diff --git a/Makefile b/Makefile index df42f914cf..aeb525411b 100644 --- a/Makefile +++ b/Makefile @@ -295,3 +295,9 @@ formal-historical-verify: 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 diff --git a/NOTICE b/NOTICE index 3769520e39..889a6679b5 100644 --- a/NOTICE +++ b/NOTICE @@ -203,3 +203,16 @@ 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. diff --git a/certificates/skip-frame-compiler.json b/certificates/skip-frame-compiler.json new file mode 100644 index 0000000000..21a8212d5d --- /dev/null +++ b/certificates/skip-frame-compiler.json @@ -0,0 +1,223 @@ +{ + "axes": { + "23": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 36432, + "baseline_pr53_roles": 32946, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 34958, + "elementary_xors": 111687, + "h": 23, + "histogram": { + "0": 224441, + "1": 41963, + "10": 3066, + "11": 199, + "12": 2842, + "13": 182, + "14": 3698, + "15": 693, + "16": 2028, + "17": 464, + "18": 8238, + "19": 4308, + "2": 37406, + "21": 28, + "22": 23, + "3": 6490, + "4": 17479, + "5": 8001, + "6": 4554, + "7": 1783, + "8": 3533, + "9": 643 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 723074, + "roles": 31416, + "scalar": { + "additions": 40329, + "all_additions_disjoint": true, + "all_partial_outputs_exact": true, + "circuit_sha256": "0e309c2023b2832f82badf010649417acfa0cf423b3137c25babf0d7746eb32c", + "every_node_has_common_point": true, + "h": 23, + "inputs": 1771, + "merged_additions": 5379, + "partial_outputs": 5336, + "roles": 45665 + }, + "source_pr53_head": "3ffd4021995c959ac02d12920e0279ae97dd03c7", + "stats": { + "augmentations": 165, + "clearing_xors": 3184, + "matched": 12029, + "multi_node_regions": 4324, + "reclaimed": 1530, + "regions": 36626 + }, + "word_path": "/private/tmp/frame-pr53-compiler/word23.json.gz", + "word_sha256": "15c6ed702033d3bc55c17bee42bbaf7ed45245c3cf1ea14e9eedd225f8af9823" + }, + "gzip_sha256": "15c6ed702033d3bc55c17bee42bbaf7ed45245c3cf1ea14e9eedd225f8af9823", + "replay": { + "elementary_xors": 111687, + "full_basis_vectors": 34958, + "h": 23, + "histogram": { + "0": 119612, + "1": 41963, + "10": 3066, + "11": 199, + "12": 2842, + "13": 182, + "14": 3698, + "15": 693, + "16": 2028, + "17": 464, + "18": 8238, + "19": 4308, + "2": 37406, + "21": 28, + "22": 23, + "3": 6490, + "4": 17479, + "5": 8001, + "6": 4554, + "7": 1783, + "8": 3533, + "9": 643 + }, + "output_roles": 5336, + "rank_mass": 723074, + "roles": 31416, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 471542 + }, + "word_sha256": "1e1160caecbdfbb75961bf7a88a53189217840262c6bb724248c38f2b8f4c61a" + }, + "25": { + "compiled": { + "all_physical_frame_inclusions": true, + "baseline_pr48_roles": 48329, + "baseline_pr53_roles": 43409, + "complete_dirty_basis_both_orientations": true, + "dirty_basis_vectors": 45864, + "elementary_xors": 148996, + "h": 25, + "histogram": { + "0": 298212, + "1": 54790, + "10": 3160, + "11": 356, + "12": 3951, + "13": 336, + "14": 2971, + "15": 155, + "16": 4523, + "17": 1151, + "18": 2722, + "19": 267, + "2": 49085, + "20": 10833, + "21": 5514, + "23": 36, + "24": 25, + "3": 8302, + "4": 24492, + "5": 10155, + "6": 4451, + "7": 2776, + "8": 5261, + "9": 696 + }, + "mode": { + "matching": true, + "reclaim": true + }, + "rank_mass": 1032200, + "roles": 41264, + "scalar": { + "additions": 53475, + "all_additions_disjoint": true, + "all_partial_outputs_exact": true, + "circuit_sha256": "52eca99391ab5b7cf85ee80e20846570cfc7b8812e2949990f4f081d6c67bfd4", + "every_node_has_common_point": true, + "h": 25, + "inputs": 2300, + "merged_additions": 7008, + "partial_outputs": 6925, + "roles": 60400 + }, + "source_pr53_head": "3ffd4021995c959ac02d12920e0279ae97dd03c7", + "stats": { + "augmentations": 231, + "clearing_xors": 5425, + "matched": 16341, + "multi_node_regions": 5875, + "reclaimed": 2145, + "regions": 48675 + }, + "word_path": "/private/tmp/frame-pr53-compiler/word25.json.gz", + "word_sha256": "cd60a7721d09dd76ed4abd5d003f28f72fb27c2b055f73fc02bc3f6d2e51705c" + }, + "gzip_sha256": "cd60a7721d09dd76ed4abd5d003f28f72fb27c2b055f73fc02bc3f6d2e51705c", + "replay": { + "elementary_xors": 148996, + "full_basis_vectors": 45864, + "h": 25, + "histogram": { + "0": 159398, + "1": 54790, + "10": 3160, + "11": 356, + "12": 3951, + "13": 336, + "14": 2971, + "15": 155, + "16": 4523, + "17": 1151, + "18": 2722, + "19": 267, + "2": 49085, + "20": 10833, + "21": 5514, + "23": 36, + "24": 25, + "3": 8302, + "4": 24492, + "5": 10155, + "6": 4451, + "7": 2776, + "8": 5261, + "9": 696 + }, + "output_roles": 6925, + "rank_mass": 1032200, + "roles": 41264, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 628184 + }, + "word_sha256": "206f27211025bea997f8c546b0e1dd40675e0d8d77febf65040554ac1b1ba900" + } + }, + "source": { + "attribution": "Avi Eisenberg / ikeboy with Anthropic Claude assistance: skip-prefix layout; inherited authors retained in NOTICE and source headers. 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"attribution": "Avi Eisenberg / ikeboy with Anthropic Claude assistance: skip-prefix layout; inherited authors retained in NOTICE and source headers. Local joint frame synthesis uses OpenAI Codex assistance.", + "files": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "40a3066696e0de23e46b565460d19e85b435990ba837da5c1ca925335f4ba829", + "research/skip-strips/skip_graph.py": "03ee019cdaf73391455aaf4f5dcb4873f4fdcb278179b296c02ea39eafd047e4" + }, + "head": "3ffd4021995c959ac02d12920e0279ae97dd03c7", + "repository": "ikeboy/integer-mult-bounds", + "scope": "Unmodified skip-prefix graph and attribution; shared circuit code and analytic/data interfaces are the byte-identical pinned PR48 sources in ../pr48.", + "shared_dependency_manifest": "../pr48/SOURCE.json", + "shared_dependency_manifest_sha256": "6ccc673f88d3650d75ed600b082fe2fc2866dd88a172d182a38c1d0cd27d24b3", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/53" + } + ], + "status": "Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed" +} diff --git a/certificates/skip-frame-mechanism-review.json b/certificates/skip-frame-mechanism-review.json new file mode 100644 index 0000000000..49b2b5b95b --- /dev/null +++ b/certificates/skip-frame-mechanism-review.json @@ -0,0 +1,63 @@ +{ + "status": "No finite-mechanism blocker found in source review of pinned PR53 combination", + "source_pr53_head": "3ffd4021995c959ac02d12920e0279ae97dd03c7", + "compiler_sha256": "bc6910c8bbe8224285164323d3c06e9035ad3eaa55416abc2867ae0066454a0c", + "word_sha256": { + "23": "15c6ed702033d3bc55c17bee42bbaf7ed45245c3cf1ea14e9eedd225f8af9823", + "25": "cd60a7721d09dd76ed4abd5d003f28f72fb27c2b055f73fc02bc3f6d2e51705c" + }, + "findings": [ + { + "area": "Region causality", + "finding": "Original edges nest core/cover envelopes. A strict change increases dimension; equal envelopes are merged. Rank/min-node order therefore respects the quotient DAG, and local node order preserves each region calculation. PR53 changes this DAG only; its scalar hash and the unchanged inherited producer modules were checked." + }, + { + "area": "Whole-region reversible map", + "finding": "Incoming deliveries occupy distinct physical roles. Independent demanded output rows, independent preserved input unit rows and unit-vector completion form an invertible square matrix on ALL incoming dirty coordinates. Reverse Gaussian row operations synthesize that literal matrix. Dependent demanded signals are computed into fresh or signal-cleared distinct roles, never by identifying occupied outputs." + }, + { + "area": "Continuation matching", + "finding": "Each recipient use is unique, each selected preserved row is independent modulo the output row space, and every continuation has a strictly later group and containing frame. Compilation asserts distinct simultaneous input roles and exact arriving signals. Matching optimality is not needed for validity and is not certified by this audit." + }, + { + "area": "Signal clearing and dirty restoration", + "finding": "Reclamation clears only the input-dependent component of a retired role using a fixed invertible sequence of XORs. Arbitrary old dirty components remain linear noise. With mixer L, injection V and read-only scatter J, JLV=I; L,J,L^-1,V,L,J,L^-1,V cancels JLz and restores every auxiliary for arbitrary initial z. Full previously completed forward and reverse-complement basis replays cover this distinction." + }, + { + "area": "Frames and terminal contract", + "finding": "All block/XOR participants meet at one original envelope. Retired clearing anchors are used only when their current frames lie in it; live output anchors are already there. Every role moves monotonically until its charged terminal/copy actions. Original envelopes are positive inside a common-point Ui; dual complements remain nondegenerate. Designated outputs remain distinct terminal roles, so copied centers and existing invocation endpoints apply unchanged." + }, + { + "area": "Cost accounting", + "finding": "Every allocated role exits, yielding copied local mass hR+h(h-1). Extra clearing XORs remain present in the literal word. The profiler independently reconstructs positive frame transitions from that word, compares against event records, charges copied-center and side endpoint costs, and separately certifies fixed I+J profiles. No positive transition is justified by role counts