Mister-Meeseeks · Oct 15, 2026 · Oct 14, 2026
diff --git a/certificates/mixed-point-audit.json b/certificates/mixed-point-audit.json
@@ -486,7 +486,7 @@
   ],
   "source_sha256": {
     "docs/research/mixed-point-audit.md": "c80527f9e98c27bd7f5858a06c7273f84c40e0c41505eb4d16029b61f80fb968",
-    "scripts/experiments/mixed_point_circuit.py": "f509362b5031976a22af351fd158ae0b4520fa4f286a5176ec37023d672a7ddc",
+    "scripts/experiments/mixed_point_circuit.py": "cc98eeada267814fa2c0bc5f3ebb844f614d667c74d16d80d7ef29b1f90e0aa5",
     "scripts/rational_span_frames.py": "7386947406d5dc4322a39fb7ccd886876a2fa1d163e823f0f231e11cf9ca0cec"
   },
   "status": "BOUNDED MIXED-POINT RESEARCH; NO NEW KAPPA",

diff --git a/certificates/parity-side.json b/certificates/parity-side.json
@@ -121,7 +121,7 @@
     "scripts/audit_parity_side.py": "7cbdd405ce11fa6f7ffcbef3811174f8685ad4640e9330176601d3b3d3e95390",
     "scripts/binary_phase_frames.py": "4148cfa313cf050ed25296e8db36d35871520b8318fd086c7d1facf0c6af67d7",
     "scripts/experiments/disjoint_tensor.py": "085600fc922ae167b5981505e1a5caba4d1c1df15482f61d83d2c086fa89eac1",
-    "scripts/experiments/mixed_point_circuit.py": "f509362b5031976a22af351fd158ae0b4520fa4f286a5176ec37023d672a7ddc",
+    "scripts/experiments/mixed_point_circuit.py": "cc98eeada267814fa2c0bc5f3ebb844f614d667c74d16d80d7ef29b1f90e0aa5",
     "scripts/experiments/parity_phase_repair.py": "1f76f3b96ed556ed901835bd101d0e2588c997d2ed39bdfca097f0187aa86d40",
     "scripts/experiments/parity_side.py": "1363ebf82d4c39e458e7bede8253688271008374db70ed4284df84253c8d092b"
   },

diff --git a/research/mixed-point-verify-masks/NOTICE.md b/research/mixed-point-verify-masks/NOTICE.md
@@ -0,0 +1,12 @@
+# Notice — mixed-point verify masks
+
+Douglas R. Colkitt authored the mixed-point / early-sharing screens, the
+`Circuit` recurrence and interning, and the original exact-intersection
+support checks consumed by this tooling package.
+
+This package adds an equivalence-preserving closed-form rewrite of the
+historical `|source ∩ target| = r` expected-support genexpr inside
+`Circuit.verify`, with identical True receipts, matching output supports,
+and updated source pins only.
+
+Prepared by Wentao Li with substantial AI assistance, under Apache-2.0.
diff --git a/research/mixed-point-verify-masks/README.md b/research/mixed-point-verify-masks/README.md
@@ -0,0 +1,112 @@
+# Faster mixed-point Circuit.verify supports with identical receipts
+
+**Tooling improvement; no new kappa.** At base
+`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, merged
+[CrocSwap/integer-mult-bounds#1984](https://github.com/CrocSwap/integer-mult-bounds/pull/1984)
+sped up mixed-point `scalar_check` digests but left the general
+`Circuit.verify` path on `scripts/experiments/mixed_point_circuit.py` on the
+historical set-intersection genexpr
+
+```text
+sum(1<<i for i,source in enumerate(inputs) if len(set(source)&set(target))==r)
+```
+
+Profiling on `build(30,3,3,1)` shows that genexpr dominates `Circuit.verify`
+wall time (seconds per call; tens of seconds at h≈40). Open SharedPoint
+construction PRs (#2039/#2054) and DisjointTensor `frame_data` (#2117) leave
+this object free.
