Ranked slot reclamation: conditional κ = 4.764513337e-5

Makefile

@@ -297,6 +297,19 @@ formal-gaussian-verify:
 	$(MAKE) -C research/gaussian-parity-synthesis verify
 	python3 scripts/check_lean_axioms.py --project research/gaussian-parity-synthesis --audit research/gaussian-parity-synthesis/AuditAll.lean
 
+.PHONY: skip-frame-verify
+skip-frame-verify:
+	python3 scripts/experiments/verify_skip_frame.py
+
+verify-community: skip-frame-verify
+
+.PHONY: joint-dual-verify
+joint-dual-verify:
+	python3 scripts/experiments/verify_joint_dual.py
+	python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v
+
+verify-community: joint-dual-verify
+
 .PHONY: verify-research
 # Historical finite searches; no current witness or production certificates change.
 verify-research:

NOTICE

@@ -203,3 +203,39 @@ Ryan S / princezuda contributes historical Lean certificate arithmetic, algebrai
 frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
 source notices and historical snapshots are preserved. Neither formal package
 claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.

README.md

@@ -28,6 +28,25 @@ AI-assistance disclosures remain credited in the source notices.
 [Maintainer review](docs/research/community-followup-review.md) ·
 [Integration record](docs/research/community-followup-integration.md)
 
+## Additional conditional composition: dual-skip strips with joint frames
+
+The [joint-dual proof and reproduction guide](research/joint-dual/README.md)
+gives **κ=4764513337/10^14=4.764513337e-5**, approximately **0.2900108%**
+above PR58's conditional saving. It retains **Rohan Gupta's PR55 dual-skip
+graph** and **eumemic's PR57 joint frame compiler** while prioritizing retired
+slots by descending current frame rank. The dedicated variant preserves the
+original shared compiler, exact recovery and all predecessor credits.
+This is an additional conditional witness; it does not extend the scope
+of the maintainer-reviewed community result above.
+
+The physical roles are R23=30688 and R25=40338, giving W=150167598. The
+[exact certificate](certificates/joint-dual-kappa.json) checks the complete
+recursive child list and all 47 strict assembly inequalities/seven margins.
+`make joint-dual-verify` regenerates both physical words, replays every dirty
+basis vector, independently reconstructs transitions and recertifies the
+actual fixed-I+J profiles. `make verify` retains all preceding checks.
+Prepared by Chafik Boukhalfa with OpenAI Codex assistance.
+
 ## What changed
 
