[CubeJerry]

Change and mathematical scope

Replace the older quoted caller bounds in #6934's precision discussion with
independently computed bounds for its actual word and changed caller. Prove
that the per-call scale1125 program has a sufficient common component format
F=p+D, W=p+h+2D+3, with W+26 temporary bits, through the retained ideal
compiler and ordinary recursion after a paid root boundary.

The exact word prefix has height24 and scaled mass below2^37. The actual
caller has height163/mass below2^126, and joint entrances have
height154/mass below2^124. Thus unfinished contexts add at most178 denominator
bits and161 mass bits. An exact integer threshold absorbs this debt. The
simulation derives exact numerical child returns from a finite ideal
instruction tree, retaining the stated nonprecision endpoint, full-root-factor,
ownership and scheduling interfaces.

No new κ. No native endpoint, full physical supplier, root H0 boundary or
unconditional multiplication theorem is admitted.

Novelty and dependencies

Base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.
Candidate: #6934 at 4e13b7acdbea1c9f12aa88126435360eecea7401.
The fixed-root/compiler method is #6901 at
4c7a4f00f09665276e145ac2cc1d12f8b8f9a7ac, with #4586/#5443/#6878.
Odd clearing originates in #104; the word, scale1125 and per-call wrapper are
#6932/#6934's. This package supplies the missing current-source envelope and
scoped recursive precision implication, not those predecessor constructions.

Reproduction and verification

python3 -B scripts/research_package.py --package research/odd-native-common-grid

Expected: two PASS_ODD_NATIVE_COMMON_GRID markers and
PASS_REGISTERED_RESEARCH_PACKAGE.

The complete rational row audit and separately authored fixed-grid integer
audit agree on14,060,742 coefficient instances. A positive78-by-78 transfer
matrix independently reproduces the caller bounds. The exact threshold,
negative controls, registered normal/optimized checks, committed-byte checks
and Git-free replay are recorded in VERIFICATION.md. Independent review found
no blocking gap under the explicitly retained interfaces; two scope wording
clarifications were applied before freeze.

Controls reject insufficient scales, source corruption, invalid frames/owners,
changed caller semantics and an unfunded odd prime. Concrete counterexamples
rule out a one-time outer scale under nesting and an active-coordinate
projection inside the fixed-root Clifford invariant.

Costs, limitations and credit

The per-call wrapper adds52,272 complete-field scaling operations per raw
caller. All positive conversion and inherited source/native/owned/recursive
costs remain. The full raw allowance, BIT supplier, strictification and outer
ledger are separate admissions. All five selected assumptions remain.

Prepared for @CubeJerry with substantial OpenAI assistance. Credit
DreamingOfClouds, icekylinx, Ross Richardson, zxv, Jacob Alan Sussman,
the lockstep/occurrence contributors and retained native/compiler/precision
lineage. The separate AI audit is not human or formal-kernel acceptance.
Apache-2.0; original source LICENSE/NOTICE retained.

Proof, exact pins, full review and open questions.