Compress final #4610 scalar word by 151 ADDs per orientation

research/cao-trace-retiming-20261023/README.md

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+# Scalar compression on the final Cao native word
+
+**Author-checked result; not yet independently reviewed; no new kappa.** Applying Cinna Davis's
+PR4692 compressor to Cao Yifan's final PR4610 word, with one paid-profile-safe
+exception, removes **151 scalar ADD macros in each orientation** while preserving
+every chronological per-owner Fourier climb. The conservative real scalar allowance falls by **1,216 per call**: forward `158120 -> 156904`, backward `158168 -> 156952`. The complete paid profile remains
+`{1:2201,2:412,3:510,4:127,5:40,8:8}`. All 408 independent helper boundaries,
+632 independent inputs, main boundaries, native maps, phases and owned operations
+are unchanged. Consequently the entire recursive moment is identical.
+
+The changed word passes both retained exact literal interpreters on all 632
+arbitrary-input columns in both directions. The formal prefix magnitude remains below the retained 2^192 envelope. A corrupted scalar sign is rejected.
+No new native phase recipe is needed: every chronological frame transition is
+exactly inherited. This is not an integer-multiplication theorem, a higher
+conditional exponent, a measured runtime speedup or a selected-result update.
+
+## Construction and predecessor credit
+
+`construct.py` imports the original commuting ADD merger and reproduces the
+credited triangle rewrite from PR4692. Its only new triangle restriction excludes
+helper 628. Without that restriction, the repeated compressor removes 152 macros
+but splits its original rank-four transition `0 -> 2085` into rank-two transitions
+`0 -> 131 -> 2085`. For `0<t<1`, strict concavity gives `2*2^t > 4^t`, so that
+additional deletion worsens the recursive bill. The restriction keeps 151 deletions
+and the entire predecessor invoice. Four productive rewrite rounds suffice;
+a fifth round confirms the fixed point.
+
+PR5265 independently supplied 17 commuting inverse pairs (34 removed ADDs) on the
+same final Cao word. This package uses PR4692's broader predecessor compressor;
+it claims neither priority for the rewrite identities nor a kappa improvement.
+Cinna Davis's original PR4692 applied the compressor to the older selected PR4470
+word. Cao Yifan's PR4610 supplies the newer native word and joint-map optimizer.
+Credit Cinna Davis, Dugongue, zxv, Jacob Alan Sussman and all retained native,
+Clifford, scalar, geometry, compiler, precision and analytic sources.
+Prepared for ahrazzle with substantial OpenAI Codex assistance; Apache-2.0.
+
+## Exact replay
+
+From the repository root, with Python 3.12 and the source files pinned in
+`SOURCES.json`:
+
+```sh
+python3 -B research/cao-trace-retiming-20261023/verify.py
+```
+
+This rebuilds the word in memory, checks every source hash, verifies both exact
+interpreters and the scalar corruption controls. The source archive and all frozen
+predecessor receipts remain unchanged. The default verifier is read-only; `--write` is an explicit authoring option. `COMPRESSION-STAGES.json` records the
+initial discovery run; `VERIFICATION.json` records the final package replay.
+
+## Bounded search for a paid gain
+
+Two full contact/helper/native-map models were run on the changed scalar graphs,
+reusing the credited PR4610 exact frame enumeration and floating SciPy/HiGHS
+optimizer. All 72 late native maps were available; the 12 prelude line contracts
+were preserved. Every enumerated quotient interval had dimension at most five.
+The helper exits, scalar chronology after the rewrite, and main boundaries were
+fixed; all 408 helper entrances and scalar contacts were variable.
+
+| Input graph | Variables | Constraints | Best local moment improvement over PR4610 |
+|---|---:|---:|---:|
+| 152 deletions, including the costly helper 628 triangle | 1,623,742 | 307,270 | -0.000223150946 |
+| 151 deletions, helper 628 triangle excluded | 1,635,654 | 308,767 | 0 |
+
+Both discovery runs retained the predecessor optimizer exponent `t = 1 - 0.00302157135`; the comparator is the final PR4610 paid/helper profile. The filtered optimum has identical complete profiles, so its zero gain holds at every exponent. Both runs completed in about 14 seconds and reported numerical finite-model optimality.
+**These are bounded numerical negative searches, not exact ceilings or universal
+impossibility results.** `UNFILTERED-SEARCH.json` and `FILTERED-SEARCH.json` preserve
+the actual outputs. No negative-screen map candidate is admitted as a new supplier.
+
+To rerun the filtered optional discovery (SciPy 1.17.0, NumPy 2.3.5 used here):
+
+```sh
+python3 -B research/cao-trace-retiming-20261023/construct.py --output /tmp/cao-trace-word.json.gz
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -B research/cao-trace-retiming-20261023/search.py --word /tmp/cao-trace-word.json.gz --operator all --seconds 180
+```
+
+The discovery writes separate `DISCOVERY-*` files and does not overwrite the
+frozen two search receipts. A solver is unnecessary for the exact positive scalar
+result. The candidate has no changed recursive invoice, so no full controller,
+compiler, BIT or outer-ledger run is claimed.
+
+## Prelude-route scope
+
+An initial attempt to free the common prelude lines was stopped when the live
+overlap check found PR5096's first-image theorem and PR5179's inverse-return
+rigidity theorem. The 152- and 151-deletion graphs both retain all 12 exact
+post-inverse line caps, checked independently through reachable main-Y exits.
+This is supplementary bounded evidence, not a new proof of those predecessors.
+
+## Open next questions
+
+A paid-profile improvement must change a restriction beyond this tested scalar
+rewrite/contact model. One concrete first step is to replace an actual chronological
+owner dependency while preserving arbitrary-input action, then test whether the
+PR5179 path cap disappears. Its single-edge deletion is a relaxed graph control,
+not a legal circuit edit. No repeated fixed-invoice search is justified by the
+present negative results alone. The retained physical/native all-size, compiler,
+precision, stock, analytic and recovery assumptions remain unresolved here.