 The community work combines recursive batching and partial-swap frames with

certificates/joint-dual-compiler.json

@@ -0,0 +1,233 @@
+{
+  "axes": {
+    "23": {
+      "compiled": {
+        "all_physical_frame_inclusions": true,
+        "baseline_pr48_roles": 36432,
+        "baseline_pr57_roles": 31416,
+        "baseline_pr58_roles": 30790,
+        "complete_dirty_basis_both_orientations": true,
+        "dirty_basis_vectors": 34230,
+        "elementary_xors": 112534,
+        "h": 23,
+        "histogram": {
+          "0": 224916,
+          "1": 42027,
+          "10": 2566,
+          "11": 385,
+          "12": 2901,
+          "13": 115,
+          "14": 3245,
+          "15": 544,
+          "16": 1935,
+          "17": 187,
+          "18": 8185,
+          "19": 4473,
+          "2": 38232,
+          "21": 27,
+          "22": 23,
+          "3": 6306,
+          "4": 18054,
+          "5": 8192,
+          "6": 4437,
+          "7": 1089,
+          "8": 3900,
+          "9": 331
+        },
+        "mode": {
+          "matching": true,
+          "reclaim": true
+        },
+        "rank_mass": 706330,
+        "reclamation_order": "descending current frame rank, then slot ID",
+        "roles": 30688,
+        "scalar": {
+          "additions": 40099,
+          "all_additions_disjoint": true,
+          "all_partial_outputs_exact": true,
+          "circuit_sha256": "1b72f612aaf99fff5a34f2224cc747324a825032367ffd8b0eebc643d6266b47",
+          "every_node_has_common_point": true,
+          "h": 23,
+          "inputs": 1771,
+          "merged_additions": 5379,
+          "partial_outputs": 5336,
+          "roles": 45435
+        },
+        "source_pr55_head": "03e991aa79f9df1a935726213bb6a8631cd0d823",
+        "stats": {
+          "augmentations": 220,
+          "clearing_xors": 4284,
+          "matched": 11974,
+          "multi_node_regions": 4370,
+          "reclaimed": 1853,
+          "regions": 36626
+        }
+      },
+      "gzip_sha256": "634da1cb39634be15c6d4070132c6bdf4f5a927331cac3b4f13dc995dd799b6b",
+      "replay": {
+        "elementary_xors": 112534,
+        "full_basis_vectors": 34230,
+        "h": 23,
+        "histogram": {
+          "0": 121045,
+          "1": 42027,
+          "10": 2566,
+          "11": 385,
+          "12": 2901,
+          "13": 115,
+          "14": 3245,
+          "15": 544,
+          "16": 1935,
+          "17": 187,
+          "18": 8185,
+          "19": 4473,
+          "2": 38232,
+          "21": 27,
+          "22": 23,
+          "3": 6306,
+          "4": 18054,
+          "5": 8192,
+          "6": 4437,
+          "7": 1089,
+          "8": 3900,
+          "9": 331
+        },
+        "output_roles": 5336,
+        "rank_mass": 706330,
+        "roles": 30688,
+        "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS",
+        "word_length": 474930
+      },
+      "word_sha256": "c83396d1ea5427eed332c45931d59ed0c8ea5eae23d16e0ea909854d41796d1e"
+    },
+    "25": {
+      "compiled": {
+        "all_physical_frame_inclusions": true,
+        "baseline_pr48_roles": 48329,
+        "baseline_pr57_roles": 41264,
+        "baseline_pr58_roles": 40446,
+        "complete_dirty_basis_both_orientations": true,
+        "dirty_basis_vectors": 44938,
+        "elementary_xors": 148820,
+        "h": 25,
+        "histogram": {
+          "0": 297333,
+          "1": 54602,
+          "10": 3073,
+          "11": 85,
+          "12": 3381,
+          "13": 310,
+          "14": 3389,
+          "15": 113,
+          "16": 4218,
+          "17": 630,
+          "18": 2510,
+          "19": 369,
+          "2": 50062,
+          "20": 10763,
+          "21": 5705,
+          "23": 39,
+          "24": 25,
+          "3": 8295,
+          "4": 24232,
+          "5": 10287,
+          "6": 4330,
+          "7": 1843,
+          "8": 5262,
+          "9": 860
+        },
+        "mode": {
+          "matching": true,
+          "reclaim": true
+        },
+        "rank_mass": 1009050,
+        "reclamation_order": "descending current frame rank, then slot ID",
+        "roles": 40338,
+        "scalar": {
+          "additions": 53175,
+          "all_additions_disjoint": true,
+          "all_partial_outputs_exact": true,
+          "circuit_sha256": "2344a4fbc7bd47f78d674d54a8b3e56d43918bbea5fe5deceb95e6fb4a655c21",
+          "every_node_has_common_point": true,
+          "h": 25,
+          "inputs": 2300,
+          "merged_additions": 7008,
+          "partial_outputs": 6925,
+          "roles": 60100
+        },
+        "source_pr55_head": "03e991aa79f9df1a935726213bb6a8631cd0d823",
+        "stats": {
+          "augmentations": 286,
+          "clearing_xors": 5714,
+          "matched": 16276,
+          "multi_node_regions": 6025,
+          "reclaimed": 2711,
+          "regions": 48675
+        }
+      },
+      "gzip_sha256": "dd2223d7ee0b91c4445f5acd0b7cad945f56f4e16456b6818f53ddef64a0cb16",
+      "replay": {
+        "elementary_xors": 148820,
+        "full_basis_vectors": 44938,
+        "h": 25,
+        "histogram": {
+          "0": 159745,
+          "1": 54602,
+          "10": 3073,
+          "11": 85,
+          "12": 3381,
+          "13": 310,
+          "14": 3389,
+          "15": 113,
+          "16": 4218,
+          "17": 630,
+          "18": 2510,
+          "19": 369,
+          "2": 50062,
+          "20": 10763,
+          "21": 5705,
+          "23": 39,
+          "24": 25,
+          "3": 8295,
+          "4": 24232,
+          "5": 10287,
+          "6": 4330,
+          "7": 1843,
+          "8": 5262,
+          "9": 860
+        },
+        "output_roles": 6925,
+        "rank_mass": 1009050,
+        "roles": 40338,
+        "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS",
+        "word_length": 627480
+      },
+      "word_sha256": "6f6dca829728cb01e6c425ada5878884b13bc6362e0ae2144347bde8a5852dbf"
+    }
+  },
+  "compiler_source": {
+    "author": "eumemic with substantial OpenAI Codex assistance",
+    "commit": "cd350f76c9bc01489ec83568bded532cb69be938",
+    "pull_request": 57
+  },
+  "reclamation_priority": {
+    "author": "Chafik Boukhalfa with OpenAI Codex assistance",
+    "base_pr58_commit": "bc2f7ed4c20dc18898305ab17165c0c995cbb804",
+    "dedicated_engine": "scripts/experiments/joint_dual_reclaim_compiler.py",
+    "order": "descending current frame rank, then slot ID",
+    "shared_pr57_engine_unchanged": true
+  },
+  "source": {
+    "author": "Rohan Gupta / gupt1156 with Anthropic Claude assistance",
+    "commit": "03e991aa79f9df1a935726213bb6a8631cd0d823",
+    "files": {
+      "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+      "NOTICE": "40a3066696e0de23e46b565460d19e85b435990ba837da5c1ca925335f4ba829",
+      "research/skip-suffix/skip_graph.py": "7c4781dcc3c134befd8abf295d1e71a99fbbe932112fb56bd5d36e79896ca5f7"
+    },
+    "shared_dependency_manifest": "../pr48/SOURCE.json",
+    "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3",
+    "upstream": "https://github.com/CrocSwap/integer-mult-bounds/pull/55"
+  },
+  "status": "Exact finite scalar/frame words; complete replay and conditional arithmetic are separately verified"
+}