UT3 rank-bounded block calls: sharp invocation count and rank tariff

[Arham-Tahir64]

DONE — PR1919, exact head f5610483cab0b5547be778a4e8983faf78aefa69, from current main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

The written theorem gives the sharp invocation count 2 max(2,ceil(2w/k)) for w central UT3/D8 targets, paid a/b calls of scalar rank at most k, and arbitrary finite restored dirty workspace. Each letter still charges at least 2w rank units. A cyclic two-block incidence construction simultaneously attains the rank mass and invocation count, so the nonnegative affine tariff is exactly t(alpha_a+alpha_b)+2w(beta_a+beta_b).

Pilot w=3,k=2: six rank-two calls instead of twelve rank-one calls or eight disjoint-block calls, with twelve total rank units in each case. This can save invocation overhead only; no physical supplier, recursive moment or new kappa is claimed.

Registered CPython 3.12.14 replay passes: optimized full checker; normal/optimized read-only export and four certificate-corruption controls; 102 full formal/faithful regular forward/inverse dirty fixtures, 16,160 regular basis columns, 27,931 short words, 900 arbitrary two-factor comparisons, 1,060 same-label decompositions, 62 call omissions, 10 model/boundary controls and 306 rational tariffs. Metadata/provenance and whitespace checks pass. The restricted Windows test temp directory was explicitly placed in writable workspace; an initial CLI flag-placement test mistake was corrected before final validation. Hosted CI is separate.

Final overlap snapshot at 13:41–13:42 UTC fully paginated 556 open PRs including drafts and 536 Discussion body/comment/reply records, with local notes and UT3/D8/dihedral aliases. Existing source heads remain unchanged. PR1792 explicitly observes same-label rank-s decomposition and the unchanged rank-linear bill; that fact and the rank-volume floor are credited predecessor consequences. The new result is the sharp invocation count, cyclic attaining construction and complete affine tariff. Credit steph4n-gh/PR1573, Arham Tahir/PR1589, Hanson Sun/PR1607, Josie Elliston/PR1792 and woklerx/PR1841, with exact heads and broader lineage in the package. Search coverage is not a novelty guarantee.

Reproduce: python scripts/research_package.py --package research/ut3-rank-bounded-block-calls. In a restricted Windows sandbox set UT3_TEST_TMPDIR to an existing writable scratch directory.

HANDOFF: implement and fully price the three-target rank-two boundary against twelve rank-one calls, including frames, scalar preparation, hosting, precision, restoration and dispatch. Scalar coupling rank is not an admitted recursive child rank. Full selected cold replay, physical/compiler/common-label realization, hosting, precision/tape, nonlinear recursive tariff, outer transfer, Lean and independent human review remain outside scope.

Prepared by Arham Tahir with substantial OpenAI Codex assistance; Apache-2.0. No subagents were used. This completes and releases the original bounded advisory claim recorded in the Discussion edit history.