[navinor]

Result (scoped finite; no new kappa)

One new complete call type added to the frozen universal-connector alphabet of research/universal-connector-boundary (#943, Ross Richardson):

DUO_{j,k}: z += B_j x_j + B_k x_k     (j != k; one dispatch, sources read-only)

The only changed premise is that package's "no combined queries" rule, and the call is charged in full (two coefficient/source traversals, one target update cycle, one dispatch/entry-exit frame/head return). Everything else is unchanged: complete calls, arbitrary dirty rows, restoration of z and all scratch, paired A_i readouts, generic admissible operators.

Exact finite result. In the extended alphabet the five-source universal source word has unique Pareto profile (k calls, W toggle-adds) = (10, 12), versus (12, 12) in the frozen singleton alphabet. For the frozen all-31-row batch this is 72 root queries at 74 toggle-adds instead of 74 at 74: the support bound 72, unattainable in the singleton alphabet, is attained exactly here. In the price model c_B = o + p, c_DUO = o + 2p, c_A = o + p the completed batch costs 72o + 74p against the frozen 74o + 74p — strictly better for every o > 0, with total adds unchanged (the saving is exactly two per-call overheads o).

Lower bounds are complete for the domain, not heuristic: k >= 10 because a complete census of all 7,888,725 nine-point sets of F2^5 finds zero difference covers (C(s,2) >= 31 forces s >= 9, k >= s), and W >= 12 by touch parity (W even, W >= 10; W = 10 leaves only the all-unit k = 10 words — the frozen 945 pairings, reproduced here with maximum coverage 31 of 32 — or k <= 9 words that need the nonexistent s <= 9 covers). The witness steps 1,2,8,18,12,16,1,2,4,2, prefixes 0,1,3,11,25,21,5,4,6,2,0 attains (10, 12), so it is Pareto-optimal. Tiny falsifying instance first: n=3 profile (5, 6) against (6, 6); n=4 side row (6, 8) against (8, 8).

Task card

Selector nonce bf263697e6c72cee43b6ded62be24c62, track recursive-interfaces, card connector-alphabet-change (scope key ff4f5113ed2256ab19ed), scope refined: the card asked for "one additional operation and a small source count for its first counterexample" without naming the operation; the operation is fixed to the two-source combined toggle and the domains to n=3 (falsification first) then n=5 (the frozen priced instance). Full card: notes/agent-18-duo-toggle-task-card.md. Base commit bce54fb3f895cbe5cd4c0eb477c3afeed100190f; head 892b28a3358b16c9083036f71e1ef505ccf5d20a. Claim thread: #1403.

Evidence and reproduction

python3 scripts/research_package.py --package research/duo-toggle-connector --check-only
# PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 scripts/research_package.py --package research/duo-toggle-connector
# PASS_REGISTERED_RESEARCH_PACKAGE research/duo-toggle-connector outcome=completed

Coverage: deterministic regeneration of CERTIFICATE.json (counts, histograms, sorted-record SHA256, witness words, the full 72-call batch word, pricing records); code-disjoint independent checks — brute-force s = 9 scan of 7,888,725 sets expecting 0 full covers, the n=3 frontier by a second enumeration, the frozen 945-pairing control by restricted-growth words (histogram matches research/universal-connector-boundary exactly); symbolic replay of the emitted batch word; 12 dense dirty replays at L = 1, 2, 3 with seeded random noncommuting matrices and arbitrary dirty connector/output rows (forward and reverse order), checking restoration and all 31 output rows; 4 mutation controls (deleted call, shrunk DUO, misplaced readout, tampered record) all detected. Python 3.12/3.13, standard library only.

python3 -B -m unittest discover -s tests -p 'test_research_*.py' on this Windows machine: 18/20 pass; the 5-then-1 errors are pre-existing and outside this diff — the fixture byte-compare breaks on core.autocrlf=true (fixture stores CRLF, git object LF) and test_dependency_plan_and_runtime_failure hits os.killpg, which does not exist on Windows. With core.autocrlf neutralized only the killpg test still fails.

Limitations and obligations not checked

No physical supplier instance of this connector interface exists (the predecessor's own limitation, unchanged here); no compiler/tape integration, frames, owner admission, precision or outer analytic obligations; no proof assistant; no weighted global optimum beyond this price model. Words with k >= 11 are outside the census and cannot beat already Pareto-minimal (10, 12). The 99,200-cover histogram ((10,12): 8,500, (10,14): 47,600, (10,16): 26,600, (10,18): 3,700) is generate.py's claim with a recorded hash; the headline witness and both lower bounds are independently re-checked. The saving is exactly two per-call overheads: with zero per-call overhead the extension gains nothing.

Overlap (refreshed at submission, 2026-10-14T02:19Z)

Complete pagination over 773 open PRs and 199 discussions. No PR or claim duplicates the read-only weight-2 combined toggle; later neighbors explicitly scope away from it: the atomic triple-sum connector (#1504, #1518), the second-dirty-root construction (#1412), and the S3 vector transport (#1467). Distinct from the mutable-source shear mechanism (#1340, #1370, discussion 1352), which needs temporarily writable source rows, and from the same-alphabet extension #1185 (f(6) = 16). No matches is not proof of novelty.

Credit

Predecessor: Ross Richardson's research/universal-connector-boundary (#943 / #934) — interface, prefix reduction, 945-pairing control and cost recurrence, all reused and reproduced as a control here. Comparison credit: Arham Tahir's mutable-source shear mechanism (#1340, #1370, discussion 1352). Prepared by Navinor with help from opencode. Apache-2.0; no frozen source, upstream file or selected record is changed.

Workflow feedback (optional thread content)

Task/revision: connector-alphabet-change, priority revision 2. Outcome: one scoped finite construction with a complete exclusion. Biggest friction: the package's unit-test fixtures fail on Windows (core.autocrlf byte compare; os.killpg in the timeout path), which costs diagnosis time every session; one concrete improvement would be newline-agnostic fixture compares and a Windows kill fallback in scripts/research_package.py.

[Mister-Meeseeks]

Batch review at 892b28a3358b16c9083036f71e1ef505ccf5d20a.

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

Reviewed scope: Complete regenerated pair-difference cover census excludes the specified lower DUO tariffs and attains the ten-call twelve-application witness. Both generation and downstream verification pass; the result remains a restricted operation-alphabet floor.

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.