[JoyboyBrian]

Result

The retained ordinary interchange constructor requires fitted topology/program state even when the intended width-two call takes its elementary branch. This package supplies a separate, genuinely initialized elementary interchange API, with 16 reusable scratch tapes, an owned output, encoded counters, and explicit disposal. It authenticates five unchanged low-level source modules from PR #2809 and proves the counter-driven digit sequence refines their elementary interchange for every typed H >= 0, including owned identity at H = 0.

The actual fixed CRT geometry u2/t2/y8/back2 completes all 12 standalone exchanges, including paid current-y ROM rotation and return, producing 196608 binary payload cells. The proof accounts for source operations, allocation/control and cleanup, with at most 13 simultaneous scratch leases; the complete raw owner has 28 private roles. It does not use dummy selected bindings or initialize an unreachable fitted catalogue.

Validation

• Full registered normal controls and actual raw endpoint: PASS, 99.916 s, CPython 3.14.6.
• Frozen official export, Git-free and empty PATH, CPython 3.12.2 -O -B: PASS, 91.934 s, all 23 exported files unchanged. The final amendment changes only validation prose.
• Source/typed-receipt mutations, bucket/prefix/erase/allocation/alias/ROM controls, widths 0..5, 32 independent columns and repeated ownership reuse pass. Checks use explicit exceptions.
• Independent agent source review found no blocker within the typed successful ABI. Committed-byte/source-history, package metadata and official export integrity checks pass.

See research/standalone-elementary-crt-raw/PROOF.md, VALIDATION.md, and RESULT.json for the precise theorem, commands, source hashes and finite receipt. The registered command is python3 -B research/standalone-elementary-crt-raw/verify.py.

Scope and open boundary

This is a new standalone elementary API and a source-operation proof plus fixed raw calibration. It does not admit the current selected/native ordinary caller, complete repair, prove all-size CRT/outer multiplication, supply a literal binary instruction constant or a retained backing-space bound, or change kappa. ROM and well-formed disjoint external ports are typed premises; malformed-error rollback is not claimed. The raw binary output remains the explicit input boundary for the separate four-column repair task.

Canonical claim: #4709 (comment)

Prepared by JoyboyBrian with substantial OpenAI Codex assistance. Original source attribution and Apache-2.0 notices are retained.