alone." + } + ], + "zero_rank_bookkeeping": { + "explanation": "Compiler emits a prealignment when each new scratch role is allocated and when each block input is gathered, then emits XOR incidence checks too. Replay initializes primary sources and visits actual XOR/output incidences only. Omitted duplicate incidences are identity frame changes: zero rank, no recursive child. All strictly positive buckets agree; profile preparation also requires the identical nonidentity transition multiset reconstructed from the XOR word. Zero-rank address bookkeeping does not remove actual scalar XORs from the program.", + "rows": [ + { + "h": 23, + "compiler_zero": 224441, + "replay_zero": 119612, + "extra_bookkeeping_incidents": 104829, + "fresh_role_prealignments": 29645, + "block_input_prealignments": 75184, + "all_positive_buckets_equal": true + }, + { + "h": 25, + "compiler_zero": 298212, + "replay_zero": 159398, + "extra_bookkeeping_incidents": 138814, + "fresh_role_prealignments": 38964, + "block_input_prealignments": 99850, + "all_positive_buckets_equal": true + } + ] + }, + "scope": { + "work_this_review": "Source inspection and lightweight comparison of saved receipts/events only; no repeated full producer, dirty basis, CRT or assembly test.", + "retained_evidence": "Previously passed complete scalar, frame, full dirty-basis both orientations, fixed-profile CRT and exact assembly receipts; parent additionally reports portable verification and byte-identical regeneration.", + "limitations": "Finite mechanism review only. General common-frame compiler/partial-swap transfer, controlled-basis physical interpretation, fixed-tape routing and analytic multiplication framework remain inherited written proof obligations." + } +} diff --git a/certificates/skip-frame-profiles-23.json b/certificates/skip-frame-profiles-23.json new file mode 100644 index 0000000000..f9c392a475 --- /dev/null +++ b/certificates/skip-frame-profiles-23.json @@ -0,0 +1 @@ +{"h":23,"v":1771,"R":31416,"loss":506,"rank_sum":723074,"field_prime":2305843009213693951,"frames":36628,"distinct_matrices":60989,"crt_matrices":6373,"crt_disagreements":0,"blocks":[0,296747,23148,15450,8944,7434,5742,6213,4059,3514,2521,2459,1609,1292,852,559,370,145,55,0,8,23,0,0]} diff --git a/certificates/skip-frame-profiles-25.json b/certificates/skip-frame-profiles-25.json new file mode 100644 index 0000000000..776d70e487 --- /dev/null +++ b/certificates/skip-frame-profiles-25.json @@ -0,0 +1 @@ +{"h":25,"v":2300,"R":41264,"loss":600,"rank_sum":1032200,"field_prime":2305843009213693951,"frames":48677,"distinct_matrices":81960,"crt_matrices":8518,"crt_disagreements":0,"blocks":[0,397490,32075,19149,11001,10196,8228,8271,5415,5322,3959,3942,2552,2192,1649,1303,816,557,398,155,79,0,7,25,0,0]} diff --git a/certificates/skip-frame-repository-validation.json b/certificates/skip-frame-repository-validation.json new file mode 100644 index 0000000000..b6bd91611d --- /dev/null +++ b/certificates/skip-frame-repository-validation.json @@ -0,0 +1,46 @@ +{ + "base_commit": "64ed4cbf872b86b81c22f104967b88d24b8e4548", + "command": "make verify", + "complete_focused_certificate_included": true, + "completed_at_utc": "2026-10-08T17:15:40.161328+00:00", + "exact_primary_prime_recoveries": 10, + "exit_code": 0, + "full_log_bytes": 89593, + "full_log_sha256": "e7d271e0db1530e2c26a157b114ad46cacc19c5e476eca6e37e909b2e766bf33", + "historical_patch_checks": [ + "patches/frozen-154.patch", + "patches/balanced-153.patch", + "patches/same-network-129.patch", + "patches/h46-111.patch", + "patches/h46-109.patch", + "patches/h46-108.patch", + "patches/h46-rational.patch", + "patches/nonadjacent-layout.patch", + "patches/frozen-nonadjacent-107.patch", + "patches/h46-nonadjacent-78.patch", + "patches/h46-nonadjacent-76.patch", + "patches/h46-shared-side-75.patch", + "patches/h46-incidence-67.patch", + "patches/h46-dag-63.patch", + "patches/h46-shared-point.patch", + "patches/h50-paired-59.patch", + "patches/compact-control-34.patch", + "patches/complex-compression-31.patch", + "patches/ternary-30.patch", + "patches/batched-23.patch" + ], + "integrated_unit_tests": 246, + "python": "3.11.5", + "scope": "Finite checks and retained historical suites; no Lean build or formal proof of inherited all-size compiler/tape/analytic interfaces is claimed.", + "status": "PASS", + "test_suite_counts": [ + 12, + 10, + 17, + 5, + 246 + ], + "tested_commit": "cd350f76c9bc01489ec83568bded532cb69be938", + "tracked_worktree_clean_after_verification": true, + "unchanged_inherited_data_pairs_replayed": 4073300 +} diff --git a/certificates/skip-frame-reproduction.json b/certificates/skip-frame-reproduction.json new file mode 100644 index 0000000000..d631356463 --- /dev/null +++ b/certificates/skip-frame-reproduction.json @@ -0,0 +1,17 @@ +{ + "axes": { + "23": { + "byte_identical_after_decompression": true, + "command": "python3 scripts/experiments/skip_frame_compiler.py --h 23 --output /tmp/skip23.json --word /tmp/skip23.json.gz", + "word_sha256": "1e1160caecbdfbb75961bf7a88a53189217840262c6bb724248c38f2b8f4c61a" + }, + "25": { + "byte_identical_after_decompression": true, + "command": "python3 scripts/experiments/skip_frame_compiler.py --h 25 --output /tmp/skip25.json --word /tmp/skip25.json.gz", + "word_sha256": "206f27211025bea997f8c546b0e1dd40675e0d8d77febf65040554ac1b1ba900" + } + }, + "compiler_sha256": "8ffd079fd2e4f055b5befefecc5f33e686de9898219e9252f5d3913df8b195d8", + "gzip_note": "Compressed headers may differ with the output filename; complete decompressed words are identical.", + "status": "PASS portable compiler regeneration for both axes" +} diff --git a/certificates/skip-frame-transitions-23.json b/certificates/skip-frame-transitions-23.json new file mode 100644 index 0000000000..140a12dbf5 --- /dev/null +++ b/certificates/skip-frame-transitions-23.json @@ -0,0 +1,35 @@ +{ + "h": 23, + "v": 1771, + "R": 31416, + "frames": 36628, + "distinct_transitions": 117385, + "singles": 15939, + "rank_mass": 723074, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 52589, + "2": 32093, + "3": 6490, + "4": 17479, + "5": 8001, + "6": 4554, + "7": 1783, + "8": 3533, + "9": 643, + "10": 3066, + "11": 199, + "12": 2842, + "13": 182, + "14": 3698, + "15": 693, + "16": 2028, + "17": 464, + "18": 8238, + "19": 4308, + "21": 28, + "22": 23 + }, + "word_sha256": "1e1160caecbdfbb75961bf7a88a53189217840262c6bb724248c38f2b8f4c61a", + "copied_centers": 23, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/certificates/skip-frame-transitions-25.json b/certificates/skip-frame-transitions-25.json new file mode 100644 index 0000000000..1f233f963d --- /dev/null +++ b/certificates/skip-frame-transitions-25.json @@ -0,0 +1,37 @@ +{ + "h": 25, + "v": 2300, + "R": 41264, + "frames": 48677, + "distinct_transitions": 155696, + "singles": 20700, + "rank_mass": 1032200, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 68590, + "2": 42185, + "3": 8302, + "4": 24492, + "5": 10155, + "6": 4451, + "7": 2776, + "8": 5261, + "9": 696, + "10": 3160, + "11": 356, + "12": 3951, + "13": 336, + "14": 2971, + "15": 155, + "16": 4523, + "17": 1151, + "18": 2722, + "19": 267, + "20": 10833, + "21": 5514, + "23": 36, + "24": 25 + }, + "word_sha256": "206f27211025bea997f8c546b0e1dd40675e0d8d77febf65040554ac1b1ba900", + "copied_centers": 25, + "transition_events_equal_independent_xor_word_reconstruction": true +} diff --git a/certificates/skip-frame-validation.json b/certificates/skip-frame-validation.json new file mode 100644 index 0000000000..700f8f3459 --- /dev/null +++ b/certificates/skip-frame-validation.json @@ -0,0 +1,236 @@ +{ + "axes": { + "23": { + "profile": { + "R": 31416, + "blocks": [ + 0, + 296747, + 23148, + 15450, + 8944, + 7434, + 5742, + 6213, + 4059, + 3514, + 2521, + 2459, + 1609, + 1292, + 852, + 559, + 370, + 145, + 55, + 0, + 8, + 23, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 6373, + "distinct_matrices": 60989, + "field_prime": 2305843009213693951, + "frames": 36628, + "h": 23, + "loss": 506, + "rank_sum": 723074, + "v": 1771 + }, + "replay": { + "elementary_xors": 111687, + "full_basis_vectors": 34958, + "h": 23, + "histogram": { + "0": 119612, + "1": 41963, + "2": 37406, + "3": 6490, + "4": 17479, + "5": 8001, + "6": 4554, + "7": 1783, + "8": 3533, + "9": 643, + "10": 3066, + "11": 199, + "12": 2842, + "13": 182, + "14": 3698, + "15": 693, + "16": 2028, + "17": 464, + "18": 8238, + "19": 4308, + "21": 28, + "22": 23 + }, + "output_roles": 5336, + "rank_mass": 723074, + "roles": 31416, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 471542 + }, + "transitions": { + "R": 31416, + "copied_centers": 23, + "distinct_transitions": 117385, + "frames": 36628, + "h": 23, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 52589, + "2": 32093, + "3": 6490, + "4": 17479, + "5": 8001, + "6": 4554, + "7": 1783, + "8": 3533, + "9": 643, + "10": 3066, + "11": 199, + "12": 2842, + "13": 182, + "14": 3698, + "15": 693, + "16": 2028, + "17": 464, + "18": 8238, + "19": 4308, + "21": 28, + "22": 23 + }, + "rank_mass": 723074, + "singles": 15939, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 1771, + "word_sha256": "1e1160caecbdfbb75961bf7a88a53189217840262c6bb724248c38f2b8f4c61a" + } + }, + "25": { + "profile": { + "R": 41264, + "blocks": [ + 0, + 397490, + 32075, + 19149, + 11001, + 10196, + 8228, + 8271, + 5415, + 5322, + 3959, + 3942, + 2552, + 2192, + 1649, + 