[Clear1nsight]

Change and mathematical scope

Proves one conditional completed ordinary API implication: the A0 supplier from #4760 has the type needed at the first A0→A1 backend edge in #4814, given the explicit P1–P3 native/compiler, older-backend/routing, recurrence/reserve and physical implementation premises. The actual helper 462 / frame 506 witness preserves rank 4f, complete spectators and restored ROW, with both matcher routes charged.

This closes a conditional composition question. It does not implement the full primitive API, promote actual_backend_API_independently_verified, change a native invoice, complete a multiplication caller or claim a new κ. The selected record remains unchanged.

Task and overlap

This is the donor-refined supplier-boundary-audit tracked in Discussion #4945. The frozen base is cef4b52f2a59009865bf8eabde1be3f159063703; source #4760 is ecdfcabd56dfa663ae020733f9f1a88c6644743c and #4814 is f56ae4533a7d97d782a2c596a33fe844cd051747. Both source commits are canonical ancestors. A later main refresh to b91956876e5b4122fd89179f1b57557ff8378f15 found no changes to the relevant guidance, priorities or selected record.

The contribution adds a source-bound interface proof and separate operator and written reviews to #4814's existing arithmetic. It retains the historical #185 / #199 / #204 bootstrap credit. The CRT threshold and placement questions in #4942 / #4944 are neighbouring obligations. This package does not audit the historical #4088 dispatch or #4100.

Validation

Exact submitted head: 3ab584de66a9220007963c7bd476241137a263c9.

Run python3 scripts/research_package.py --package research/bit-completed-backend-api. All six registered normal and optimized commands pass. The author study checks 22 fixtures, 384 basis columns and seven rejecting controls. The independent checker replays 21,988 source records, all 658 Boolean source columns, 436 exact signed helper rows and nine owned COPY episodes; it separately reconstructs the projector, matchers, basis columns and elementary-factor product. A second reviewer checks the all-width conditional argument, noncircularity, nested ROW borrowing, padding and ledger.

For the selected eight-dimensional matcher pair, the derived bill is 80 completed ordinary chunk interchanges, 80 fixed unit scalings, 224 linear shifts, at most 128 carry shifts and two low-type permutations. Larger fixed compiler dimensions need their own finite constants. Finite fixtures corroborate the written argument; they do not execute an astronomical physical template.

The package preserves all 52 frozen science, proposal, control-history and review files byte for byte. Two initially weak controls were corrected, with their original snapshots retained. The portable wrapper replaces only one authenticated Git byte-reader in memory. Source-history and committed-input checks pass for all 65 module files. Official export SHA-256 is a7d6ba0f92edfc744db8ed4926afd9eed28711fc892fe91072144a85bc0beb82; all six exported commands pass read-only without Git, and normal/optimized outputs match. Exact-head hosted run 39898684344 passed: 362 helper tests / 11 expected skips, all six registered normal/optimized modes and the committed-input mutation gate. The outcome remains partial, with primitive_API_admitted=false and new_kappa=false.

The full primitive ROW, native compiler, routing/tape, precision, analytic and outer hypotheses remain unproved here. The registered outcome is partial. Independent reviews are separate computational and written reviews, not formal-kernel or human acceptance.

Credit

Credit ai-nanachi's #4760 / #4814 / #4326; rohanarun's #185 / #199 and Maxime Fleury's #204; Cinna Davis / 1337isnot1337, zxv, Jacob Alan Sussman, Mark / Matarener's #4697 / #4612, and the retained native, E8, ordinary, ROW, stock, weighted-leaf, delayed-cover, precision, tape and outer lineage. Chris R / Clear1nsight used separate construction, source/operator-review, written-review and packaging agents with substantial OpenAI Codex assistance. Apache-2.0.

Open next questions

Supply one literal source-bound physical stock/owner/route generator for a fixed N-dimensional invocation satisfying P1–P3, including restored ROW and the finite route, fallback, tape and precision ledger. That is the next missing implementation obligation. Another root calculation or local fixture cannot discharge it. The package's README and TASK retain the first step, scope and blockers. The public handoff links this exact head and states the remaining implementation obligation.