+
+This change replaces the genexpr with an equivalent closed-form point-incidence
+mask: precompute `vertex[p]`, then for each r-subset `U` of the target keep
+inputs that contain every point of `U` and avoid every other target point. Every
+output support still matches the historical checker, `verify` still returns
+`True`, and support admission uses `require` so it stays enforced under `-O`.
+Only the source pin for `scripts/experiments/mixed_point_circuit.py` changes
+inside the two certificates that bind that file.
+
+## Reproduce
+
+Python **3.12**, standard library only, from the repository root:
+
+```sh
+python3.12 -I -B research/mixed-point-verify-masks/verify.py
+python3.12 -I -O -B research/mixed-point-verify-masks/verify.py
+python3.12 -B scripts/research_package.py --package research/mixed-point-verify-masks
+python3.12 -I -B research/mixed-point-verify-masks/benchmark.py --rounds 5
+```
+
+Expected:
+
+```text
+PASS_MIXED_POINT_VERIFY_MASKS verify_cases=11 mask_cases=3994 certs=2 no_new_kappa
+PASS_REGISTERED_RESEARCH_PACKAGE research/mixed-point-verify-masks outcome=completed
+PASS_IDENTICAL_MIXED_POINT_VERIFY_MASK_RECEIPTS
+```
+
+Default verify is read-only. Full `make verify`, selected cold replay, Lean, and
+multiplication-theorem obligations were not rerun for this isolated
+historical-checker change.
+
+## Result
+
+On Linux / CPython 3.12.3 (Linux-6.12.94+-x86_64-with-glibc2.39), five
+alternating fresh-process pairs timing only `Circuit.verify` on the fixed
+fixture set `build(20,3,3,{0,1})`, `build(26,3,3,{0,1})`, `build(30,3,3,1)`
+(construction excluded) gave median wall time
+**8.331 → 0.121 seconds (69.03×)**.
+Timing is host-descriptive and is not a correctness gate; all samples and
+environment pins are in [RESULT.json](RESULT.json). Every verify receipt matches
+the baseline checker (`True` return and identical output-support fingerprints).
+
+## Equivalence
+
+For inputs indexed `0..p-1` and target point set `T` with `|T|=l`,
+
+- historical: bits of inputs `S` with `|S ∩ T| = r`
+- closed form: `OR_{U ⊆ T, |U|=r} ( (AND_{p in U} vertex[p]) & (AND_{p in T\U} (full ^ vertex[p])) )`
+
+where `vertex[p] = OR {1<<i : input i contains point p}` and
+`full = (1<<len(inputs))-1`. An XOR-of-vertex mutant (r=0) or OR-of-vertex
+mutant (r>0) differs and is rejected by the package controls. Topology of the
+constructed DAG is untouched; only the expected-support check is rewritten.
+
+## Open next questions
+
+1. **Question:** Is mixed-point `Circuit.add` / `build` construction worth a
+   separate identical-structure rewrite after this verify-path change?
+   **Why it matters:** On `build(50,3,3,1)`, `add()` is ~37% of wall time via
+   huge-int dict lookups; local binding alone was only ~1.09× in this session.
+   **First step:** Profile `Circuit.add` on the hybrid h=50 build with a
+   structure-identity oracle and prototype a faster intern path only if ≥~1.5×
+   with identical DAGs.
+   **Blocked by:** Out of this session’s stop rule.
+
+2. **Question:** Should `DisjointTensor.verify`'s `dag_sha256` `json.dumps` path
+   still get a hand-rolled formatter after #2117 `frame_data` lands?
+   **Why it matters:** Post-mask verify residual is mostly json/sha of huge
+   support strings; a streaming hand-roll was only ~1.22× on full verify here.
+   **First step:** Re-profile on a tip that includes #2117.
+   **Blocked by:** Micro-opt under the session bar; pin conflict with open #2117.