research/cao-trace-retiming-20261023/SOURCES.json

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+{
+  "canonical_base": "ff3cc58e370d0f678e529246f8c73e8094e18fcf",
+  "predecessors": {
+    "native_word": "Cao Yifan / intqwq, PR4610 final round3 payload cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+    "scalar_compressor": "Cinna Davis /1337isnot1337, PR4692",
+    "bounded_inverse_pairs": "Chrisbryan17, PR5265",
+    "underlying": "Cinna Davis PR4470, Dugongue, zxv, Jacob Alan Sussman and retained Apache2.0 source notices"
+  },
+  "files": [
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+    },
+    {
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+      "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326"
+    },
+    {
+      "path": "research/joint-helper-lattice/NATIVE.json.gz",
+      "sha256": "74582cce642c80f0235be7fcbce3716174666326ac6a1d46d02a62a75d7be4c6"
+    },
+    {
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+      "sha256": "296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727"
+    },
+    {
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+    {
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+      "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7"
+    },
+    {
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+    },
+    {
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+    },
+    {
+      "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz",
+      "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39"
+    },
+    {
+      "path": "research/kappa-rebuild/complex/native_extensions.py",
+      "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3"
+    },
+    {
+      "path": "research/kappa-rebuild/complex/power_two_balance.py",
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+    {
+      "path": "research/kappa-rebuild/complex/rebuild_native.py",
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+    {
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+      "sha256": "b464b18dde15a4f3f0f71252f4eacf5a1883115fdff87734819e0b8e59b26285"
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+    {
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
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+    {
+      "path": "research/kappa-round3-warp-20261022/helper_line_milp.py",
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+      "sha256": "52b73c482f9aa171ac266bf0f5752bb520b100d79949f615d0aa26cb926452ba"
+    },
+    {
+      "path": "research/native-warp-extraction-boundary/operators.py",
+      "sha256": "4427aa6bb35b095868381de947d177bdbfc2c92e8e0ef9c5a75731ac4d0ca5bd"
+    },
+    {
+      "path": "research/scalar-reorder-20261022/intervals.py",
+      "sha256": "ce8571b2446debaecd83b43441417e102ae1ca3322eb8e118b3e84994f214eed"
+    },
+    {
+      "path": "research/scalar-trace-compression/verify.py",
+      "sha256": "b41d69aca44852b4b7b880b74b3b482c2274f7b093573ca663a8f5419c8858be"
+    },
+    {
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+    {
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+    },
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+    {
+      "path": "research/warp-interface-20261022/verify_candidate.py",
+      "sha256": "7aae8922f456673f3be7045c064e4700cf929c51da1316368758fb5cdd3a3e50"
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+    }
+  ]
+}

research/cao-trace-retiming-20261023/TASK.json

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+{
+  "task": "paid-profile gain from broader exact scalar rewriting on final PR4610",
+  "base": "ff3cc58e370d0f678e529246f8c73e8094e18fcf",
+  "declared_target": "Strict decrease of complete paid-minus-productive moment against PR4610, followed by exact native and full outer admission",
+  "outcome": "Target not achieved. Exact local 151-macro and 1216-scalar-allowance reduction preserves the complete paid profile. Two bounded global frame/native-map optimizations find no strict gain.",
+  "scope": "changed scalar chronology, fixed main endpoints/helper exits, free helper entrances and 72 late native maps with 12 retained prelude lines",
+  "source_delta": "PR4692 broader compressor applied to final PR4610; skip helper 628 triangle because it splits a rank-4 job into two rank-2 jobs",
+  "related": "PR5265 supplies the 34-macro commuting inverse subset; PR5096/5179 block fixed-scalar-graph prelude freeing",
+  "stop_rule": "Two complete changed-graph optimizations without positive paid gain; no further fixed-model rounds",
+  "unrun": "No new full supplier/controller/compiler/outer replay; no end-to-end theorem or exact global-optimum certificate",
+  "open_next_question": "Replace a chronological owner dependency with a legal arbitrary-input circuit and demonstrate removal of a specific forcing path before further optimization",
+  "evidence": "VERIFICATION.json, UNFILTERED-SEARCH.json, FILTERED-SEARCH.json",
+  "status": "AUTHOR_CHECKED_UNREVIEWED"
+}