[RossRichardson]

Change and mathematical scope

Proves a sharp 3B-call theorem for the fixed two-bank, three-port orbit grammar. First variation or two evaluations supply the lower bound, even with arbitrary restored dirty scalar spectators and invertible parameter-independent bridges. Three cyclic port-conjugates per bank pair attain it. BIT, complex C4 and the C3 regular-cover models have separate explicit hypotheses.

Only research/orbit-closed-call-bound/ changes. The pinned E8 census supplies 54 eligible root lines in 18 orthogonal triples. It is geometric motivation, not a reduction of arbitrary native callers to the formal query alphabet. No native cost, complete supplier, new kappa or selected-result change is claimed.

Task and overlap

Base 12fa8c5c844be21bfefb38a19503fbd867a11244, priority 7. The explicit user request to finish preserved C09 work changes the current joint-query-controller scope; the installed QQ16 caller's complete bill remains outside this result.

PR4023 proves a different one-bank order-four/quartic query theorem. The present contribution completes the two-bank orbit bound to sharpness and permits arbitrary restored scalar spectators. The separate cubic scalar-caller theorem is excluded from this PR. Live PR/Discussion and current manifest searches were reconciled; their bounded text coverage is not a novelty certificate.

Validation

• Separate mathematical and source/verification review of the final candidate.
• Committed-byte/source-history preflight and all three registered Python 3.12 commands.
• Official exact-commit export and all direct commands from a read-only Git-free path with spaces; unchanged inventory.
• Automatic package CI on the published exact head: run 39510292882, both plan and package replay passed.

Exact reviewed head: 647de55efebbffd34375d5019b3a92259b54a546. Local and official export checks passed with unchanged read-only inventory. Wrapper integrity controls also pass in normal/optimized Python 3.12: 58 intended rejections and 14 check deletions per mode.

Run python3.12 -B scripts/research_package.py --package research/orbit-closed-call-bound. Finite cases use B=1,2,4 and h=0,1,3, retaining full formal coefficients and 1,104 BIT / 8,832 C4 regular-action columns. Thirty deliberate defects and thirty named-guard deletion controls exercise the mathematical components. The all-B/h/f result is a written proof under the specified formal models, not an exhaustive finite search or formal-kernel proof. The larger retained R865 circuit and unrelated frontier packages are not replayed.

Credit

Scientific data are pinned to 20ecf2891d80b5acf18d980b2164fb44ea7faa90. The E8 chart retains Dylan Crow / utcorvusvolat-dotcom's PR370 ancestry through eumemic's carrier-skeleton package, with original notices. Earlier group-algebra rank/specialization methods, including eumemic's retained PR288 and Ali Romman's PR468, are credited. Historical C09 bytes remain unchanged. Ross Richardson with substantial OpenAI Codex assistance, including separate mathematical review contexts. Apache-2.0; no independent human acceptance is implied.

Open next questions

Bind one literal paid native caller to the local-generator and parameter-independent bridge contracts before applying this formal floor. README.md and TASK.json state the smallest useful follow-up and the missing native reduction and complete physical-cost obligations.