[Chrisbryan17]

Scoped result: 34 fewer ADD macros on Cao Yifan's newer #4610 native word (NO new kappa)

On the frozen, merged #4610 native word CrocSwap/integer-mult-bounds@20bb93cd990d2ff683e4d0fc56b87a42cd5d3296 (canonical payload SHA256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd), find two exactly inverse rational scalar ADD operations separated only by commuting instructions and cancel the pair in both native orientations.

The 160-raw-event bounded scanner checked 542 matching inverse pairs, found 19 dual-legal commuting pairs, then selected 17 disjoint intervals. Deleting those 34 ADD instructions from the actual 21,449-event word and resynthesizing yields:

• Forward real scalar allowance 158120 -> 157808 (312 saved per native call).
• Backward real scalar allowance 158168 -> 157856 (312 saved per native call).
• The paid rank histogram is identical: {1:2201, 2:412, 3:510, 4:127, 5:40, 8:8} (3,298 local paid jobs).
• Every per-role native Fourier chart climb is preserved in chronological order. Every warp, owned centre, adapter and phase marker is unchanged.
• Two independent literal interpreters replay all 632 arbitrary independent input columns, forward and inverse-transpose, with C0 cleared and the same full paid profile.
• An adversarial mutation removing just one of a matched inverse pair is rejected.
• The changed scalar word, complete invoice and source-pinned deleted-event patch are regenerated deterministically without a numerical optimizer.

The 18 local calls in the p16 controller imply 5,616 units of scalar-allowance headroom at the unchanged 18-call placement; this affects finite constants, not the claimed exponent. The selected #4470 ? and Cao #4610 conditional ?=0.0030217758 are unchanged. No end-to-end integer multiplier, new physical rank-changing primitive, global optimum or proof of a higher ? is asserted. Fixed-tape, stock/precision/analytic transfer retain original conditional contracts.

Validation

On Windows Dell, source-bound CPython 3.13 run passed combined_inverse_add_certificate.py with both 632-column interpreters and the negative control, printing:

PASS_CAO_DUAL_632_SCALAR_CANCELLATION removed_pairs 17 forward_scalar_allowance 157808 backward_scalar_allowance 157856 native_pairs_preserved {'backward': True, 'forward': True}

A Python 3.11/3.13 Actions workflow is committed for hosted verification; hosted success is not asserted.

Reproduce

python -I -B research/p16-cao-scalar-dag/inverse_add_dag_search.py /path/to/frozen-pr4610-checkout
python -I -B research/p16-cao-scalar-dag/combined_inverse_add_certificate.py /path/to/frozen-pr4610-checkout

Credit / overlap

Not a priority claim for scalar cancellation. Cinna Davis's already merged #4692 previously removed 116 ADDs from the older selected #4470 word, using commuting and noncommuting rewrite patterns. This PR proves a smaller bounded commuting-inverse subset applies to Cao Yifan's newer #4610 native word, with full dual tests; further application of #4692's broader compressor to the Cao word could improve on this number. Credit Cao Yifan/intqwq (#4610), Cinna Davis (#4470/#4692), Dugongue's transported native maps, zxv, Jacob Alan Sussman, and all inherited authors. Authored for Chrisbryan17 with substantial GPT-6 assistance; Apache-2.0.

Research branches for independent follow-ups: research/p16-cao-paid-fusion-20261023 (59 source-compatible F2-F2 candidates no positive legal one-contact fusion) and research/p16-cao-controller-20261023 (all 16 retained prefix/suffix choices screened; selected 7/8 best and 8/7 ties in pure invoice). These are NOT part of the present PR.