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Advance and subdivide one paid main-register move to expose an independent helper output. The complete 18-call construction supports conditional κ=0.00330814, up 0.00000094 (0.0284%) over #6726. This changes the native schedule, beyond the predecessor's fixed-caller allocation ceiling.
The exact local saving is H4+H6-H1-H9>0 for H_r=r^t, 0<t<1. Every fresh input is arbitrary and separately allocated. Complete ordinary work is 535,415,008<10^9, including the canonical adapters identified by #6763. The raw crossing is in (0.0033081451891,0.0033081451892), leaving over 5.1891e-9 above the claim; this is construction-specific, not a global ceiling.
Base: 7c49fe3.
#6702 native: edd6a37.
#6726 caller: 435bbe9.
#6763 audit: c3e0500.
All required bytes and Git/SHA256 pins are retained.
Reproduce (Python 3.12, stdlib):
Expected: PASS_RETIMED_NATIVE_HELPER_SPLIT and PASS_REGISTERED_RESEARCH_PACKAGE.
Executed: normal/optimized registered and Git-free replays; separate native and invoice implementations; all physical maps, 1,536 changed columns, 7,488 caller contacts, both rational interval engines, compiler and 54+4 outer inequalities. Wrong phases, malformed ownership, omitted adapters, aliased inputs and insufficient BIT budget reject. Commit/export checks pass; complete remote tree matches tested bytes. Discovery coverage and stopping rules are in RESEARCH-NOTES.md.
All five assumptions remain: native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery. Selected κ=0.003125804 is unchanged. External mathematical review remains open; no formal proof-kernel or unconditional theorem claim. Further helper retirements need new witnesses and complete accounting.
By @CubeJerry with substantial OpenAI Codex assistance and separate source reviews. Credit Ali Romman, DreamingOfClouds (#6702), zxv (#6726), #6763 and retained native/compiler/interval authors. Original notices preserved; Apache-2.0.
Proof, sources, validation and open questions:
https://github.com/CubeJerry/integer-mult-bounds/tree/0ecd4fd79f4f7fc21b2ef7a9cdc73912fa4a804b/research/native-retimed-helper-split