+
+## Overlap and credit
+
+Closest priors (different objects):
+[CrocSwap/integer-mult-bounds#756](https://github.com/CrocSwap/integer-mult-bounds/pull/756),
+[CrocSwap/integer-mult-bounds#1793](https://github.com/CrocSwap/integer-mult-bounds/pull/1793),
+[CrocSwap/integer-mult-bounds#1861](https://github.com/CrocSwap/integer-mult-bounds/pull/1861)
+(open; primary pin `binary_phase_frames.py` — same `parity-side.json` file,
+different key),
+[CrocSwap/integer-mult-bounds#1984](https://github.com/CrocSwap/integer-mult-bounds/pull/1984)
+(mixed-point `scalar_check` digests; this package answers the remaining general
+`Circuit.verify` support-genexpr object),
+[CrocSwap/integer-mult-bounds#1994](https://github.com/CrocSwap/integer-mult-bounds/pull/1994),
+[CrocSwap/integer-mult-bounds#2001](https://github.com/CrocSwap/integer-mult-bounds/pull/2001),
+[CrocSwap/integer-mult-bounds#2117](https://github.com/CrocSwap/integer-mult-bounds/pull/2117)
+(DisjointTensor `frame_data`; different file). No competing open PR on
+`Circuit.verify` at refresh.
+
+Douglas R. Colkitt authored the mixed-point and early-sharing screens and
+original checkers. Prepared by Wentao Li
+([VictorLiwentao](https://github.com/VictorLiwentao),
+[@Is__Victor](https://x.com/Is__Victor)) with substantial AI assistance, under
+Apache-2.0.
diff --git a/research/mixed-point-verify-masks/RESULT.json b/research/mixed-point-verify-masks/RESULT.json
@@ -0,0 +1,50 @@
+{
+  "environment": {
+    "executable": "/usr/bin/python3.12",
+    "platform": "Linux-6.12.94+-x86_64-with-glibc2.39",
+    "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]"
+  },
+  "fixture": "Circuit.verify on build(20/26/30,*,*,*) set (construction excluded)",
+  "median_baseline_seconds": 8.33077911800001,
+  "median_optimized_seconds": 0.12068828400003895,
+  "median_ratio": 69.0272397774528,
+  "no_new_kappa": true,
+  "rounds": 5,
+  "samples": [
+    {
+      "baseline_seconds": 8.394247341999971,
+      "optimized_seconds": 0.12226998500000263,
+      "ratio": 68.65337672201228,
+      "round": 0
+    },
+    {
+      "baseline_seconds": 8.326817022,
+      "optimized_seconds": 0.12068828400003895,
+      "ratio": 68.99441060904729,
+      "round": 1
+    },
+    {
+      "baseline_seconds": 8.33077911800001,
+      "optimized_seconds": 0.1204055650000555,
+      "ratio": 69.1893195966164,
+      "round": 2
+    },
+    {
+      "baseline_seconds": 8.44291771799999,
+      "optimized_seconds": 0.11961175099997945,
+      "ratio": 70.58602225463149,
+      "round": 3
+    },
+    {
+      "baseline_seconds": 8.279030670999987,
+      "optimized_seconds": 0.12259075400004349,
+      "ratio": 67.53389143031985,
+      "round": 4
+    }
+  ],
+  "source_sha256": {
+    "baseline": "f509362b5031976a22af351fd158ae0b4520fa4f286a5176ec37023d672a7ddc",
+    "production": "cc98eeada267814fa2c0bc5f3ebb844f614d667c74d16d80d7ef29b1f90e0aa5"
+  },
+  "status": "PASS_IDENTICAL_MIXED_POINT_VERIFY_MASK_RECEIPTS"
+}
