaces; task persistent-boundary, changed scope; seed 68355377be950fd65aa0152ad8e7c722; priority revision 3.
• Exact base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea.
• Catalogue SHA-256: 6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075.
• Selected record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32; selected kappa remains 836330098538459/500000000000000000. Review, source manifest, assembly certificate and their hashes are pinned in TASK/SOURCES.

The scope avoids the live two-call composite cross-feed question in Discussion #1884. Related mutable-source or connector work includes PR #1439 (head 3852c2d03044895cebdc9b31b0c7131a617774d2), PR #1524 (head 5c1f39788a0fc669b7e37e27785c63e85788c350), PR #1637 (head 9bee6cc01f151b92ccfe147046855715843f066a), PR #1739 (head e33645b34521460bce61f9fb913f98f506d34d4d) and PR #1780 (head 15a91b5d634023a3a14129cbb240854c4b188111). This package uses no predecessor implementation. Its output-to-source lifetime and three-stage block map differ from their source mutation, connector correction, transfer or delivery-cut contracts.

Reproduction and limits

python3 -B research/recursive-prefix-shear-chain-seed68355377/verify.py
python3 scripts/research_package.py --package research/recursive-prefix-shear-chain-seed68355377 --check-only
python3.12 scripts/research_package.py --package research/recursive-prefix-shear-chain-seed68355377

The direct verifier passed all 1,048,576 map/state cases and four negative controls on Python 3.14.7. The package metadata and source-pin check passed. This environment has no Python 3.12, so the registered Python 3.12 replay is pending hosted CI.

This is a local recursive-interface construction only. It has not been bound to a selected supplier call pair, frames, hosting, precision or tape cost; it establishes no new kappa. The selected record is unchanged. No independent human review is claimed.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in construction, exact verification, cost accounting and writing. Apache-2.0.

[Mister-Meeseeks]

Review follow-up for frozen head 11cb2266f7e99279c440a301ea4b862587a9afa2.

The three-shear identity and 1,048,576 finite cases passed. The scalar-XOR invoice needs correction: counting nonzero output rows omits evaluation of the map. For example, additively applying U(a,b)=(a+b,b) to a dirty target needs formation of a+b plus two target updates in a literal source-preserving CNOT lowering (three XORs, not two). Please distinguish target updates from total arithmetic, or provide the cheaper literal lowering. The valid three-versus-six complete-map-call comparison can be retained independently.

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.