1303, + 816, + 557, + 398, + 155, + 79, + 0, + 7, + 25, + 0, + 0 + ], + "crt_disagreements": 0, + "crt_matrices": 8518, + "distinct_matrices": 81960, + "field_prime": 2305843009213693951, + "frames": 48677, + "h": 25, + "loss": 600, + "rank_sum": 1032200, + "v": 2300 + }, + "replay": { + "elementary_xors": 148996, + "full_basis_vectors": 45864, + "h": 25, + "histogram": { + "0": 159398, + "1": 54790, + "2": 49085, + "3": 8302, + "4": 24492, + "5": 10155, + "6": 4451, + "7": 2776, + "8": 5261, + "9": 696, + "10": 3160, + "11": 356, + "12": 3951, + "13": 336, + "14": 2971, + "15": 155, + "16": 4523, + "17": 1151, + "18": 2722, + "19": 267, + "20": 10833, + "21": 5514, + "23": 36, + "24": 25 + }, + "output_roles": 6925, + "rank_mass": 1032200, + "roles": 41264, + "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS", + "word_length": 628184 + }, + "transitions": { + "R": 41264, + "copied_centers": 25, + "distinct_transitions": 155696, + "frames": 48677, + "h": 25, + "rank_histogram_with_side_growth_split_into_singletons": { + "1": 68590, + "2": 42185, + "3": 8302, + "4": 24492, + "5": 10155, + "6": 4451, + "7": 2776, + "8": 5261, + "9": 696, + "10": 3160, + "11": 356, + "12": 3951, + "13": 336, + "14": 2971, + "15": 155, + "16": 4523, + "17": 1151, + "18": 2722, + "19": 267, + "20": 10833, + "21": 5514, + "23": 36, + "24": 25 + }, + "rank_mass": 1032200, + "singles": 20700, + "transition_events_equal_independent_xor_word_reconstruction": true, + "v": 2300, + "word_sha256": "206f27211025bea997f8c546b0e1dd40675e0d8d77febf65040554ac1b1ba900" + } + } + }, + "bit_saving": "116741511/2500000000000", + "certificate_sha256": "d6d2ed145539af1acfe95c0df1ceac155fa359d43590ac772cbe1938f92f0092", + "kappa": "4669442391/100000000000000", + "margins": 7, + "scope": "Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.", + "source_binding": "Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.", + "status": "PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly", + "strict_constraints": 47 +} diff --git a/certificates/skip-frame-word-23.json.gz b/certificates/skip-frame-word-23.json.gz new file mode 100644 index 0000000000..6d59a725de Binary files /dev/null and b/certificates/skip-frame-word-23.json.gz differ diff --git a/certificates/skip-frame-word-25.json.gz b/certificates/skip-frame-word-25.json.gz new file mode 100644 index 0000000000..e802225380 Binary files /dev/null and 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/references/frame-compiler/pr48/NOTICE b/references/frame-compiler/pr48/NOTICE new file mode 100644 index 0000000000..a8474f5c31 --- /dev/null +++ b/references/frame-compiler/pr48/NOTICE @@ -0,0 +1,149 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The new research note, scripts, certificates, patches, and documentation +were prepared by Douglas Colkitt with assistance from OpenAI Codex. +This project is not an official OpenAI release or an OpenAI endorsement. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. diff --git a/references/frame-compiler/pr48/SOURCE.json b/references/frame-compiler/pr48/SOURCE.json new file mode 100644 index 0000000000..4e38e34dc8 --- /dev/null +++ b/references/frame-compiler/pr48/SOURCE.json @@ -0,0 +1,16 @@ +{ + "files": { + "research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86", + "research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22", + "research/copied-fixed/changed_graph.py": "375a7ca6cac6d153c1880fd5ea5b4525e5dca9d4ee3018d24d679c219b59c5b3", + "research/copied-fixed/profiles.cpp": "b9fbd71c746609948b60c441ba4601e88436956fe636d1810f270ce4ce6a63a6", + "research/copied-fixed/verify.py": "44932182ce6c4d39776650311262ef0ac1ea9b5da7220bc0f728e2789881f84a", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1", + "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7", + "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34" + }, + "head": "b7194b8586844956904b33e9fe18f0c75606c11b", + "scope": "Unmodified producer inputs for experimental frame compiler; attribution retained in each file", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/48" +} diff --git a/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py b/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py new file mode 100644 index 0000000000..c7fd42867d --- /dev/null +++ b/references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py @@ -0,0 +1,196 @@ +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit', 'complex'): + data = finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit', 'complex')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_above_bit=(1-beta)*b-a, + q_positive=q, q_below_internal=1-internal-q, q_below_leaf=1-leaf-q, + c_positive=c, c_below_one=1-c, q_below_reservations=c-q, + lambda_above_tau=lam-tau, lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal, lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf, compact_reservations=lp-(1-c), lambda_prime_below_one=q, + epsilon_positive=eps, epsilon_below_one=1-eps, guard_width=1-eps*C1, + K_geometry=1-eps*(1+c), K_dominates_log=eps*c, + record_suffix=1-eps, phase_local=1-eps-delta, phase_boundary=r-delta, + gamma_sublinear=1-eps-r, cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps, alpha_positive=r, alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r, delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta, short_record_fallback=eps-a, + small_field_exposure=1-eps-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f['bit']['m'],f['complex']['m']) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/references/frame-compiler/pr48/research/copied-fixed/certificate.json b/references/frame-compiler/pr48/research/copied-fixed/certificate.json new file mode 100644 index 0000000000..fa4b29c06d --- /dev/null +++ b/references/frame-compiler/pr48/research/copied-fixed/certificate.json @@ -0,0 +1,17916 @@ +{ + "assembly": { + "absorption_gap": "74937627730682908927817/3333470626501666392080330000000000000", + "constraints": { + "K_dominates_log": "13729316916625478716083360791967/333347062650166639208033000000000000", + "K_geometry": "250013729316916639208033/333347062650166639208033000000000000", + "a_below_b": "61024099/2000000000000", + "a_positive": "82375901/2000000000000", + "alpha_below_one": "666666666666333347062650166639208033/666694125300333278416066000000000000", + "alpha_below_one_fourth": "166646072691083388250600666639208033/666694125300333278416066000000000000", + "alpha_positive": "27458633999931353415833360791967/666694125300333278416066000000000000", + "artificial_boundary": "18667545342947664950502062499917624099/2666776501201333113664264000000000000", + "b_below_one_over32": "311783/10000000", + "beta_below_one": "19/20", + "beta_positive": "1/20", + "c_below_one": "999958812049250082375901/1000000000000000000000000", + "c_positive": "41187950749917624099/1000000000000000000000000", + "cell_above_band": "666666666665666652937349833360791967/1333388250600666556832132000000000000", + "compact_leaf": "26927049500082375901/1000000000000000000000000", + "compact_reservations": "1/4000000000000", + 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Exact scalar/label/matching/profile reconstruction is producer.py. OpenAI base theorem, written residual compiler, fixed-tape recursion, analytic/semantic/routing/recovery and eventual-threshold interfaces remain assumed.", + "sources": { + "PR34": { + "author": "James Chang (jamesyc)", + "commit": "7fecbe3651e095fb0f450756afdeefd2a9ee80a2", + "contribution": "reversed geometry and all-weight rank-cut identities" + }, + "PR35": { + "author": "Dominik Scholz", + "commit": "9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c" + }, + "PR36": { + "author": "icekylinx", + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + }, + "PR37": { + "author": "Rohan Arun", + "commit": "2f7578affce416ad4b6c41f3438ebb734f66a899", + "contribution": "dimension-23 reversed geometry checker" + }, + "PR38": { + "author": "Dominik Scholz", + "commit": "605323bab4ba330de3d1785dc5b3ecb14e8ab747", + "contribution": "contemporaneous independent fixed-both composition, comparison and credit" + }, + "PR39": { + "author": "Rohan Arun", + "commit": 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b/references/frame-compiler/pr48/research/copied-fixed/changed_graph.py @@ -0,0 +1,60 @@ +"""Changed exclusion graphs with more admissible retained carriers. + +Underlying cancellation-free generators: icekylinx PR18/36. Alternating +point order: RaD/hipotures PR41, checkpoint 7e488e6b25dc1713c1f41baaf1cefbf677507cf3. +Compared with PR46, reorder the vector leave-one-out construction by source +support size, breaking ties by ascending support at h23 and descending at +h25; restore the original output indexing. The h23 total folds in reverse +input order, while h25 retains descending (support size, support) order. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +from partial_swap.paired import PairedExclusionCircuit +from partial_swap.shared import SharedPointCircuit + + +def alternating_points(h,common): + pairs=[(a,a+1) for a in range(0,h-1,2) if common not in (a,a+1)] + if common%2: + pairs.reverse() + head=[x for pair in pairs for x in pair] + return head+[x for x in range(h) if x!