Research: an optimal 144-call seven-source sparse-mask connector

[commdata2338]

Change and mathematical scope

The seven-source connector handoff in PR #2236 left the 144-complete-call lower boundary unattained. This adds one 18-event closed source path covering all 63 masks of Hamming weight 1,2,3, with two readouts per target:18 B+126 A=144 complete calls.

The explicit source word is 0 1 2 3 1 0 4 2 0 5 1 4 1 6 5 0 3 6. Its profile is (4,4,2,2,2,2,2). The package supplies all 63 readout pairs, the literal 144-event stream, an all-dimension F2-linear proof, a free noncommutative root/leaf checker, arbitrary-dirty scratch checks and the full invoice. Separate stars use 434 complete calls; the construction saves 290 source calls, 1160 root descriptor bits and 290 root dispatches under the stated complete-call contract. The concrete composed-map fixture uses 984 primitive leaves instead of 2906.

This is a finite construction and scoped proof. Combined with Cinna Davis's credited, freshly replayed 14/16-event exclusions, it attains the unit-call minimum in the original one-root source-toggle/single-target alphabet. It is not a global weighted optimum or a supplier/κ claim. Only research/seven-source-18event-connector/ is added; inherited interfaces and selected artifacts remain unchanged.

Task and overlap

• Task ID / scope key: connector-alphabet-change / 9ba764a68e96fac776b5 (seven-source-weight123/18-singleton-events/144-call-attainment).
• Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; contribution commit 5a306ee4115848883ff297adbec59e81ab85f14b. Final canonical-main refresh 2026-10-15T07:03:12Z found no change, and main was rechecked unchanged at 07:25 UTC before submission; priority revision 4.
• Exact predecessors: PR Research: 16-event seven-source connector boundary (no new kappa) #2236 be03870d764e7875ea9a9f6cc69933c9b1a2456a; PR Seven-source sparse connector boundary at 14 toggles (no new kappa) #2229 b4eab83755969d406edba9f25b7890e4db4c4931. No pending code is imported. Main's Research: sharp four/five-source dirty-connector boundary (no new kappa) #943 interface inputs have exact Git-blob and SHA256 pins in SOURCES.json; predecessor replay files have exact hashes there too.
• Concrete object/question: arbitrary dirty F2 connector and targets, seven immutable source maps, all 63 weight 1/2/3 outputs; attain the first open complete-call boundary.
• Scope status: changed. This takes the live released handoff in Discussion #2221, retaining the alphabet and resolving its explicit 18-event next question. It is a declared side result rather than completion of the card's changed-operation gate.
• Restriction changed: the smaller 14/16-source-call domains become 18; no operation is granted free.
• Method/domain: bounded heuristic discovery in the two even 18-event profiles, followed by exact witness certification. Candidate discovery is not an exhaustive search or a negative result. The found (4,4,2,2,2,2,2) word is the only new construction claimed.
• Nearest overlap: Seven-source sparse connector boundary at 14 toggles (no new kappa) #2229/Research: 16-event seven-source connector boundary (no new kappa) #2236 supply smaller-path exclusions and the handoff; Research: prove four-root minimum for seven-source paired-call connectors #2282 treats all 127 masks with multiple roots; Exact exclusion for a six-source TRIO connector path #2146 treats six sources with TRIO calls. Added value is the requested attaining word and complete executable invoice. The original claim is in the canonical thread above.
• Optimistic complete budget: 18 B+126 A+954 stored root bits+144 dispatches, plus common admission/preparation and fully charged map implementation. The separate-star comparison is 308 B+126 A+2114 bits+434 dispatches. No physical conversion is silently granted.
• **Success/falsification/cap:**63/63 support, complete arbitrary-dirty boundary, scratch restored after every completed child, source-bound receipt and rejecting controls. Search capped at 25minutes within a 60-minute session; a miss would not establish impossibility. A witness was found after 89,042 candidate swaps.
• Artifact/reproduction: eight-file package, python3 -I -O -B research/seven-source-18event-connector/verify.py.

