Bound heterogeneous orbitwise partial fusion with restored-dirt feedback

[Clear1nsight]

Result

Allow the selected target195/donor521 boundary to use coordinate-orbit blocks of unequal volumes, with a separate partial-fusion choice k on each block. The two native child ranks become f+k and f-k; the exact middle transfer is B_K y/2.

For any fixed block-wide feedback adapter with restored donor and arbitrary dirty helpers, at least k+1 shears are necessary. Relative to the original one ADD, let W = sum(block_volume * k). Extra arithmetic is at least W, while the rank-only recursive saving is at most A delta f^(-alpha) W, where delta = 2-2^(1-alpha) and A is one fixed coefficient in matching arithmetic units. Thus this whole heterogeneous-volume family fails the uniform optimistic screen for sufficiently large f, even when block volumes and every k vary with f.

The written proof combines exact Clifford orbit structure, support growth and convexity. This extends the full-fusion endpoint of #3989/#4009 to all partial cuts and their orbitwise combinations.

Scope

The native calls act on the target before and after an adapter with no recursive calls. Every adapter shear processes one entire chosen block; monomial maps, arbitrary source mixtures, feedback and any finite number of restored dirty helpers are allowed. Blocks are unions of joint Pauli orbits. Cross-block mixing, masked sub-block operations, overlapping native supports, data-dependent partitions and recursive calls inside the adapter remain outside the theorem.

Native wrappers, hosting, precision and routing are granted free only for this optimistic obstruction. No physical supplier, optimal-runtime lower bound, numerical finite threshold without A, new kappa or selected-frontier change is claimed.

Evidence

Publication head: 9cdd8d6f4389d8e8e26b910f4b139e1cc7b86173.

• Source-authenticated reconstruction of 1,536 literal child columns, 128 joint orbits and the complete intervening dependency region.
• 3,184 complete reduced two-payload basis cases for all k at f=1,2,3,4, plus 96 heterogeneous-block basis cases and exact direct monomial transfers.
• Four wrong constructions rejected; exact integer support controls and 8,384 high-precision controls supplement the analytic all-f convexity proof.
• Registered Python 3.12 replay, source-pin validation, isolated optimized replay, committed-byte/history and official export integrity checks passed. Read-only Git-free empty-PATH normal and optimized export replays passed with all 10 files unchanged.
• Hosted CI passed for this head, including the registered mathematical replay and unchanged-input check. No review feedback was present at 11:16 UTC on 2026-10-19.
• Separate Codex conceptual proof review. This is not independent human or formal-kernel acceptance.

Reproduce with python3.12 scripts/research_package.py --package research/native-orbit-partial-fusion.

Credit and overlap

Canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Entry overlap covered all 733 open PR bodies including drafts, current handoffs and active discussions; a checkpoint through #4033 found no same scoped claim. Wider closed/discussion coverage is partial.

Gonzalo Mier/#3975 supplied the sequential caller. Credit Clear1nsight's #3989/#4009 Pauli and feedback work, Cinna Davis/#1836, Adam Gall, Arham Tahir/#1920, ToikY/#1924 and the selected #1094/#679 lineage. Source notices and exact pins are retained. Prepared by Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0.