[ahrazzle]

Change and mathematical scope

Apply Cinna Davis's #4692 scalar compressor to Cao Yifan's final #4610 word, excluding the helper-628 triangle that worsens the recursive invoice. This removes 151 scalar ADD macros per orientation and reduces the conservative real scalar allowance by 1,216 per native call: forward 158120 → 156904, backward 158168 → 156952.

Every chronological per-owner Fourier climb, all 408 independent helper boundaries, main boundaries, native maps, phases and owned operations are preserved. The complete paid profile remains {1:2201,2:412,3:510,4:127,5:40,8:8}, so κ is unchanged. This is an exact scalar construction, not a measured runtime speedup, full multiplication theorem or selected-result update.

Two bounded numerical frame/helper/native-map searches found no paid improvement. These floating MILP results are not exact ceilings or universal obstructions.

Task and overlap

• Base: canonical main ff3cc58e370d0f678e529246f8c73e8094e18fcf, rechecked before submission.
• Explicit donor assignment. Scope key: final-pr4610/broader-scalar-compression/paid-profile-preservation. The target was a paid-moment gain. The achieved result is a scalar reduction with the same invoice. Scope and stopped routes are in TASK.json.
• Cinna Davis's work supplies the broader compressor and rewrite identities. Cao Yifan's work supplies the final native word. Cao P16: remove 34 commuting inverse ADDs with dual 632-column replay (no new kappa) #5265 already removes the 34-ADD commuting inverse-pair subset. This package claims no priority for those identities or that subset.
• Parallel Certify no gain in a joint productive-helper/native fusion family #5301 applies the commuting equal-ADD rule to the same final word and removes 98 scalar events per orientation. It then proves an exact no-gain certificate for its specified binary joint helper/native family.
• This package applies the broader repeated rewrite, including triangles with the helper-628 exception, to remove 151 macros. Its floating optimization screens do not replace or extend the exact symbolic certificate in the parallel work.
• The unfiltered 152-deletion rewrite splits one H4 into two H2 jobs and loses. Excluding that triangle retains 151 deletions without changing the invoice.
• All predecessor files are pinned by SHA-256 at the base in SOURCES.json. The canonical native-word payload is cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd.

Validation

CPython 3.12.14, Linux x86-64. Standard library only for the positive result:

python3 -B research/cao-trace-retiming-20261023/verify.py
python3 -O -B research/cao-trace-retiming-20261023/verify.py

Passed: both retained exact interpreters on all 632 arbitrary-input columns in both directions, owned-center cleanup, identical chronological transports and paid profile, prefix bounds below the retained 2^192 envelope, corrupt-sign rejection, source hashes and deterministic receipt comparison. The default verifier is read-only.

Optional discovery used SciPy 1.17.0 / NumPy 2.3.5. Commands and both frozen search receipts are included. No new complete controller/compiler/BIT/outer-ledger replay or all-size supplier admission is claimed.

Credit

Prepared with substantial OpenAI Codex assistance. Author-checked, not yet independently reviewed.

Credit Cao Yifan / @intqwq, Cinna Davis / @1337isnot1337 (also the #4470 work), and @Chrisbryan17. Credit also @flyingviper, @Dugongue, @zxv, and Jacob Alan Sussman / @jacobalansussman and all retained native, Clifford, compiler and analytic sources. Source notices and Apache-2.0 licensing are preserved.

Open next questions

The README identifies a concrete next step: legally replace one chronological owner dependency while preserving arbitrary-input action, then check whether a #5179 forcing path disappears. Repeated optimization of the unchanged model is not justified by these negative results.

Automated posting by agentic team with human oversight.

[jwr404]

Independent review (James Reed, with Claude Code). Head 9bdd01dd0d3142517f5268285a9fb4ce35469172.

Verdict: the rewrite identities are sound, and the exact replay passes. There is one packaging gap: the result isn't registered, so hosted CI never replayed it.

Rewrite identities (construct.py::triangles)

With add(t, s, c) meaning t += c·s (as in the sample events, e.g. ['add', ['L',273], ['L',115], -1, 1]):

• source_update. a += αb; b += βy; a −= αb gives b += βy, a −= αβ·y, which equals [B, add(a, y, −αβ)]. Order is irrelevant because y is untouched. ✓
• target_update. a += αb; x += βa; a −= αb gives x += βa + αβ·b, which equals [add(x, a, β), add(x, b, αβ)]. ✓

The two scans ensure that no event between i and k touches {a, b, x, y} other than B. The scan breaks at phases, a 180-event window bounds it, and the frame-nesting condition spaces[first] ⊆ spaces[middle] ⊆ spaces[last] is the #4692 legality condition, retained. The ('L', 628) exclusion is visible and justified by the unchanged paid profile.

Replay

I copied the package into a canonical-main checkout (ff3cc58e3) and ran python3.12 -I -B …/verify.py. It printed PASS backward 1216, PASS forward 1216 and PASS_DETERMINISTIC_CAO_TRACE_RECEIPT in about 10 s:

• all 632 arbitrary-input columns pass in both directions under both retained interpreters;
• every climb, warp, centre and phase is unchanged;
• the paid profile is unchanged;
• the sign-corruption control is rejected.

Event counts from construct(): scalar macros 17,453 → 17,302 and ADD events 16,089 → 15,938 per direction, so exactly 151 removed.

Issues

1. No VERIFY.json. scripts/check_research_commit.py --package research/cao-trace-retiming-20261023 reports missing or external file: …/VERIFY.json. The package is not registered, and the green hosted check is only the planner. Adding a VERIFY.json with the verify.py command (~10 s) would put the replay under CI.
2. Allowance arithmetic. 151 removed ADDs at 8 each is 1,208, but the reported saving is 1,216 per direction. Please state where the extra 8 comes from in real_scalar_allowance (e.g. a frame or denominator term), so the per-macro accounting is checkable from the README.
3. The equivalence evidence relies on the two retained interpreters (trace_cao_rows, trace_cao_literal). That's fine, but the README should say they are retained rather than new implementations. The docstring does; the README could too.

No change to κ, consistent with the unchanged paid profile.