Prove sharp concave tariffs for rank-capped UT3 block calls

[petalas]

Summary

Complete the nonlinear-pricing gap in Arham Tahir's #1919, head f5610483cab0b5547be778a4e8983faf78aefa69, without changing its formal UT3 alphabet.

K = min(rank_cap, central_targets)
q, remainder = divmod(2*central_targets, K)
optimal per-letter ranks = [K]*q + [remainder when positive]

research/ut3-concave-rank-tariff/ proves the sharp complete tariff for nonnegative invocation overhead plus any nondecreasing concave rank price. An extreme-degree incidence word attains it for every finite target count, rank cap and restored dirty workspace. The proof also excludes cheaper words that spend additional rank mass.

This is an abstract interface-cost side result. No physical supplier, recursive child-rank binding, multiplication exponent or selected frontier change is claimed. The package includes source pins, explicit replay registration, scope metadata and open next questions.

Evidence

• Before, the predecessor's five-target cap-four cyclic construction has per-letter ranks (4,3,3), priced at 23/10 for f(d)=d/(d+1). After, (4,4,2) costs 34/15, saving exactly 1/15 across both letters with unchanged six calls and twenty rank units.
• Registered Python 3.12.15 replay passes 624 formal/faithful dirty-restored fixtures, 114,176 basis columns, 2,492 relaxed rank lists and eleven rejection controls. Six focused tests pass normally and under -O, including independent count-vector arithmetic, relocated read-only CLI and receipt corruption controls.
• All 65 repository test_research_*.py tests pass. Metadata/source pins, AST checks and git diff --cached --check pass. The retained Research: sharp invocation tariff for rank-bounded UT3 block calls #1919 verifier also passes unchanged.

python3.12 -B scripts/research_package.py --package research/ut3-concave-rank-tariff
python3.12 -B -m unittest discover -s tests -p 'test_research_*.py'

Started from canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Final overlap refresh at 20:12 UTC covered 381 open PRs and 789 Discussion records with complete pagination and no warnings; canonical main and the predecessor head were unchanged. No matching nonlinear UT3 tariff was found, with the helper's stated coverage limits. The existing investigation is Discussion #1890; no Discussion post was made because the engineering-mode communication rule forbids it.

Credit #1919 and its #1573/#1589/#1607/#1792 rank-volume and alphabet lineage. The written proof was reviewed locally, not by an independent human or proof kernel. Native conversion, H1-H5 admission, hosting, precision/tape, selected cold replay and outer analytic transfer remain unrun. Hosted CI is separate from local verification.

Merge danger

Door: Two-way.

Blast radius: Package-only. Seven new files and an opt-in replay manifest. No predecessor, frozen source, selected record or existing verifier changes.