diff --git a/research/mixed-point-verify-masks/SOURCES.json b/research/mixed-point-verify-masks/SOURCES.json
@@ -0,0 +1,54 @@
+{
+  "schema_version": 1,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "e8870e5917057d59b730eb14721a778639eca050",
+      "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "certificates/mixed-point-audit.json",
+      "usage": "provenance",
+      "git_blob": "e97c2e4e24a5e3f92bd9db6abc8e890e0417b3f6",
+      "sha256": "54659a3844c6f233b1d5b9f30ffab65742a5b2fe4a4b510dc809253b1180e95c"
+    },
+    {
+      "path": "certificates/parity-side.json",
+      "usage": "provenance",
+      "git_blob": "bcc1a78412d297424db1727f49636598206b9392",
+      "sha256": "44ab9d7b781a28228498aa0e73229c700eac4a3a3cf93ffe8f82f52f8c52226c"
+    },
+    {
+      "path": "docs/research/mixed-point-audit.md",
+      "usage": "provenance",
+      "git_blob": "31f712b8f78cee8a05b8cb490c8c979c79265ee2",
+      "sha256": "c80527f9e98c27bd7f5858a06c7273f84c40e0c41505eb4d16029b61f80fb968"
+    },
+    {
+      "path": "scripts/audit_mixed_point.py",
+      "usage": "provenance",
+      "git_blob": "53a2e05d0e82df7feb18eed271264f060874335d",
+      "sha256": "fc7ca3e07d8a3ad54e894c387a89b310ae0b7048763cd48bb27f5daeb0d73dba"
+    },
+    {
+      "path": "scripts/experiments/mixed_point_circuit.py",
+      "usage": "provenance",
+      "git_blob": "b7f561f416f815d0fd135f0a0464c291a9a68468",
+      "sha256": "f509362b5031976a22af351fd158ae0b4520fa4f286a5176ec37023d672a7ddc"
+    },
+    {
+      "path": "tests/test_mixed_point.py",
+      "usage": "provenance",
+      "git_blob": "1d97e9f9bbcd4d61f618fc562a0e22b58af59ad5",
+      "sha256": "bb279af4bf072e9709d70cefe0cdf0230688d865f9c5e902350c4aade9218452"
+    }
+  ]
+}
diff --git a/research/mixed-point-verify-masks/TASK.json b/research/mixed-point-verify-masks/TASK.json
@@ -0,0 +1,70 @@
+{
+  "schema_version": 1,
+  "task_id": "replay-runtime",
+  "priority_revision": 4,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "chooser_seed": "a41c9e7b2d805f63e0b1c7489a6d5e20",
+  "original_card": {
+    "id": "replay-runtime",
+    "question": "Can one measured replay bottleneck be sped up without dropping coverage?",
+    "starting_points": [
+      "scripts/run_isolated_tests.py",
+      "scripts/verify_replay_coverage.py",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Profile one isolated replay and optimize the measured bottleneck.",
+      "Design source-bound reuse with explicit dependency invalidation and negative controls."
+    ],
+    "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the selected reproduction command and choose a single replay stage for profiling.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.",
+    "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.",
+    "allowed_variations": [
+      "Profile one stage or design one source-bound cache boundary."
+    ],
+    "scope_change_triggers": [
+      "Skipping coverage or comparing different fixtures to claim speedup."
