Research: exact nine-source Johnson-chain connector construction

[1337isnot1337]

Exact connector construction; no selected-kappa change

This package constructs one sparse output-support path in the existing singleton F2 dirty-connector alphabet. For nine read-only source maps and five separate dirty outputs with supports 01234, 01235, 01256, 01567, 05678, the source walk visits 0 → S1 → S2 → S3 → S4 → S5 → 0. Each output is read once at q=0 and once at its support.

The schedule uses 18 source calls and ten output readouts, totaling 28 complete calls, the exact 2n+2p floor for this interface. Five independent restored row stars cost 60 calls, so this family saves 32 complete calls in the unit-call model. With stable per-call source prices c_j > 0, the exact saving is 2 Σ_j (d_j-1)c_j; output-call prices cancel.

Exact pins and evidence

• Task: recursive-interfaces / connector-alphabet-change, seed 923edf31ad6e8cfdc58bb11a6c6d6b3d.
• Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; catalogue revision 4 and selected-record hash are recorded in the package's TASK.json.
• Contribution commits: 05670a6f (construction), b4af93f2 (overlap provenance), and b2c9ead9 (handoff status).
• Latest live PR check at 2026-10-15 04:04:59 UTC: open and mergeable at head b2c9ead9ee4a9468deed3d4c96efff8b7d0bb306, against exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; all 60 visible hosted checks were queued.
• python3 -B research/nine-source-johnson-chain-seed923edf/verify.py passes exact replay for 32,768 arbitrary dirty scalar states, both shared and row-star schedules, three failure controls, and a nonuniform price control.
• python3 scripts/research_package.py --package research/nine-source-johnson-chain-seed923edf --check-only passes metadata and source pins.

The lower-floor proof specializes to scalar identity maps; linearity gives the schedule identity for arbitrary compatible F2 maps. Source incidence is (5,4,3,2,1,4,3,2,1).

Scope and related work

Open PR #2208, head 28480ef4fdb4caeab89765ea56595bf1f6f37688, develops all-word two-root dirty-connector bounds and a minimum-read compiler for supplied source walks across many outputs. It is adjacent walk work; this package gives a one-connector five-mask chain with an exact 28-call floor and does not reuse the two-root framed interface. The package also records PRs #2271, #2283, #2229 and #2266 and active neighboring claims.

Targeted live PR searches through 2026-10-15 04:00 UTC found no exact J(9,5), support-vector, or construction-name match. The complete Discussions snapshot was fetched at 03:26 UTC; the authenticated GraphQL refresh hung and a final 50-second pre-submission retry timed out without output. The package records the stale snapshot and local-only claim rather than treating it as a fresh Discussions census.

No position-dependent transition, concrete supplier placement, hosting, precision, tape or recursive-child mapping is priced. This is a local connector cost reduction, not a selected-supplier result or a new κ. The selected record remains 836330098538459/500000000000000000; its reproduction was not rerun in this cycle.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in scope selection, derivation, implementation and verification. Apache-2.0.