=common and x not in head] + + +def graph(h): + assert h in (23,25) + class Changed(PairedExclusionCircuit): + base_threshold=2 + def total(self,values): + values=[x for x in values if x] + if h==23: + values.reverse() + else: + values.sort(key=lambda node:(self.support[node].bit_count(),self.support[node]),reverse=True) + result=0 + for node in values: + result=self.add(result,node) + return result + def vector(self,values,two=True): + if two: + return super().vector(values,two) + sign=1 if h==23 else -1 + order=sorted(range(len(values)),key=lambda i: + (self.support[values[i]].bit_count(),sign*self.support[values[i]])) + total,one,_=super().vector([values[i] for i in order],False) + restored=[0]*len(values) + for position,original in enumerate(order): + restored[original]=one[position] + return total,restored,{} + local=Changed(h-1) + total=local.pair(list(range(h-1)))[0] + local.outputs[()]=total + stack=[total] + while stack: + node=stack.pop() + if not node or node in local.active: + continue + local.active.add(node) + if local.args[node]: + stack.extend(local.args[node]) + local.additions=sum(local.args[node] is not None for node in local.active) + return SharedPointCircuit(h,local,point_order=alternating_points) diff --git a/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp b/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp new file mode 100644 index 0000000000..410e50f475 --- /dev/null +++ b/references/frame-compiler/pr48/research/copied-fixed/profiles.cpp @@ -0,0 +1,107 @@ +#include +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){assert(argc==2||argc==3);std::ifstream f(argv[1],std::ios::binary);U hdr[4];read_array(f,hdr);U h=hdr[0],v=hdr[1],n=hdr[2],q=hdr[3];assert(h==23||h==25); +std::vector>args(n);std::vectorcore(n),cover(n);std::vectorroots(q),kind(q);std::vectoractive(n);readv(f,args);readv(f,core);readv(f,cover);readv(f,roots);readv(f,kind);readv(f,active); +std::vectorranks(n),degree(n),begin(n+1);V c=0,inputs=0,loss=0; +for(U x=1;xuses(begin.back()),cursor(begin.begin(),begin.end()-1);for(U x=1;xU{return e>>31?roots[e&0x7fffffff]:e/2;}; +auto before=[&](U a,U b){U x=nd(a),y=nd(b);if(ranks[x]!=ranks[y])return ranks[x]>31?V(n)+(a&0x7fffffff):x,oy=b>>31?V(n)+(b&0x7fffffff):y;return oxdonors;for(U x=1;xleftmatch(n),rightmatch(uses.size()),distance(n,UINT32_MAX),queue;V matches=0;U phase=0,inf=UINT32_MAX,shortest=inf; +const char* lin=getenv("LINKS_IN"); +assert(lin && "A pinned carrier matching is required"); +if(lin){std::ifstream lf(lin,std::ios::binary);U hd[2];read_array(lf,hd);assert(hd[0]==n);std::vectorisdonor(n);for(U x:donors)isdonor[x]=1;for(U i=0;i=shortest)continue;adjacency(x,[&](U j){U y=rightmatch[j];if(!y)shortest=distance[x]+1;else if(distance[y]==inf){distance[y]=distance[x]+1;queue.push_back(y);}return false;});}if(shortest==inf)break; +auto aug=[&](auto&&self,U x)->bool{bool ok=adjacency(x,[&](U j){U y=rightmatch[j];if((!y&&distance[x]+1==shortest)||(y&&distance[y]==distance[x]+1&&self(self,y))){leftmatch[x]=j+1;rightmatch[j]=x;return true;}return false;});if(!ok)distance[x]=inf;return ok;};V gained=0;for(U x:donors)if(!leftmatch[x]&&aug(aug,x)){matches++;gained++;}std::cerr<<"h="<hist(h+1);for(U x=1;x=ranks[y]);hist[r-ranks[y]]++;}}else hist[1]+=degree[x];} +for(U j=0;j>31?target:args[target][e&1];assert(value==args[donor][0]||value==args[donor][1]);if(value==args[donor][0])changed++;U ru=ranks[donor],rv=ranks[value],rt=ranks[target];assert(rt>=ru&&ru>=rv);hist[h-ru]--;hist[rv]--;hist[rt-rv]--;hist[rt-ru]++;} +V R=c+q-matches,sum=0;for(U r=0;r<=h;r++){assert(hist[r]>=0);sum+=r*hist[r];}assert(sum==h*R+2*loss); +if(argc==3){std::ofstream out(argv[2],std::ios::binary);U header[2]={n,U(matches)};write_array(out,header);for(U donor:donors)if(leftmatch[donor]){U edge[2]={donor,uses[leftmatch[donor]-1]};write_array(out,edge);}assert(out);} +std::cout<<"{\"h\":"<frames{{0,0,0},{0,0,h}};std::map,U>frame_lookup;std::vectorfi(n); +for(U x=1;xsecond;} +std::map,int64_t>transitions;int64_t singles=0; +auto edge=[&](U a,U b,int64_t count){if(a==b)return;transitions[{a,b}]+=count;}; +for(U x=1;x>31?target:args[target][e&1];edge(fi[donor],1,-1);edge(0,fi[value],-1);edge(fi[value],fi[target],-1);edge(fi[donor],fi[target],1);} +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".round3_rankone_certified_profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +def tree(edges, n): + require(len(edges) == n-1 and len(set(edges)) == n-1, 'Wrong tree edge count') + seen = {0} + while True: + new = seen | {v for u,v in edges if u in seen} | {u for u,v in edges if v in seen} + if new == seen: + break + seen = new + require(len(seen) == n, 'Disconnected restriction graph') + + +def data_corners(): + c = read(HERE/'data-corners.json') + prime = c['prime'] + require(prime == 1000003 and all(prime % j for j in range(2,isqrt(prime)+1)), + 'Data witness prime not proved') + require(c['dimensions'] == [23,25], 'Data dimensions') + require([tuple(r[:3]) for r in c['records']] == list(combinations(range(23),3)), + 'Incomplete first triple coverage') + require(all(0 <= r[3] <= 2300 and 0 < r[4] < prime for r in c['records']), + 'Invalid modular product record') + failures = c['fallback_pairs'] + require(len({tuple(r[:6]) for r in failures}) == len(failures), 'Duplicate fallback') + counts = Counter() + for aa,bb,cc,u,v,w,row in failures: + require(0<=aa= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + + +def profile(): + a,b = 23,25 + m = a*b + rows = [read(HERE / f'original-{h}.json') for h in (a,b)] + N = comb(a,3)*comb(b,3) + W = 2*N+sum(N//r['v']*r['R'] for r in rows) + L = sum(N//r['v']*r['loss'] for r in rows) + data = data_corners() + good,bad = data['good'],data['fallback'] + parts = {'data':Counter({1:2*(9*good+47*bad),21:2*good,17:2*good,481:2*N}), + 'paid_endpoint_copy':Counter({1:N})} + axes = [] + for row in rows: + h = row['h'] + require(row['v'] == comb(h,3), 'Triple count') + require(row['R'] == row['c']+row['q']-row['matched'], 'Role allocation') + require(row['loss'] == h*(h-1), 'Retained center loss') + require(sum(r*n for r,n in enumerate(row['histogram'])) == h*row['R']+2*row['loss'], + 'Original frame rank mass') + f = read(HERE / f'profiles-{h}.json') + for key in ('h','v','R','loss','rank_sum'): + require(f[key] == row[key], 'Fixed/original mismatch: '+key) + require(f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1, + 'Invalid CRT profile') + blocks = f['blocks'][:] + require(len(blocks) == h+1 and all(type(n) is int and n>=0 for n in blocks), + 'Invalid fixed blocks') + require(sum(t*n for t,n in enumerate(blocks)) == f['rank_sum'], 'Fixed profile mass') + require(blocks[h] == h, 'Exactly h full center cleanup calls expected') + # Preserve every transformed copy. Replace only its original's full cleanup. + blocks[h] -= h + blocks[1] += h + require(sum(t*n for t,n in enumerate(blocks)) == h*row['R']+row['loss'], + 'Copied fixed profile mass') + rep = N//row['v'] + bank = rep*row['R'] + parts[f'internal_{h}'] = Counter({t:n*rep for t,n in enumerate(blocks) if t and n}) + parts[f'exterior_{h}'] = Counter({h:bank,m-2*h:bank}) + parts[f'data_growth_{h}'] = Counter({1:2*N,h-2:2*N}) + axes.append(dict(original=row,fixed=f,copied_blocks=blocks,exactness=exactness(h))) + hist = sum(parts.values(),Counter()) + s = sum(t*n for t,n in hist.items()) + require(s == W*m-N+L == 102078397025, 'Complete rank mass') + require((m,N,W,L) == (575,4073300,177530859,2226400), 'Physical constants') + require(max(hist) == 529 and all(00 for t,n in hist.items()), 'Proper children') + return dict(m=m,N=N,W=W,L=L,total_rank=s,deficit=W*m-s,maxchild=max(hist), + child_multiplicities=dict(sorted(hist.items())),parts=parts,axes=axes) + + +def run(): + require(not sys.flags.optimize, 'Assertions must remain enabled') + sources = check_sources() + prior = baseline.certificate() + geo,p = geometry(),profile() + exact = moment(p['m'],p['W'],p['child_multiplicities'],AB) + require(exact['upper'] < 1, 'Bit characteristic failed') + old = prior['bit']['counts'] + old_at_new = moment(old['m'],old['W'],old['child_multiplicities'],AB) + require(old_at_new['lower'] > 1, 'Old construction not excluded at new saving') + forward=read(HERE/'comparison-pr40.json') + forward_rows={int(t):n for t,n in forward['child_multiplicities'].items()} + require(sum(t*n for t,n in forward_rows.items())==108202762275, 'PR40 rank mismatch') + forward_at_new=moment(forward['m'],forward['W'],forward_rows,AB) + require(forward_at_new['lower']>1,'PR40 network not excluded at new saving') + rad=read(HERE/'comparison-pr41.json') + rad_rows={int(t):n for t,n in rad['child_multiplicities'].items()} + require(sum(t*n for t,n in rad_rows.items())==rad['total_rank']==102565738275,'PR41 rank mismatch') + rad_at_new=moment(rad['m'],rad['W'],rad_rows,AB) + require(rad_at_new['lower']>1,'PR41 alternating network not excluded at new saving') + newest=read(HERE/'comparison-pr42.json') + newest_rows={int(t):n for t,n in newest['child_multiplicities'].items()} + require(sum(t*n for t,n in newest_rows.items())==newest['total_rank']==102565738275,'PR42 rank mismatch') + newest_at_new=moment(newest['m'],newest['W'],newest_rows,AB) + require(newest_at_new['lower']>1,'PR42 network not excluded at new saving') + previous=read(HERE/'comparison-pr43.json') + previous_rows={int(t):n for t,n in previous['child_multiplicities'].items()} + require(sum(t*n for t,n in previous_rows.items())==previous['total_rank']==102565738275,'PR43 rank mismatch') + previous_at_new=moment(previous['m'],previous['W'],previous_rows,AB) + require(previous_at_new['lower']>1,'PR43 