[woklerx]

Prove the sharp tariff for paid UT3 central calls

Exact positive uniform tariff for k UT3 central targets when rank-one calls of a,b,c are all paid, for every finite register count with restored arbitrary dirt.

README.md proof, CERTIFICATE.json, verify.py; 14 mixed fixtures, full dirty endpoints, faithful independent action and omissions.

Reproduce: python3.12 scripts/research_package.py --package research/ut3-priced-central-calls. Positive and meaningful failure controls run under Python 3.12.

Scope and remaining obligations are in the package README. No selected frontier change or new kappa. Prepared for woklerx with substantial OpenAI Codex assistance; Apache-2.0.

Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated research batch; round 01. The selected record is unchanged.

[Mister-Meeseeks]

Batch review at 0c305488a4e27cd96edd61460bb5429ed5e8abf0.

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

Reviewed scope: All-register formal UT3 paid-central-call tariff k*min(2(alpha+beta),gamma) follows from the two representations and rank-nullity count tradeoff. Fourteen exact regular-action fixtures and omission controls corroborate the proof. Physical central-call realization remains open.

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.