[RossRichardson]

Change and mathematical scope

Proves necessary query and layer bounds for scalar callers over the full algebra Q[N]/(N^3-1). Three independent banks need at least five queries with constant rational rank-one nilpotent directions, even allowing arbitrary scalar-polynomial coefficients. For the two-power alphabet E_ij(±N) / E_ij(±N^2), the general bound is k >= n + ceil((n+1)/3), with explicit power-balance constraints. Three matching layers are impossible; four are impossible when every layer is pure in one power. Four internally mixed layers remain open.

Only research/cubic-scalar-caller-bounds/ changes. This completes the strict equality and four-pure-layer arguments, adds a power-balance screen and independent rational-matrix verification, and preserves both original complete receipts. The full-ring hypothesis is essential: primitive-only native operators do not automatically inherit these bounds. The optimistic matching invoice is conditional; no positive caller, native implementation, new kappa or selected-result change is claimed.

Task and overlap

Base 12fa8c5c844be21bfefb38a19503fbd867a11244, priority 7. The explicit assignment to finish preserved C09 work changes the current joint-query-controller scope. The installed QQ16 caller's complete bill remains unresolved.

PR4023 treats a different order-four/quartic unary alphabet. PR4081 treats actual primitive cubic Clifford operators and fixed response interfaces. This full cubic-ring constant-direction theorem supplies no reduction from either model. The orbit theorem in PR4267 and the historical quadratic caller are excluded. Bounded live and source searches are scope reconciliation, not novelty certification.

Validation

• Separate mathematical and final source/integration review.
• 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.

Exact reviewed head: 4bfdb52e72c701f27966041f66a35ec8278929ed. Local committed/source-history and official read-only export checks passed with unchanged inventory.

Run python3.12 -B scripts/research_package.py --package research/cubic-scalar-caller-bounds. The two complete historical receipts are reproduced with exact JSON types. The separate ordinary rational-matrix engine checks normalization prefixes, all nine full-ring input columns, an excluded four-factor word and its inverse, augmentation loss, projectors and complete interaction/layer defects. Cross-component reconciliation agrees on 36 matrices and 1,569 coefficients.

The components execute 39 deliberate mathematical defects with 39 named-guard deletions; compact integration controls independently execute 54 rejections and six deletions per normal/optimized mode. Finite checks support explicitly written all-word proofs; they are not a formal-kernel proof. No unrelated historical search or native compiler is replayed.

Credit

Preserves the historical cubic lane from scientific snapshot 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Normalization, rank and specialization methods retain credit to eumemic's PR288 source and Ali Romman's PR468. Six original files 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

Specify one bounded four-layer mixed-power alphabet and check its complete full-ring target under the balance constraints. Applying the theorem to a native operator first requires the full algebra representation, not merely order three. README.md and TASK.json preserve that gate and the complete physical-cost obligations.