network not excluded at new saving') + frontier=read(HERE/'comparison-pr44.json') + frontier_rows={int(t):n for t,n in frontier['child_multiplicities'].items()} + require(sum(t*n for t,n in frontier_rows.items())==frontier['total_rank']==102565738275,'PR44 rank mismatch') + frontier_at_new=moment(frontier['m'],frontier['W'],frontier_rows,AB) + require(frontier_at_new['lower']>1,'PR44 network not excluded at new saving') + parent=read(HERE/'comparison-pr46.json') + parent_rows={int(t):n for t,n in parent['child_multiplicities'].items()} + require(sum(t*n for t,n in parent_rows.items())==parent['total_rank']==102565738275,'PR46 rank mismatch') + parent_at_new=moment(parent['m'],parent['W'],parent_rows,AB) + require(parent_at_new['lower']>1,'PR46 network not excluded at new saving') + latest=read(HERE/'comparison-pr47.json') + latest_rows={int(t):n for t,n in latest['child_multiplicities'].items()} + require(sum(t*n for t,n in latest_rows.items())==latest['total_rank']==latest['W']*latest['m']-1846900,'PR47 rank mismatch') + latest_at_new=moment(latest['m'],latest['W'],latest_rows,AB) + require(latest_at_new['lower']>1,'PR47 network not excluded at new saving') + phase = prior['complex']['counts'] + phase_row = read(ROOT / 'certificates/copied-centers-complex-input.json') + bridge = baseline.finite_bridge(p,phase,[phase_row,phase_row]) + require(all(js(bridge[k])==js(prior['finite_bridge'][k]) for k in ('complex','semantic','rows')), 'Unexpected phase or stock change') + final = assembly(bridge,AB,KAPPA,a_complex=AC) + eventual = cutoffs(bridge,final) + require(KAPPA > PR47_KAPPA > PR46_KAPPA > PR44_KAPPA > PR43_KAPPA > PR42_KAPPA > PR41_KAPPA > PR40_KAPPA > PR39_KAPPA > PR38_KAPPA > PR37_KAPPA > prior['kappa'] > Q(1,2**15), 'Comparison failed') + require(KAPPA < Q(1,2**14), 'Unexpected power-of-two bracket') + own_files = sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.cpp'))+[HERE/'PROOF.md',HERE/'SOURCE.json'] + own_files += [HERE/f'{kind}-{h}.json' for h in (23,25) for kind in ('profiles','original','scalar')] + own_files += [HERE/'data-corners.json',HERE/'comparison-pr40.json',HERE/'comparison-pr41.json',HERE/'comparison-pr42.json',HERE/'comparison-pr43.json',HERE/'comparison-pr44.json',HERE/'comparison-pr46.json',HERE/'comparison-pr47.json',HERE/'search-record.json',HERE/'links-23.uses',HERE/'links-25.uses'] + return dict(status='Conditional exact arithmetic witness; general transfer proofs are dependencies', + kappa=KAPPA,bit=dict(counts=p,**exact),complex=prior['complex'], + geometry=geo,finite_bridge=bridge,assembly=final,eventual_bounds=eventual,sources=sources, + comparison=dict(PR47=PR47_KAPPA,ratio_PR47=KAPPA/PR47_KAPPA,PR46=PR46_KAPPA,ratio_PR46=KAPPA/PR46_KAPPA,PR44=PR44_KAPPA,ratio_PR44=KAPPA/PR44_KAPPA,PR36=prior['kappa'],PR37=PR37_KAPPA,PR38=PR38_KAPPA,PR39=PR39_KAPPA,PR40=PR40_KAPPA,PR41=PR41_KAPPA,PR42=PR42_KAPPA,PR43=PR43_KAPPA, + ratio_PR36=KAPPA/prior['kappa'],ratio_PR37=KAPPA/PR37_KAPPA, + ratio_PR38=KAPPA/PR38_KAPPA,ratio_PR39=KAPPA/PR39_KAPPA,ratio_PR40=KAPPA/PR40_KAPPA,ratio_PR41=KAPPA/PR41_KAPPA,ratio_PR42=KAPPA/PR42_KAPPA,ratio_PR43=KAPPA/PR43_KAPPA, + dyadic_corollary='2^-15',next_dyadic_not_reached='2^-14'), + controls=dict(PR47_bit_at_new_lower=latest_at_new['lower'],PR46_bit_at_new_lower=parent_at_new['lower'],PR44_bit_at_new_lower=frontier_at_new['lower'],old_bit_at_new_lower=old_at_new['lower'],PR40_bit_at_new_lower=forward_at_new['lower'],PR41_bit_at_new_lower=rad_at_new['lower'],PR42_bit_at_new_lower=newest_at_new['lower'],PR43_bit_at_new_lower=previous_at_new['lower']), + local_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in own_files}, + scope='Changed leave-one-out graphs with RaD alternating point order, newly pinned weighted carrier matching and fixed-basis internal blocks at (23,25); ' + 'all actual data pairs checked for 9 singletons +21+17+481; ' + 'ten failed modular tests are recovered by exact rational elimination. Exact scalar/label/' + 'matching/profile reconstruction is producer.py. OpenAI base theorem, ' + 'written residual compiler, fixed-tape recursion, analytic/semantic/' + 'routing/recovery and eventual-threshold interfaces remain assumed.') + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--output',type=Path) + args = parser.parse_args() + result = run() + if args.output: + args.output.write_text(json.dumps(js(result),indent=2,sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB)) + print('47 strict inequalities; seven margins; all-exact enclosures; inherited balanced assembly') diff --git a/references/frame-compiler/pr48/scripts/exclusion_circuit.py b/references/frame-compiler/pr48/scripts/exclusion_circuit.py new file mode 100644 index 0000000000..aaa99986c4 --- /dev/null +++ b/references/frame-compiler/pr48/scripts/exclusion_circuit.py @@ -0,0 +1,184 @@ +#!/usr/bin/env python3 +"""Cancellation-free circuit for all pair sums avoiding two specified points. + +Every addition has disjoint input supports. Node interning shares equal sums; +support tracking verifies the full linear map, not sampled input values. +""" +from itertools import combinations +from hashlib import sha256 +import json + + +class ExclusionCircuit: + def __init__(self,n): + assert n>=4 + self.n=n + self.inputs=list(combinations(range(n),2)) + self.support=[0]+[1< +#include + +inline unsigned popcount64(uint64_t value) { + unsigned count = 0; + while (value) { value &= value-1; ++count; } + return count; +} + +inline bool little_endian() { + const uint16_t one = 1; + return *reinterpret_cast(&one) == 1; +} +template void normalize_le(T& value) { + static_assert(std::is_integral::value, "integer array required"); + if (!little_endian()) { + auto p = reinterpret_cast(&value); + std::reverse(p, p + sizeof(T)); + } +} +template void normalize_le(std::array& row) { + for (auto& value : row) normalize_le(value); +} +template void readv(std::ifstream& f, std::vector& values) { + f.read(reinterpret_cast(values.data()), values.size()*sizeof(T)); + if (!f) throw std::runtime_error("Truncated producer array"); + if (!little_endian()) for (auto& value : values) normalize_le(value); +} +template void read_array(std::ifstream& f, T (&values)[N]) { + f.read(reinterpret_cast(values), sizeof(values)); + if (!f) throw std::runtime_error("Truncated producer header"); + for (auto& value : values) normalize_le(value); +} +template void write_array(std::ofstream& f, const T (&values)[N]) { + for (auto value : values) { + normalize_le(value); + f.write(reinterpret_cast(&value), sizeof(T)); + } + if (!f) throw std::runtime_error("Cannot write producer array"); +} diff --git a/references/frame-compiler/pr48/scripts/partial_swap/paired.py b/references/frame-compiler/pr48/scripts/partial_swap/paired.py new file mode 100644 index 0000000000..b879293977 --- /dev/null +++ b/references/frame-compiler/pr48/scripts/partial_swap/paired.py @@ -0,0 +1,46 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Cancellation-free pair exclusion with recursively aggregated vertex weights. + +At each level group vertices in pairs. Internal edges become vertex weights +in the smaller graph. Keeping those weights in the recursion avoids a separate +leave-two-out circuit for each level. All coefficients are checked exactly. +""" +from exclusion_circuit import ExclusionCircuit +from itertools import combinations +class PairedExclusionCircuit(ExclusionCircuit): + base_threshold = 2 + def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points}) + def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)] + def block(self,points,edges,weights): + if len(points)<=self.base_threshold: + total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit]) + return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)} + groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))] + coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)} + wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)} + total,outside,far=self.block(list(range(ng)),coarse,wt) + strips={};sums={} + for i,g in enumerate(groups): + other=[j for j in range(ng) if j!=i] + for a in g: + carry=self.total([weights[u] for u in g if u!=a]) + vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other] + st,one,_=self.vector([carry]+vals,False) + strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st + out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g} + for i,g in enumerate(groups): + for a,b in combinations(g,2):out[a,b]=outside[i] + for i,j in combinations(range(ng),2): + for a in groups[i]: + left=self.add(far[i,j],strips[a][j]) + for b in groups[j]: + cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b]) + out[a,b]=self.add(left,self.add(strips[b][i],cross)) + return total,single,out +if __name__=='__main__': + for n in (15,25,45,49): + c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True) diff --git a/references/frame-compiler/pr48/scripts/partial_swap/shared.py b/references/frame-compiler/pr48/scripts/partial_swap/shared.py new file mode 100644 index 0000000000..a2f0190704 --- /dev/null +++ b/references/frame-compiler/pr48/scripts/partial_swap/shared.py @@ -0,0 +1,163 @@ +# Copyright 2026 icekylinx. Licensed under Apache-2.0. +# Adapted with AI assistance from the archived partial-swap research producer. +# Underlying circuit modules: jacklightChen/integer-mult-bounds, PR7 +# commit 6725c6a17b17871a35353fd29157f4ed851bc114; original credits retained. +#!