+    ],
+    "overlap_terms": [
+      "replay runtime",
+      "cache invalidation",
+      "isolated tests"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Can scripts/experiments/mixed_point_circuit.py:Circuit.verify replace its exact-|source∩target|=r expected-support genexpr with an equivalent closed-form point-incidence mask (OR over r-subsets U of the target of inputs that contain every point of U and avoid every other target point) so verify still returns True, every output support matches the historical checker, and support require() rejection is preserved on mixed-point and early-sharing replay sizes?",
+  "scope_change_reason": "The catalogue card asks for one measured replay bottleneck with before/after wall time and retained checks. Expertise override selected verifier-engineering after mixed-point scalar_check digests (#1984), SharedPoint digests (#1994), ExclusionCircuit/DisjointTensor support masks (#2001), and open leave-alone construction PRs (#2039/#2054). Profiling named Circuit.verify's set-intersection genexpr (tens of seconds on h≈40) as the next unclaimed mixed-point hot path; DisjointTensor.dag_sha256 hand-roll was measured at only ~1.22× on full verify and deferred.",
+  "bottleneck_link": "Side result on review throughput: tests/test_mixed_point.py and any caller of Circuit.verify pay the historical genexpr. A faster identical support check does not change kappa, scalar_check digests, or the binding complex supplier.",
+  "budget_minutes": 60,
+  "stop_rule": "Ship an equivalence-preserving Circuit.verify support-mask change with frozen baseline, identical True receipts plus matching output supports on historical sizes through h=30, updated source pins only on the two binding certificates, registered replay and a measured before/after median. Do not touch audit_mixed_point.scalar_check, SharedPoint, DisjointTensor.frame_data, or run the selected cold frontier replay.",
+  "outcome": "completed",
+  "evidence": "PASS_MIXED_POINT_VERIFY_MASKS via research/mixed-point-verify-masks/verify.py (also under -O); PASS_IDENTICAL_MIXED_POINT_VERIFY_MASK_RECEIPTS via benchmark.py; two certificates differ from base only in the scripts/experiments/mixed_point_circuit.py source pin.",
+  "author": "Wentao Li",
+  "github": "VictorLiwentao",
+  "email": "wentaol4@illinois.edu",
+  "ai_assistance": "Substantial AI assistance for orientation, overlap search, profiling, implementation, packaging, benchmarking and writing. Not independent human peer review.",
+  "open_questions": [
+    {
+      "question": "Is mixed-point Circuit.add / build construction worth a separate identical-structure rewrite after this verify-path change?",
+      "why_it_matters": "On build(50,3,3,1), add() is ~37% of wall time via huge-int dict lookups; local binding alone was only ~1.09× in this session.",
+      "first_step": "Profile Circuit.add on the hybrid h=50 build with a structure-identity oracle (args/support/lookup order) and prototype a faster intern path only if ≥~1.5× with identical DAGs.",
+      "blocked_by": "Out of this session's stop rule; Circuit.verify support masks were the measured bottleneck."
+    },
+    {
+      "question": "Should DisjointTensor.verify's dag_sha256 json.dumps path still get a hand-rolled formatter after #2117 frame_data lands?",
+      "why_it_matters": "Post-mask verify residual is ~69% json/sha of huge support strings; a streaming hand-roll was only ~1.22× on full verify here because bigint str() dominates.",
+      "first_step": "Re-profile on a tip that includes #2117 and decide whether a ≥1.5× identical-receipt residual remains.",
+      "blocked_by": "Micro-opt under the session bar; leave-alone pin conflict with open #2117 until that PR merges or a fold tip is chosen."
+    }
+  ]
+}
diff --git a/research/mixed-point-verify-masks/VERIFY.json b/research/mixed-point-verify-masks/VERIFY.json
@@ -0,0 +1,55 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "scripts/experiments/mixed_point_circuit.py",
+    "scripts/audit_mixed_point.py",
+    "certificates/mixed-point-audit.json",
+    "certificates/parity-side.json",
+    "docs/research/mixed-point-audit.md",
+    "tests/test_mixed_point.py",
+    "tests/test_mixed_point_verify_masks.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 480,
+      "checks": "Exact baseline copy of the base-commit mixed_point_circuit.py; closed-form exact-r masks match the historical genexpr with a mutant rejected; Circuit.verify returns True with identical output supports through h=30; two certificates differ from base only in the mixed_point_circuit.py source pin; duplicate JSON keys rejected."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 480,
+      "checks": "Same equivalence and certificate pin discipline under -O (require() gates, not assert)."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "-m",
+        "unittest",
+        "discover",
+        "-s",
+        "tests",
+        "-p",
+        "test_mixed_point_verify_masks.py",
+        "-v"
+      ],
+      "timeout_seconds": 180,
+      "checks": "Focused mixed-point verify-mask package controls."
+    }
+  ]
+}