Speed up complete P104 precision replay with proved exact integer arithmetic

research/p104-integer-error-replay/BENCHMARK.json

@@ -0,0 +1,124 @@
+{
+  "platform": "macOS-26.6.1-arm64-arm-64bit",
+  "python": "3.12.14 (main, Aug 25 2026, 13:50:33) [Clang 22.1.3 ]",
+  "code_sha256": {
+    "integer.py": "82a73e4bcf1835bfdd510c7ad5538625c1b380c559b671e6a67be490615a743a",
+    "contract.py": "ecf1f000e4aef11d5d5e1191a8e6fa44518ba8736e14505071f4ebc32d1409ce",
+    "verify.py": "aaa392ca9aa9aead0eee0ac6c64ff44ea66e1f251b0a79d18cd60baa946261a1",
+    "benchmark.py": "59c451bd1fcb1e8fcaebe5d6d7002bb85ccbd68c2f0f8d14e70de8fbcf949c69",
+    "inputs/source.tar": "f8252a90dc504ce8a77d781e558691fe8d21014b0f3f720d8dfd5274b5e8aadc"
+  },
+  "order": [
+    "baseline",
+    "candidate",
+    "candidate",
+    "baseline",
+    "baseline",
+    "candidate"
+  ],
+  "runs": [
+    {
+      "mode": "baseline",
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+      "internal_seconds": 31.07993,
+      "receipt": {
+        "coordinates": 799,
+        "events": 25984,
+        "guards": {
+          "owned": 22,
+          "prefix": 26,
+          "public": 23
+        },
+        "source_controls": 6,
+        "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+      }
+    },
+    {
+      "mode": "candidate",
+      "wall_seconds": 9.81022679200396,
+      "internal_seconds": 9.748412,
+      "receipt": {
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+        "events": 25984,
+        "guards": {
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+          "prefix": 26,
+          "public": 23
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+        "source_controls": 6,
+        "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+      }
+    },
+    {
+      "mode": "candidate",
+      "wall_seconds": 3.2594693331047893,
+      "internal_seconds": 3.213043,
+      "receipt": {
+        "coordinates": 799,
+        "events": 25984,
+        "guards": {
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+          "prefix": 26,
+          "public": 23
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+        "source_controls": 6,
+        "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+      }
+    },
+    {
+      "mode": "baseline",
+      "wall_seconds": 24.090562083059922,
+      "internal_seconds": 24.048647,
+      "receipt": {
+        "coordinates": 799,
+        "events": 25984,
+        "guards": {
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+          "prefix": 26,
+          "public": 23
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+        "source_controls": 6,
+        "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+      }
+    },
+    {
+      "mode": "baseline",
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+        "guards": {
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+          "prefix": 26,
+          "public": 23
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+        "source_controls": 6,
+        "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+      }
+    },
+    {
+      "mode": "candidate",
+      "wall_seconds": 4.3006944169756025,
+      "internal_seconds": 4.239551,
+      "receipt": {
+        "coordinates": 799,
+        "events": 25984,
+        "guards": {
+          "owned": 22,
+          "prefix": 26,
+          "public": 23
+        },
+        "source_controls": 6,
+        "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+      }
+    }
+  ],
+  "baseline_median_seconds": 24.090562083059922,
+  "candidate_median_seconds": 4.3006944169756025,
+  "speedup": 5.601551690808398,
+  "wall_reduction_fraction": 0.8214780376585825,
+  "cold_processes": true,
+  "parallel_replays": false,
+  "scope": "Complete contract with source authentication, extraction, all original endpoint/error/guard/control checks. Local shared-host timings; no Linux or hosted speed claim. Qualification is a separate cost."
+}

research/p104-integer-error-replay/CONTRACT-EDITS.json

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+[
+  [
+    "def authenticate():",
+    "def authenticate(P=P):"
+  ],
+  [
+    "def calculate():",
+    "def calculate(P=P, backend=None):"
+  ],
+  [
+    "    authenticate()",
+    "    authenticate(P)"
+  ],
+  [
+    "    a = module('noisy_precision', P / 'precision.py')",
+    "    a = backend if backend is not None else module('noisy_precision', P / 'precision.py')"
+  ]
+]