/usr/bin/env python3 +"""Merge equal sums across the common-point circuits, with exact certificates. + +Supports are represented by their provenance in the small pair circuit, not +by half a million dense global bit vectors. A sum that occurs in two distinct +common-point groups must be a pair-star; its fixed pair and union of vertices +identify its support exactly. +""" +from functools import lru_cache +from hashlib import sha256 +from itertools import combinations +import json + +from exclusion_circuit import ExclusionCircuit + + +class SharedPointCircuit: + def __init__(self,h,circuit=None,point_order=None): + assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate' + self.h=h + self.local=circuit or ExclusionCircuit(h-1) + assert self.local.n==h-1, 'Pair circuit has the wrong ground size' + self.inputs=list(combinations(range(h),3)) + self.variables={t:i+1 for i,t in enumerate(self.inputs)} + self.args=[None]*(len(self.inputs)+1) + self.core=[0]+[sum(1<=2 and key in lookup: + mapping[node]=lookup[key];self.merged+=1 + continue + new=len(self.args);mapping[node]=new + self.args.append((a,b));self.core.append(core);self.union.append(union) + self.provenance.append((common,node)) + if core.bit_count()>=2:lookup[key]=new + for pair,node in sorted(self.local.outputs.items()): + t=tuple(sorted((common,*(self.points[common][x] for x in pair)))) + self.outputs[common,t]=mapping[node] + self.active=set();stack=list(self.outputs.values()) + while stack: + n=stack.pop() + if n in self.active:continue + self.active.add(n) + if self.args[n]:stack.extend(self.args[n]) + self.additions=sum(self.args[n] is not None for n in self.active) + + @lru_cache(maxsize=16384) + def support_in(self,node,common): + """Exact pair-input support in coordinates with this common point.""" + assert self.core[node]&(1<1 for b in blocks) + def new(g): + s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s + def raise_(s,g): + old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g)) + def xor(a,b,g): + assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g)) + def acquire(g,anchors): + if reclaim: + bb={} + def ins(s): + row=slots[s];expr=1<>s&1;e^=1<>i&1) + if j!=i: + # Synthesize swap as three XORs at the single common frame. + for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z)) + for j in range(len(ins)): + if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i)) + assert rr==[1<>i&1:xor(s,value_slots[y],g) + assert slots[s]==signal[x];value_slots[x]=s + used=set() + for u in outuses: + x=uses[u][0];s=value_slots[x] + if x in used: + ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss + used.add(x);assert u not in assign;assign[u]=s + if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr) + output_slots=[];output_records=[];scatter=[0]*v;J=[] + for u,(x,g,target)in enumerate(uses): + if target is None:continue + s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s) + common,triple=target;output_records.append((s,g,common,triple)) + targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)] + for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s)) + rank=blocks[g]['rank'] + if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1 + else:hist[h-1-rank]+=1;hist[1]+=1 + assert len(set(output_slots))==len(output_slots) + for s in retired:hist[h-blocks[frames[s]]['rank']]+=1 + assert len(retired)+len(output_slots)==len(slots) + assert scatter==[1<= 3 and all(exponent % d for d in range(2, isqrt(exponent)+1)), + 'Composite Lucas-Lehmer exponent') + p = 2**exponent - 1 + s = 4 + for _ in range(exponent - 2): + s = (s*s-2) % p + require(s == 0, 'Lucas-Lehmer failed') + return p + + +def exactness(h): + require(h in (23, 25), 'Uncertified dimension') + primes = [mersenne(e) for e in (61, 31, 19)] + Z = 3*h-7 + B0 = (4*h-2)*Z + 27*(h+1) + D = 3*(h+1)*(h-1)**2 + B = 2*(h-1)*B0 + bounds = {r: sum(comb(h,j)*factorial(j)*B**j*D**(r-j) + for j in range(r+1)) for r in (2,3,4)} + require(bounds[2] < primes[0], 'Rank-two minor modulus insufficient') + require(max(bounds[3],bounds[4]) < prod(primes), 'CRT minor modulus insufficient') + require(3*(h+1)*(h-1) < min(primes), 'Denominator may vanish') + return dict(h=h, primes=primes, prime_product=prod(primes), + single_numerator_bound=B0, common_denominator_bound=D, + correction_numerator_bound=B, minor_bounds=bounds, + modulus_gaps={2: primes[0]-bounds[2], + 3: prod(primes)-bounds[3],4: prod(primes)-bounds[4]}) + + +@lru_cache(None) +def logs(x): + x = Q(x) + require(x >= 1, 'Log domain') + k = 0 + while x > 2: + x /= 2 + k += 1 + def small(y): + z = (y-1)/(y+1) + lo = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(32)), Q()) + return lo, lo+2*z**65/(65*(1-z*z)) + lo,hi = small(x) + lo2,hi2 = small(Q(2)) + lo,hi = lo+k*lo2,hi+k*hi2 + scale = 10**30 + return Q((lo*scale).numerator//(lo*scale).denominator,scale), \ + Q(-(-(hi*scale).numerator//(hi*scale).denominator),scale) + + +def moment(m,W,rows,saving): + require(type(saving) is Q and 0 < saving < 1, 'Exact positive saving required') + lower,upper = Q(),Q() + enclosure = {} + for t,n in sorted(rows.items()): + require(type(t) is int and type(n) is int and 00, 'Invalid child') + lo,hi = logs(Q(m,t)) + u,v = saving*lo,saving*hi + require(0 <= u <= v < 1, 'Exponential enclosure domain') + weight = Q(t*n,m*W) + lower += weight*(1+u+u*u/2+u*u*u/6) + upper += weight*(1+v+v*v/(2*(1-v/3))) + enclosure[t] = dict(lower=lo,upper=hi) + return dict(saving=saving,exponent=1-saving,lower=lower,upper=upper, + strict_gap=1-upper,logarithms=enclosure) + diff --git a/scripts/experiments/binary_frame_profile_prepare.py b/scripts/experiments/binary_frame_profile_prepare.py new file mode 100644 index 0000000000..85ad7b77bd --- /dev/null +++ b/scripts/experiments/binary_frame_profile_prepare.py @@ -0,0 +1,88 @@ +"""Extract positive-rank transitions from independently replayed block words.""" +from collections import Counter +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import json,struct,sys,gzip,argparse + + +def prepare(path,destination): + raw=Path(path).read_bytes();raw=gzip.decompress(raw) if str(path).endswith('.gz') else raw;d=json.loads(raw) + h,v,R=d['h'],d['v'],d['R'] + frames=[(0,0,0),(0,0,h)]+[(c,u,1 if c==u else u.bit_count()-c.bit_count()) for c,u in d['frames']] + physical=[None]*R;transitions=Counter() + for s,a,b in d['events']: + assert 0<=s0 + histogram[r]+=count + with Path(destination).open('wb') as f: + f.write(struct.pack('<6I2Q',h,v,R,len(frames),len(transitions),singles,mass,h*(h-1))) + for c,u,r in frames:f.write(struct.pack('<2QI',c,u,r)) + for (a,b),count in sorted(transitions.items()):f.write(struct.pack('<2Iq',a,b,count)) + receipt=dict(h=h,v=v,R=R,frames=len(frames),distinct_transitions=len(transitions),singles=singles,rank_mass=mass, + rank_histogram_with_side_growth_split_into_singletons=dict(sorted(histogram.items())),word_sha256=sha256(raw).hexdigest(),copied_centers=centers, + transition_events_equal_independent_xor_word_reconstruction=True) + Path(str(destination)+'.json').write_text(json.dumps(receipt,indent=2)+'\n') + return receipt + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('word',type=Path);parser.add_argument('destination',type=Path) + args=parser.parse_args();print(json.dumps(prepare(args.word,args.destination),indent=2)) diff --git a/scripts/experiments/binary_frame_profiles.cpp b/scripts/experiments/binary_frame_profiles.cpp new file mode 100644 index 0000000000..1b52bd057d --- /dev/null +++ b/scripts/experiments/binary_frame_profiles.cpp @@ -0,0 +1,85 @@ +// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik +// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32. +// Change: with LINKS_IN=, the carrier matching is read from a pinned file +// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible +// adjacency (causal order and frame inclusion); donors and uses are distinct. +// This replay-only adaptation omits the discovery edge dumper. The original +// optimizer and profiler are preserved in references/copied-fixed/pr44. +// Replay-only adaptation prepared with OpenAI Codex assistance. +// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0. +// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx. +// Dimension adaptation at 45/47; extra primes for all source-growth cases. +// Exact bounded-minor inequalities are checked by verify.py. Original credit below. +// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration. +// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128. + +// Adapted input reader for complete serialized frame-compiler transitions. +// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp. +// All projector, pivot and CRT formulas below are unchanged. