Prove partial capture preserves the paid profile

[RossRichardson]

Summary

• Construct the partial sum capture left open by PR4061: share helpers 600/601 for consumers 175/183 while retaining consumers 123/202.
• Verify arbitrary dirty inputs and exact cleanup. After cancelling two adjacent inverse shears, the complete recursive profile, helper widths and scalar count are unchanged.
• Prove a sharp four-rank-one-child floor for monotone rewrites with these six physical block endpoints. The original block already attains it.

Scope and limits

Two frozen PR3945 words retained by PR4061. The finite whole-word checks cover all 723 data, helper and private-buffer coordinates over dyadic free-operator algebra; the separate written floor fixes the block boundaries and single-register child interface. Changed boundaries, surrounding retiming, storage and joint-child interfaces remain open.

The larger-kappa target was not achieved. No new supplier, owner allocation, physical/native-phase/precision/tape/all-size admission, formal-kernel theorem or selected-frontier improvement is established. Separate AI mathematical review is not independent human review.

Test plan

Tested commit: c8d11b68d86b091c44629813f788234c154e489a, CPython 3.12.12.

• python3.12 -B scripts/research_package.py --package research/partial-helper-capture — four public normal/optimized commands; full dirty forward/inverse-transpose/reverse maps, literal/cancelled cleanup, complete frame invoice, independent matrix/row-basis check and rejection controls.
• python3.12 -B scripts/check_research_commit.py --package research/partial-helper-capture --check-source-history — all 23 committed files and canonical/source-freeze ancestry. Original source bytes also match all nine declared public Git blobs.
• Official export/integrity and all four unchanged public commands in a read-only Git-free export with empty PATH/PYTHONPATH; all 24 exported files retain bytes, modes and inodes. Every mathematical checker is public; checkpoint/export orchestration receipts are local-only.
• Hosted CI — natural run 39326767433 completed successfully on this exact head (planning and this package replay). No rerun or dispatch requested.
• Independent human review — not observed.

Sources and credit

Canonical investigation; proofs, source mapping and separate AI review.

Riquelme Soares (@hevlyo)/PR4061 supplies the question and exact frozen inputs; Dugongue/3945 supplies the words, retained through Chris R/Clear1nsight/4045. Tekalign/4048 supplies the capture idea. Rohan Arun/4076 retains Sagar Thakrar's 3687 audit core and Arham Tahir's contract lineage. Original notices and the staged-entry/native/owner/compiler/outer credit remain in the package. Exact original heads/paths are in SOURCE-EXPORT.json; canonical base bb4bccbf, priority 6, and source-only publication ancestry are separately pinned.

Ross Richardson with substantial OpenAI GPT-6.1 Sol assistance. Apache-2.0.