research/p104-integer-error-replay/PROOF.md

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+# Exact dyadic scale and complete replay equivalence
+
+The frozen source is PR5826 at58f93cf41751920f3d6766a39caccc2974ce18b0.
+Its official source export is retained unchanged. The candidate changes the
+arithmetic representation of sparse coefficients. It changes no native word,
+error allowance, operation count, endpoint, guard inequality or scientific claim.
+
+For each row, keep an upper bound d on the exponent of two in the denominator
+of any coefficient. Start d=0. A reset sets d=0. MOVE leaves it unchanged.
+SCALE by n/2^k sets d to d+k. ADD or additive COPY from s into r sets
+`d_r=max(d_r,d_s+k)`. Injection of a new unit defect requires only exponent0.
+The same rule on the transposed word uses `d_s=max(d_s,d_r+k)`. These bounds
+ignore cancellations and powers of two in n; thus they can be conservative.
+Take E to be the largest bound on either traversal and S=2^E.
+
+Induction on each event proves that every exact forward and transposed
+coefficient is an integer multiple of 1/S. Store its numerator at this common
+scale as a Python arbitrary-size integer. Multiplication by n/2^k is exact:
+first multiply by n, then divide by 2^k. The implementation checks divisibility
+before every division. It does not truncate, use a modulus or accept a floating
+comparison. A nondyadic coefficient is rejected. The same scale covers ideal
+input coefficients; it is a representation bound, not a numerical precision
+or magnitude promise for the physical caller.
+
+Choose separate power-of-two scales A and C for the nonnegative local weights
+a_j and c_j. If a coefficient is z/S, its three exact score contributions are
+
+`abs(z)*a_j*A/(S*A)`, `abs(z)*c_j*C/(S*C)`, and `abs(z)/S`.
+
+The numerator updates use the signed sum z_old+q*z_source before taking its
+absolute value. Thus a cancellation changes the score by
+`abs(z_new)-abs(z_old)`, including negative changes. The candidate does not
+replace signed transfer by an absolute-value propagation bound. All score units
+are fixed, so comparisons, tie choices and Pareto order agree with the rational
+reference. Fraction conversion occurs only at the result and hash boundaries.
+Canonical reduced numerator/denominator encodings preserve all source hashes.
+
+The transposed pass uses a separate traversal with the same proved scale. It
+checks every final signed coefficient and score. The original literal scalar
+execution and reverse-cut oracles remain unchanged. The original contract's
+complete ideal endpoint, native frame/ownership checks, guards, attaining
+fixtures and six rejection controls remain active.
+
+`contract.py` is an explicit adapted copy of the source runner. Its four declared
+edits add source-directory and backend parameters. Its obsolete direct CLI is
+removed; this package supplies its own CLI. The checker reconstructs these
+exact edits before loading the runner. This is ordinary dependency injection;
+no module, global function, source file or import hook is patched at runtime.
+
+Qualification compares the complete baseline and candidate results, all actual
+signed witness rows, and120 separate finite dyadic error words with cancellation,
+scaling, reset, COPY and varied defect sites. It also compares each finite
+transposed result and rejects nondyadic scalars, nondyadic weights and inexact
+integer divisions. The frozen source and package code remain distinct.
+
+The default command runs the fast complete source contract and compares the
+entire result to the frozen expected record. `--qualify` additionally runs the
+slow reference and the extra cross-checks; its cost is not hidden in the speedup.
+`--baseline` runs the unmodified source contract for a matched timing. Timings
+include source authentication, archive extraction and full original controls.
+No cache is shared between processes. Local measurements are not a promise
+about another machine or hosted CI.
+
+The original precision theorem remains conditional. Native unitary gauges,
+physical resets, exact owned return, compiler, precision-tape and analytic
+admission retain their prior status. Faster verification is not a new kappa.