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using U=uint32_t;using V=uint64_t; +#include "binary_io.hpp" +int main(int argc,char**argv){ +assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr); +U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25); +V sum,loss;f.read(reinterpret_cast(&sum),8);f.read(reinterpret_cast(&loss),8); +struct Frame{V core,cover;U rank;};std::vectorframes; +for(U i=0;i(&a.core),8);f.read(reinterpret_cast(&a.cover),8);f.read(reinterpret_cast(&a.rank),4);frames.push_back(a);} +std::map,int64_t>transitions; +for(U i=0;i(&a),4);f.read(reinterpret_cast(&b),4);f.read(reinterpret_cast(&count),8);transitions[{a,b}]=count;} +assert(f);assert(sum==h*V(R)+loss); +V p=2305843009213693951ULL; +auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;}; +auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;}; +auto sub=[&](V a,V b)->V{return (a+p-b)%p;}; +std::vector>matrix_cache(frames.size()); +auto matrix=[&](U id)->const std::vector&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;} + assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2); + for(U i=0;i>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10; + V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p; + }return A;}; + +std::vectorblocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::mapcorrection_hist; +for(auto&[key,count]:transitions){if(!count)continue;assert(count>0);U aa=key.first,bb=key.second;U rr=frames[bb].rank-frames[aa].rank;assert(frames[bb].rank>=frames[aa].rank);if(!rr)continue; + if(rr<=2){blocks[1]+=count*rr;continue;}if(aa==0&&bb==1){blocks[h]+=count;continue;} + if(aa>1&&bb>1){ + assert(!(frames[bb].core&~frames[aa].core)); + assert(!(frames[aa].cover&~frames[bb].cover)); + U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core); + assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1)); + } + const auto&A=matrix(aa);const auto&B=matrix(bb);std::vectorM(h*h);for(U x=0;x>pivots; + for(U i=0;i=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k core-one use all three primes at these dimensions. +if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){ + assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector>> all{pivots}; + for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vectorY(h*h);for(U z=0;z> pp; + for(U i=0;i=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k corner((h+1)*(h+1));for(U i=0;i=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;} + pivots.clear();for(U i=0;i=0);mass+=t*blocks[t];}assert(mass==sum); +std::string target=std::string(argv[1])+".profiles.json";std::ofstream out(target);assert(out);out<<"{\"h\":"< 2^-15. +This is 3.10003% above PR54's reported 4529040672 / 10^14. +These are asymptotic exponent savings, not measured runtime improvements. + +From the repository root, with Python 3 and a C++17 compiler: + + python3 scripts/experiments/verify_skip_frame.py + +The verifier independently replays the serialized physical XOR words on +every input and dirty basis vector in both orientations, checks every +original-envelope frame inclusion and terminal output, reconstructs all +transitions from the actual XOR word, freshly computes the ordered fixed-I+J +profiles with bounded-minor/CRT checks, and verifies the exact recurrence, +47 strict assembly inequalities, seven margins and eventual cutoff arithmetic. + +To regenerate the producer words separately: + + python3 scripts/experiments/skip_frame_compiler.py --h 23 --output /tmp/skip23.json --word /tmp/skip23.json.gz + python3 scripts/experiments/skip_frame_compiler.py --h 25 --output /tmp/skip25.json --word /tmp/skip25.json.gz + +The word contents reproduce the certificates/skip-frame-word-{23,25}.json.gz +records exactly after decompression. Gzip headers may name different files. +The compiler groups identical rational frames, synthesizes invertible binary +maps on whole regions, retains compatible incoming signals, and clears +retired signal components while preserving arbitrary dirty state. It does +not assume zero-initialized scratch or free endpoint/copy operations. + +Roles: h23 = 31,416; h25 = 41,264. Physical width W = 153,481,944. +The exact bit saving is 116741511 / 2500000000000. The data-pair count +4,073,300, rank deficit 1,846,900, and maximum child width 529 are unchanged. + +Scope: the new verifier regenerates every new auxiliary profile. The unchanged +data geometry, complex branch, all-size residual compiler and finite-alphabet +tape/analytic/routing/recovery interfaces remain inherited from pinned PR48. +The full data-pair calculation is not repeated by this command. This is a +finite conditional witness, not formal verification of those interfaces. + +Source: Avi Eisenberg / ikeboy with Anthropic Claude assistance supplied PR53's +skip-prefix graph (3ffd4021995c959ac02d12920e0279ae97dd03c7). Chafik Boukhalfa, +Rohan Arun, RaD / hipotures, icekylinx and earlier contributors supplied the +inherited pipeline; all original credits remain under references/frame-compiler. +This local joint frame compiler and integration used OpenAI Codex assistance. +PR54 was tested as a graph alternative; its paid clones are not used here. + +The publication branch contains the selected skip-prefix witness and its +pinned dependencies. + +Finite mechanism +---------------- +For each identical original envelope, independent requested output rows, +selected independent incoming signals, and unit-vector completion form an +invertible binary matrix on every incoming physical role. Gaussian elimination +synthesizes that matrix as literal XOR gates in the shared frame. Dependent +outputs are delivered to distinct fresh or signal-cleared roles. Every retained +continuation goes to a strictly later region with a containing frame. + +Clearing a retired role removes its input-dependent signal, not its arbitrary +dirty value. If L is the resulting invertible mixer, V the injection and J the +read-only scatter, the exact output identities give J L V = I. The chronological +word L,J,L^-1,V,L,J,L^-1,V cancels the contribution of any initial dirty vector +and restores every auxiliary. The verifier checks this full word and its dual +on all basis vectors, independently of the compiler's internal symbol tracking. + +Each role has a monotone frame path. Every nonidentity transition in the +compiler's event list must equal the multiset reconstructed from XOR incidences. +The inherited fixed-I+J projector formulas and bounded-minor checks then give +the actual contiguous recursive children, including copied centers and endpoint +corrections. Their total rank is mW-N+L, with m=575, N=4073300, L=2226400. +The exact moment at the reported bit saving is strictly below one; the inherited +balanced assembly at kappa=4669442391/10^14 checks all 47 inequalities and seven +positive margins. The all-size transfer and analytic hypotheses above remain +assumptions rather than conclusions of these finite computations. diff --git a/scripts/experiments/skip_frame_compiler.py b/scripts/experiments/skip_frame_compiler.py new file mode 100644 index 0000000000..2bbb9f2c44 --- /dev/null +++ b/scripts/experiments/skip_frame_compiler.py @@ -0,0 +1,58 @@ +#!/usr/bin/env python3 +"""Joint frame synthesis on Avi Eisenberg's PR53 skip-prefix producer. + +The source graph is unmodified and hash-pinned, including its original credits. +The circuit dependencies are byte-identical to the pinned PR48 files. This +wrapper changes only the graph supplied to the existing binary frame compiler. +Every generated word checks the full input and dirty basis in both orientations; +verify_skip_frame.py separately replays the word, profiles, and conditional bound. +""" +import sys +sys.dont_write_bytecode = True +import argparse +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + +import binary_frame_compiler as compiler + +ROOT = Path(__file__).resolve().parents[2] / 'references/frame-compiler/pr53' +MANIFEST = json.loads((ROOT / 'SOURCE.json').read_text()) +for name, digest in MANIFEST['files'].items(): + assert sha256((ROOT / name).read_bytes()).hexdigest() == digest, name +assert sha256((ROOT / MANIFEST['shared_dependency_manifest']).read_bytes()).hexdigest() == MANIFEST['shared_dependency_manifest_sha256'] +spec = importlib.util.spec_from_file_location('pinned_skip_frame_graph', ROOT / 'research/skip-strips/skip_graph.py') +producer = importlib.util.module_from_spec(spec) +spec.loader.exec_module(producer) + + +def compile_axis(h): + assert h in (23, 25) + previous = compiler.graph + compiler.graph = producer.graph + try: + result, word = compiler.compile_(h, matching=True, reclaim=True, dirty=True) + finally: + compiler.graph = previous + result['baseline_pr53_roles'] = {23: 32946, 25: 43409}[h] + return result, word + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--h', type=int, choices=(23, 25), required=True) + parser.add_argument('--output', type=Path, required=True) + parser.add_argument('--word', type=Path, required=True) + args = parser.parse_args() + result, word = compile_axis(args.h) + raw = (json.dumps(word, separators=(',', ':')) + '\n').encode() + if args.word.suffix == '.gz': + with args.word.open('wb') as stream: + with gzip.GzipFile(fileobj=stream, mode='wb', mtime=0) as archive: + archive.write(raw) + else: + args.word.write_bytes(raw) + args.output.write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps(result), flush=True) diff --git a/scripts/experiments/skip_frame_compose.py b/scripts/experiments/skip_frame_compose.py new file mode 100644 index 0000000000..d9961c9c7f --- /dev/null +++ b/scripts/experiments/skip_frame_compose.py @@ -0,0 +1,135 @@ +"""Exact conditional assembly of the PR53 skip producer and frame compiler. + +Uses the unchanged fixed-I+J profiles and balanced assembly interfaces from +PR48. All auxiliary counts come from complete serialized new physical words. +The fixed rational witness is independent of discovery or floating arithmetic. