Research: fuse aligned FANIN4 coefficient stream

[1337isnot1337]

Result

This package constructs one physically scheduled FANIN4 connector update in the aligned coefficient frame of F2[C2^2]. Four arbitrary read-only source vectors and an arbitrary dirty target are updated in one synchronized pass. The per-coefficient arithmetic remains four XORs; the saving is in data traffic and complete head returns.

At L=4, the singleton sequence has 32 reads, 16 writes, 16 XORs, 64 head moves, four call records, four source-reference fields and four target-reference fields. FANIN4 has 20 reads, four writes, 16 XORs, 40 head moves, one call record, four source references and one target reference. Both use no scratch and return every head. Equal unit prices on all listed resources yield a local saving of 54. For variable record prices, the exact difference is recorded in PROOF.md; external opcode-table or source-frame conversion expense must be subtracted.

The verifier checks all 1,048,576 dirty states at L=4, the forward/inverse identity, the resource vectors, four omitted-source controls, and an omitted-return control.

Scope

This is a local connector-stream construction, not a complete 63-mask path, a selected supplier admission, or a kappa change. The sources are already aligned and use identity maps. No full multiplication-theorem claim is made.

The task began from recursive-interfaces / connector-alphabet-change, seed 9983a6144fbaa6291d717b9b2076e816, with the scope refined from abstract call counts to one explicit physical stream schedule. Base: 0fdd7d8; priority revision 4; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Sources and relation to prior work

PR #2128 supplies the two-source DUO connector construction and leaves physical supplier realization open. Cycle 43 PR #2249 gives the scoped six-source high-arity query/addition floor at full per-tap price; this package retains all four source XORs and prices stream traffic. PRs #2171 and #2207 supply adjacent ordered single-source controlled-stream and fallback work; no predecessor code is imported.

Replay

python3 -I -B research/fanin4-aligned-source-stream-seed9983a614/verify.py
python3 -B scripts/research_package.py --package research/fanin4-aligned-source-stream-seed9983a614 --check-only

Local verification: CPython 3.14.7 passed both commands. Python 3.12 is not installed locally; the registered Python 3.12 replay remains for CI. No hosted check is claimed here.

Prepared by Cinna Davis with substantial OpenAI Codex assistance.