Bound correction sharing between two staged helpers

[RossRichardson]

Summary

• Test whether the staged helper pair 608/609 can share correction work and lower recursive cost. Exact inverse rows rule out every scalar entrance change on the pair with terminal changes confined to the six natural receiver registers.
• Prove the four released correction demands need at least two persistent linear channels in the stated factorization model. Construct the genuine common-sum release: its paid frame profile and helper widths are unchanged, while complete scalar additions increase by two. This closes the specified sharing route.

Scope and limits

Both PR4076 providers, arbitrary dirty inputs, rational/dyadic scalar bases, and three explicitly mapped current-state cuts. The exact fixed-word certificate supports the written all-scalar obstruction. Larger source/terminal sets, changed interiors and time-varying channel reuse remain open. No native-phase, owner/source-window, precision/tape, full supplier, formal-kernel or kappa improvement is established.

Test plan

Tested commit: 8d1e3b9399a2a7914f1ab538242cf2e6e6c4cd9f.

• python3.12 -B scripts/research_package.py --package research/shared-staged-helper-interface — both public checkers; full 723-input forward/dual checks including 91 dirty buffers, exact cut bindings, frame invoice and 20 rejection controls.
• Four fresh source-bound normal/optimized checker stages; exact committed-result matches. Both public commands also pass in a read-only Git-free export with empty PATH.
• python3.12 -B scripts/check_research_commit.py --package research/shared-staged-helper-interface --check-source-history — 22 committed files and canonical/source-freeze ancestry. Official export/integrity passes, including LICENSE.
• Natural CI39303042812 completed successfully on the tested commit: plan and registered package replay. No workflow rerun or dispatch requested.
• Independent human review — not observed. The local export harness is orchestration only; both mathematical checkers are public.

Sources and credit

Rohan Arun/PR4076 at 9744f9df268590295a9872b1952c695a678192b9; Tekalign/PR4087's rewrite-defect observation. Proofs, exact source manifest and retained notices preserve the Ross Richardson/3605, dataisfire/3734, ChaloupeMusic/Erwan Secousses, Dugongue/David Ganz, frame, audit and native lineage. Canonical investigation. Base bb4bccbf, priority 6, refreshed at 18:21 UTC; overlap rechecked with complete pagination at 18:22 UTC, which does not prove novelty.

Ross Richardson with substantial OpenAI GPT-6.1 Sol assistance and separate mathematical AI checks; Apache-2.0. AI checks are not independent human or formal-kernel acceptance.