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import comb +from pathlib import Path +import gzip +import importlib.util +import json + +import binary_frame_math as arithmetic + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OUT = ROOT / 'certificates' +INHERITED = ROOT / 'references/frame-compiler/pr48' +OLD = INHERITED / 'research/copied-fixed' +PR53 = ROOT / 'references/frame-compiler/pr53' +AB = Q(116741511, 2500000000000) +KAPPA = Q(4669442391, 10**14) +EXCLUDED_ABOVE = Q(466966047, 10**13) +PR53_KAPPA = Q(4498144, 10**11) +PR54_CLAIMED_KAPPA = Q(4529040672, 10**14) + +spec = importlib.util.spec_from_file_location('skip_frame_balanced_assembly', OLD / 'balanced_assembly.py') +balanced = importlib.util.module_from_spec(spec) +spec.loader.exec_module(balanced) + + +def check_sources(): + manifests = [] + for directory in (INHERITED, PR53): + path = directory / 'SOURCE.json' + document = json.loads(path.read_text()) + for name, digest in document['files'].items(): + assert sha256((directory / name).read_bytes()).hexdigest() == digest, name + if 'shared_dependency_manifest' in document: + dependency = directory / document['shared_dependency_manifest'] + assert sha256(dependency.read_bytes()).hexdigest() == document['shared_dependency_manifest_sha256'] + manifests.append(document) + return manifests + + +def profile(): + a, b = 23, 25 + m, N = a*b, comb(a, 3)*comb(b, 3) + profiles = [json.loads((OUT / f'skip-frame-profiles-{h}.json').read_text()) for h in (a, b)] + words = json.loads((OUT / 'skip-frame-compiler.json').read_text()) + W = 2*N + sum(N//f['v']*f['R'] for f in profiles) + L = sum(N//f['v']*f['loss'] for f in profiles) + parts = {'data': Counter({1: 18*N, 21: 2*N, 17: 2*N, 481: 2*N}), + 'paid_endpoint_copy': Counter({1: N})} + receipts = [] + for f in profiles: + h = f['h'] + rep, bank = N//f['v'], N//f['v']*f['R'] + recorded = words['axes'][str(h)] + replay = recorded['replay'] + receipt = json.loads((OUT / f'skip-frame-transitions-{h}.json').read_text()) + for key in ('h', 'v', 'R'): + assert f[key] == receipt[key] + assert f['R'] == replay['roles'] + assert f['v'] == comb(h, 3) and f['loss'] == h*(h-1) + assert f['crt_disagreements'] == 0 and f['field_prime'] == 2**61-1 + assert sum(t*n for t, n in enumerate(f['blocks'])) == h*f['R']+f['loss'] == f['rank_sum'] == receipt['rank_mass'] == replay['rank_mass'] + assert f['blocks'][h] == 0 # Copied centers already included. + assert receipt['transition_events_equal_independent_xor_word_reconstruction'] + packed = (OUT / f'skip-frame-word-{h}.json.gz').read_bytes() + assert sha256(packed).hexdigest() == recorded['gzip_sha256'] + assert sha256(gzip.decompress(packed)).hexdigest() == recorded['word_sha256'] == receipt['word_sha256'] + histogram = {str(k): v for k, v in replay['histogram'].items() if int(k)} + side = replay['output_roles']-h + histogram['2'] -= side + histogram['1'] += 2*side + assert histogram == receipt['rank_histogram_with_side_growth_split_into_singletons'] + arithmetic.exactness(h) + parts[f'internal_{h}'] = Counter({t: n*rep for t, n in enumerate(f['blocks']) if t and n}) + parts[f'exterior_{h}'] = Counter({h: bank, m-2*h: bank}) + parts[f'data_growth_{h}'] = Counter({1: 2*N, h-2: 2*N}) + receipts.append(receipt) + rows = sum(parts.values(), Counter()) + mass = sum(t*n for t, n in rows.items()) + assert mass == m*W-N+L and max(rows) == 529 and all(0 < t < m for t in rows) + assert (W, mass, m*W-mass) == (153481944, 88250270900, 1846900) + return dict(m=m, N=N, W=W, L=L, total_rank=mass, deficit=m*W-mass, + maxchild=max(rows), child_multiplicities=dict(sorted(rows.items())), + parts=parts, axes=profiles, words=receipts) + + +def compose(): + sources = check_sources() + compiler_record = json.loads((OUT / 'skip-frame-compiler.json').read_text()) + assert compiler_record['source'] == sources[1] + p = profile() + exact = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], AB) + excluded = arithmetic.moment(p['m'], p['W'], p['child_multiplicities'], EXCLUDED_ABOVE) + assert exact['strict_gap'] > 0 and excluded['lower'] > 1 + prior = json.loads((OLD / 'certificate.json').read_text()) + bridge = prior['finite_bridge'] + bridge['bit']['W'] = p['W'] + assert p['W'].bit_length() == bridge['bit']['wire_bits'] + assembled = balanced.assembly(bridge, AB, KAPPA, a_complex=Q(717, 10**7)) + assert len(assembled['constraints']) == 47 and len(assembled['margins']) == 7 + local_sources = [HERE / name for name in ( + 'skip_frame_compiler.py', 'skip_frame_compose.py', 'verify_skip_frame.py', + 'binary_frame_compiler.py', 'binary_frame_math.py', 'binary_frame_replay.py', + 'binary_frame_profile_prepare.py', 'binary_frame_profiles.cpp')] + result = dict( + status='Conditional exact fixed-basis moment and balanced assembly; inherited transfer hypotheses remain assumed', + kappa=KAPPA, bit_saving=AB, bit_saving_excluded_above=EXCLUDED_ABOVE, + bit=dict(p, moment=exact, excluded_above_lower=excluded['lower']), + assembly=assembled, eventual_bounds=balanced.cutoffs(bridge, assembled), finite_bridge=bridge, + comparison=dict(pr48_kappa=Q(prior['kappa']), pr53_kappa=PR53_KAPPA, + ratio_pr53=KAPPA/PR53_KAPPA, pr54_claimed_kappa=PR54_CLAIMED_KAPPA, + ratio_pr54=KAPPA/PR54_CLAIMED_KAPPA, + next_dyadic_reached=KAPPA > Q(1, 2**14)), + exactness=[arithmetic.exactness(h) for h in (23, 25)], sources=sources, + local_source_sha256={str(p.relative_to(ROOT)): sha256(p.read_bytes()).hexdigest() for p in local_sources}, + dependencies=dict( + data_profile='Unchanged inherited all-pairs data profile: 9 singletons +21+17+481; ten exact rational recoveries', + producer='PR53 skip graph with exact original-envelope block compilation; complete serialized physical words', + geometry='Unchanged fixed-I+J original-envelope projector and CRT formulas', + proof_scope='Ordered affine residual compiler, fixed-tape recursion, finite scalar overhead, balanced transfer, analytic/routing/recovery interfaces remain inherited.')) + (OUT / 'skip-frame-kappa.json').write_text(json.dumps(arithmetic.js(result), indent=2, sort_keys=True)+'\n') + print('PASS conditional kappa='+str(KAPPA)+'; bit saving='+str(AB), flush=True) + return result + + +if __name__ == '__main__': + compose() diff --git a/scripts/experiments/verify_skip_frame.py b/scripts/experiments/verify_skip_frame.py new file mode 100644 index 0000000000..4dbdb25d9f --- /dev/null +++ b/scripts/experiments/verify_skip_frame.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Replay the PR53/frame-compiler words, actual fixed profiles and assembly. + +Every new XOR word, dirty basis column, frame incidence and fixed-basis +profile is checked. Unchanged data geometry and general transfer proofs +remain inherited dependencies; this is a finite conditional certificate. +""" +from hashlib import sha256 +from pathlib import Path +import json +import subprocess +import tempfile + +from binary_frame_profile_prepare import prepare +from binary_frame_replay import replay +from skip_frame_compose import compose + + +def verify(): + here = Path(__file__).resolve().parent + root = here.parents[1] + certificates = root / 'certificates' + stored = json.loads((certificates / 'skip-frame-compiler.json').read_text()) + axes = {} + with tempfile.TemporaryDirectory(prefix='skip-frame-verify-') as directory: + work = Path(directory) + profiler = work / 'profiles' + subprocess.run([ + 'c++', '-O3', '-std=c++17', + '-I', str(root / 'references/frame-compiler/pr48/scripts/partial_swap'), + str(here / 'binary_frame_profiles.cpp'), '-o', str(profiler), + ], check=True) + for h in (23, 25): + word = certificates / f'skip-frame-word-{h}.json.gz' + receipt = replay(word) + assert json.loads(json.dumps(receipt)) == stored['axes'][str(h)]['replay'] + transitions = work / f'word{h}.bin' + prepared = prepare(word, transitions) + expected = json.loads((certificates / f'skip-frame-transitions-{h}.json').read_text()) + assert json.loads(json.dumps(prepared)) == expected + subprocess.run([str(profiler), str(transitions)], check=True, capture_output=True, text=True) + profile = json.loads(Path(str(transitions)+'.profiles.json').read_text()) + expected = json.loads((certificates / f'skip-frame-profiles-{h}.json').read_text()) + assert profile == expected + axes[str(h)] = dict(replay=receipt, transitions=prepared, profile=profile) + print(f'PASS h={h}: full dirty basis, exact frame path, every fixed-basis profile', flush=True) + result = compose() + assert len(result['assembly']['constraints']) == 47 + assert len(result['assembly']['margins']) == 7 + validation = dict( + status='PASS complete serialized-word replay, actual CRT profiles, exact recurrence and balanced assembly', + axes=axes, kappa=str(result['kappa']), bit_saving=str(result['bit_saving']), + strict_constraints=47, margins=7, + certificate_sha256=sha256((certificates / 'skip-frame-kappa.json').read_bytes()).hexdigest(), + source_binding='Source manifests, inherited manifest digest, compiler receipt source, both word digests, and all local compiler/verifier sources are bound by the exact composition certificate.', + scope='Finite conditional witness; unchanged data geometry and general transfer proofs are inherited dependencies.') + (certificates / 'skip-frame-validation.json').write_text(json.dumps(validation, indent=2, sort_keys=True)+'\n') + print('PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs', flush=True) + return result + + +if __name__ == '__main__': + verify()