Pre-commit offline overlap used complete shared snapshots: 583 open PRs fetched 2026-10-15T06:55:23.240869+00:00 and 1111 Discussion records fetched 2026-10-15T06:57:32.010338+00:00. Queries included --task connector-alphabet-change and --all-terms 'seven-source' '144'. The final handoff recheck used 587 open PRs fetched 2026-10-15T07:07:38.026722+00:00 and 1116 Discussion records fetched 2026-10-15T07:09:50.407275+00:00, again with complete pagination and the same relevant matches. The matching new public claim was this investigation. Cached/offline coverage is not proof of novelty. Full task metadata and next questions are in TASK.json.

Validation

CPython 3.12.3, standard library, no third-party dependencies.

python3 -I -O -B research/seven-source-18event-connector/verify.py
python3 -I -O -B research/seven-source-18event-connector/test_verify.py
python3 -B scripts/research_package.py --package research/seven-source-18event-connector

All pass. Expected primary marker:

PASS_SEVEN_SOURCE_18EVENT masks=63 source_calls=18 target_calls=126 total=144 controls=10

Evidence: 63 prefix-pair checks plus 63 interval-XOR checks; 73 free arbitrary-input rows; forward and inverse root/leaf programs; 144 completed child boundaries; 438 forward and 438 inverse dense basis cases in dimensions 1–3; exact 984/2906 primitive-leaf and 144/434 complete-call invoices. Ten controls cover source restoration, root dirt, source/target map identity, noncommuting factor order, primitive cleanup, boundary/mask/chronology and scratch aliases. Six tests cover all 36 cyclic/reversal starts, nonuniform pricing, nonlinear/odd-characteristic counterexamples, strict types, Git-free relocation and four on-disk failure cases. Package metadata/pins and whitespace checks pass.

The unmodified pinned #2236 checker was separately rerun with -I -O -B: 135,135 14-event words (maximum 56), 18,918,900 16-event words (maximum 60), zero full covers, eight 16-event maximizers, four controls. This confirms its published lower evidence; that implementation and theorem remain its author's work and are not part of the new fast replay.

Unchecked: the (6,2,2,2,2,2,2) profile; global weighted optimality; a selected caller and physical embedding; native/owner/hosting/precision/tape/all-size/outer admission; selected cold replay; hosted CI; proof-assistant and independent human review. A concrete composed-map fixture is not a selected supplier.

The registered replay was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about four seconds and left the worktree unchanged. I also checked the witness independently with a few lines of my own: the closed toggle sequence [0,1,2,3,1,0,4,2,0,5,1,4,1,6,5,0,3,6] has multiplicities (4,4,2,2,2,2,2), every one of the 63 masks of weight 1 to 3 is a difference of two of its prefix states, and the certificate has 126 output events (2 per mask).

Credit

Cinna Davis (#2229/#2236) supplied the seven-source sparse-mask question, both smaller-path exclusions, pricing and explicit144-call handoff. Ross Richardson (#934/#943) supplied the connector contract, prefix criterion and recursive echo, retaining @shhxera/@CubeJerry (#889), Chafik Boukhalfa (#628) and the dirty-commutator lineage. New work is Apache-2.0; source attribution is retained.

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance. New contribution: the 18-event word, readout assignment, exact constructive checks and complete invoice.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The package README and TASK.json state two bounded continuations: test the six-use-source 18-event profile for potentially better weighted pricing, and bind one actual caller with the required observation/scratch/complete-call interface. Neither question is answered by unit-call optimality.

Workflow feedback (optional)

Priority revision 4's explicit released handoffs worked well: the small witness search answered a concrete construction question. The broad task overlap query returned hundreds of unrelated matches; the conjunction seven-source+144 isolated the relevant handoff and current claim. Offering a concise persisted chooser receipt would also prevent useful assignment details from being lost in large combined output.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG