Research: six-call GF(4) scalar-source connector for all two-source rows

[1337isnot1337]

Result

Adds a charged single-source scalar update S(j,a): z += a B_j x_j for a = w,w^2 over GF(4)=F2[w]/(w^2+w+1). For exactly two read-only sources and the 15 nonzero coefficient rows of GF(4)^2, one dirty connector path uses six complete source calls, the minimum possible, and 30 complete target readouts. It restores arbitrary connector dirt and uses no extra helper or source copy.

The six prefix points have all 15 distinct pairwise differences. The lower bound is binom(k,2) >= 15, since a closed k-event path has at most k distinct prefix points. Each target gets two A_r readouts at its certified boundary pair; characteristic two cancels the arbitrary dirty connector term.

The complete parametric bill compares this shared path with an explicit per-target schedule under the same added alphabet:

• source map calls: 6 versus 48;
• nonunit GF(4) scalar work: 4L versus 32L bitwise XORs;
• prefix-coded event storage: 174 versus 342 bits.

With c_Bj the fully charged unit-coefficient source event price (map child, source access, connector update, dispatch, frame/head travel, and scratch restoration), and beta the descriptor-bit price, the saving is 21(c_B0+c_B1) + 28L + 168 beta; both schedules use the same 30 complete A_r calls and common interpreter bill. The full model and literal event stream are in the package. No supplier admission or new kappa is claimed.

Verification

Locally on CPython 3.14.7:

PASS_GF4_SCALAR_SOURCE_CONNECTOR targets=15 source_calls=6 minimum=6 readouts=30 short_closed_words=594 max_short_cover=7 dirty_cases=245760 scalar_ops=4_vs_32 descriptor_bits=174_vs_342 controls=3
PASS_GF4_SCALAR_CONNECTOR_INDEPENDENT rows=15 pair_differences=15 dirty_states=245760 omitted_source_and_misplaced_read_controls=2
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)

The original connector baseline also passed: PASS_UNIVERSAL_CONNECTOR_BOUNDARY pairings=945 max_coverage=31 queries=74 leaves=182. Python 3.12 is not installed locally; the registered Python 3.12 replay is enabled in VERIFY.json for CI. No hosted pass is claimed in advance.

Pins and scope

• Seed: a472dd8c6aee62b83f9dbc2e489790b0; track/task: recursive-interfaces / connector-alphabet-change; priority revision 4.
• Exact base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.
• Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Package: research/gf4-scalar-source-connector-seeda472dd8c/.
• Live scope claim: Discussion #2262.

The latest overlap refresh at 2026-10-15 02:48 UTC covered 490 open PRs and 974 discussion/comment/reply records with complete pagination and no warnings. The closest new result, PR #2259, bundles four aligned F2[C2^2] source contributions into one physical event for one target and saves traffic/head returns. This contribution keeps one source per event, works over GF(4) on two sources and all 15 coefficient rows, and reduces repeated recursive source-map calls with a six-point difference cover. The mechanisms, domains, and charged cost terms differ. Other nearest connector work (#1518, #1531, #2128, #2146, #2249) is discussed in README.md.

Prepared by OpenAI Codex with substantial AI assistance. The selected frontier and frozen sources are unchanged.