research/p104-integer-error-replay/README.md

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+# Exact integer replay for the complete P104 precision contract
+
+The complete PR5826 precision replay now has an exact integer backend for its
+ideal input, signed error and transposed passes. A proved common dyadic scale
+replaces Fraction operations in the inner loops. Every division is checked;
+no floating or modular result decides acceptance. The word, full799-coordinate
+endpoint, all25,984 events, signed coefficients, guards and six source rejection
+controls remain unchanged. See [PROOF.md](PROOF.md).
+
+The local complete-process median falls **24.091 to 4.301 seconds**
+(**5.60x**, 82.1% less wall time). The host was not reserved:
+baseline runs range from 19.791 to 31.149 seconds; candidate runs range
+from 3.259 to 9.810 seconds. `BENCHMARK.json` records six serial fresh-process runs of the complete baseline
+and candidate, with code hashes, all receipts and the local timing limits.
+The candidate still authenticates and extracts the frozen source, executes the
+literal attaining oracles, and compares the full source result. It has no
+persistent cache. Qualification is a separate cost and is not hidden in the
+claimed runtime.
+
+Run the fast complete replay:
+
+```sh
+python3 -I -B research/p104-integer-error-replay/verify.py
+```
+
+Run the full independent arithmetic qualification:
+
+```sh
+python3 -B scripts/research_package.py --package research/p104-integer-error-replay
+```
+
+Qualification compares the entire original/candidate result, every actual
+signed witness row, the ideal metadata and all local weights. It also checks120
+separate dyadic words with4,240 events, varied defect sites, reset, COPY and
+cancellation, plus three integer-contract rejection controls. The source's six
+controls remain active in every normal replay. `RESULT.json` records this scope.
+
+To repeat timings with Python3.12, run `benchmark.py --output /tmp/p104-error-times.json`
+from this package directory. Six complete processes run in sequence. Local
+macOS timings do not establish Linux or hosted CI performance. Python3.12 and
+the standard library suffice. The source export and source NOTICE files are
+retained unchanged. Registered, source-corruption and read-only Git-free
+optimized checks are separate from timing.
+
+`contract.py` adds four explicit parameter edits to the source runner and removes
+its old CLI. `CONTRACT-EDITS.json` authenticates that adaptation. The backend is
+passed as an ordinary argument. No runtime monkeypatch or import hook is used.
+The candidate keeps the original literal scalar and reverse-cut oracles.
+
+## Open next questions
+
+- Reproduce the complete six-process measurement on an idle Linux runner. Keep
+  all endpoint, error and failure checks, and report qualification cost separately.
+- If a later word needs new operations or nondyadic coefficients, prove a new
+  representation contract before using this backend. This package rejects them.
+- Bind actual native/rounded child and reset implementations to the retained
+  precision theorem. A faster replay does not discharge those assumptions.
+
+Source PR5826 at58f93cf41751920f3d6766a39caccc2974ce18b0. Credit PR5819,
+Adam Gall, ywz65, PR2878, Mason Hale/PR5811 and all retained P104/native/compiler
+sources. New backend and qualification by Ali Romman with substantial OpenAI
+Codex assistance; no subagents. Apache-2.0. No new kappa, frontier change,
+physical supplier admission or independent human acceptance is claimed.
+
+The source manifest pins replay inputs to copies in this publication history.
+Its `retained_predecessors` records keep each original head, path, blob and
+SHA256, plus its exact retained file or archive member. Each source was checked
+byte-for-byte before this rebind. This removes an unavailable side-commit
+dependency from clean CI; no source bytes or scientific checks are changed.

research/p104-integer-error-replay/RESULT.json

@@ -0,0 +1,22 @@
+{
+  "all_actual_witness_rows_equal": true,
+  "coefficient_scale_bits": 55,
+  "coordinates": 799,
+  "events": 25984,
+  "finite_fixtures": {
+    "cases": 120,
+    "controls": [
+      "nondyadic scalar",
+      "inexact scale division",
+      "nondyadic weight"
+    ],
+    "events": 4240
+  },
+  "guards": {
+    "owned": 22,
+    "prefix": 26,
+    "public": 23
+  },
+  "source_controls": 6,
+  "source_result_sha256": "cc7739703ed23532d187949c8507d09c13ac4c152e07a930f0087cde0d7a3d98"
+}

research/p104-integer-error-replay/SOURCES.json

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+  "base_commit": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
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+}