Research: weighted five-source connector optimum (no new kappa)

[1337isnot1337]

This adds an exact weighted optimum for the pinned five-source dirty connector, with complete source leaf prices [1, 4, 10, 16, 28] and unit target readout prices across all 31 nonzero masks.

The predecessor's 12-source-call universal word repeats B2 and costs 200 leaf calls. Swapping source labels 0 and 2 preserves full prefix-difference coverage, repeats the cheapest source B0, and costs 182. The alternate 10-source word misses only mask 21; using four A21 readouts also costs 182. Both schedules are replayed on all 37 basis coordinates of the arbitrary dirty state.

The invoice is optimal in this model. With exactly 10 source calls, the pinned complete 945-path census forces at least one nonzero target mask to be absent, requiring at least two extra unit-price readouts. Any legal schedule with 12 or more source calls pays at least the cheapest restored source pair, also a surcharge of 2. The baseline invoice is 180, so the exact minimum is 182. The cheaper relabeling saves 18 against the published repeated-B2 schedule without changing the root record count or primitive alphabet.

This is a bounded weighted connector result. It does not claim a new selected κ or an occurrence in the selected supplier. It is distinct from Discussion #1579's expired minimum-query/readout-price claim (this package optimizes one exact unequal source-leaf price vector) and PR #1526's signed characteristic-zero connector with paid root scaling.

Reproduce with Python 3.12:

python3 scripts/research_package.py --package research/weighted-connector-readouts-seed1275309492 --check-only
python3.12 scripts/research_package.py --package research/weighted-connector-readouts-seed1275309492

The package pins its exact base, selected record, predecessor certificate and source manifest. It discloses substantial OpenAI Codex assistance and retains PR #934 attribution.

[Mister-Meeseeks]

Batch review at caae2d1a0b4497fbd5a7cd2d057d9a9b099f8873.

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

Reviewed scope: Fixed heterogeneous five-source prices admit exact182 weighted leaf optimum versus200 for the predecessor displayed word. Even-incidence lower bound plus945-path ten-call exclusion and two74-record attaining programs checked. This is an abstract weighted interface, not a located selected supplier.

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.