From ae9baba241f87bc004693a60b45e8c57d88092b0 Mon Sep 17 00:00:00 2001 From: eumemic Date: Thu, 8 Oct 2026 21:43:38 -0700 Subject: [PATCH] Paired cubes at p = 11 with an h = 21 bit word: kappa = 5.108289e-4 Run PR144's paired-cube complex construction at p = 11 (h = 22) with frozen carrier arcs, and replace the PR97 bit word by a hash-pinned h = 21 word in PR97's frozen format (strict link spans, PR144-style gauge subset). The complex side binds: AC = 5113520/10^10, bit COARSE = 5164125/10^10, and the 47-constraint assembly gives kappa = 5108289/10^10. Co-Authored-By: Claude Opus 5.5 (1M context) --- SOURCES.json | 31 + certificates/paired-cube-bit-input.json | 176 ++--- certificates/paired-cube-complex-input.json | 136 ++-- certificates/paired-cube-input.json | 115 ++- certificates/paired-cube-network.json | 498 ++++++------ docs/paired-cube.md | 9 +- notes/paired-cube-assembly.tex | 46 +- notes/paired-cube-bit.tex | 37 +- notes/paired-cube-construction.tex | 14 +- notes/paired-cube-note.tex | 4 +- notes/paired-cube-sharing.tex | 10 +- references/paired-cube/fib-bit-h21/README.md | 34 + .../paired-cube/fib-bit-h21/SOURCE.json | 29 + .../fib-bit-h21/bit-ledger-result.json | 104 +++ .../paired-cube/fib-bit-h21/deferred.py | 189 +++++ .../fib-bit-h21/deferred_21.json.gz | Bin 0 -> 981701 bytes .../fib-bit-h21/producer/bitcomp.py | 743 ++++++++++++++++++ .../fib-bit-h21/producer/bitcomp_w.py | 646 +++++++++++++++ .../fib-bit-h21/producer/circuit.py | 56 ++ .../fib-bit-h21/producer/export97.py | 229 ++++++ .../fib-bit-h21/producer/linalg_p.py | 98 +++ .../fib-bit-h21/producer/producer.py | 548 +++++++++++++ .../fib-bit-h21/producer/run_producer.py | 21 + .../paired-cube/fib-bit-h21/selection.json | 1 + .../fib-bit-h21/witness_21.json.gz | Bin 0 -> 404213 bytes .../paired-cube/selected-module/SOURCE.json | 4 +- .../selected-module/matching-arcs.json | 2 +- scripts/paired_cube/verify.py | 2 +- scripts/paired_cube_bit.py | 33 +- scripts/paired_cube_network.py | 14 +- scripts/paired_cube_producer.py | 2 +- 31 files changed, 3287 insertions(+), 544 deletions(-) create mode 100644 references/paired-cube/fib-bit-h21/README.md create mode 100644 references/paired-cube/fib-bit-h21/SOURCE.json create mode 100644 references/paired-cube/fib-bit-h21/bit-ledger-result.json create mode 100644 references/paired-cube/fib-bit-h21/deferred.py create mode 100644 references/paired-cube/fib-bit-h21/deferred_21.json.gz create mode 100644 references/paired-cube/fib-bit-h21/producer/bitcomp.py create mode 100644 references/paired-cube/fib-bit-h21/producer/bitcomp_w.py create mode 100644 references/paired-cube/fib-bit-h21/producer/circuit.py create mode 100644 references/paired-cube/fib-bit-h21/producer/export97.py create mode 100644 references/paired-cube/fib-bit-h21/producer/linalg_p.py create mode 100644 references/paired-cube/fib-bit-h21/producer/producer.py create mode 100644 references/paired-cube/fib-bit-h21/producer/run_producer.py create mode 100644 references/paired-cube/fib-bit-h21/selection.json create mode 100644 references/paired-cube/fib-bit-h21/witness_21.json.gz diff --git a/SOURCES.json b/SOURCES.json index f7117f0f98..26ce6af4b1 100644 --- a/SOURCES.json +++ b/SOURCES.json @@ -500,5 +500,36 @@ ], "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape contracts; complete local paired-cube schedule, exact core sharing and scalar charge supplied in the proof.", "curation": "Selected paired-coordinate cube only, compact frozen carrier arcs and bit subset, exact suppliers and assembly. Excludes fallback shared_core results, paired-five motifs, other candidate graphs, search screens and PDFs." + }, + "paired_cube_h21_bit_extension": { + "contributor": "eumemic", + "assistance": "Prepared with Anthropic Claude assistance.", + "predecessor_pr": 144, + "predecessor_commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff", + "kappa": "5108289/10000000000", + "proof": "notes/paired-cube-note.tex", + "certificate": "certificates/paired-cube-network.json", + "bit_word": "references/paired-cube/fib-bit-h21/SOURCE.json", + "change": "PR144 paired cubes at p=11 (h=22) with frozen carrier arcs, and a hash-pinned h=21 bit word in PR97 format with a PR144-style gauge subset; PR144 scripts, checks and assembly otherwise unchanged.", + "adopted": [ + { + "pr": 144, + "contributor": "icekylinx", + "commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff", + "role": "Paired-cube complex construction, shared cores, bit gauge-subset rule, finite bridge and assembly." + }, + { + "pr": 97, + "contributor": "Zhihao Chen (jacklightChen)", + "commit": "e15350b66e4bf796153a68c240a6cc1b788abe3e", + "role": "Unchanged frozen-word reader deferred.py and literal frame ledger, run on the h=21 word." + }, + { + "contributor": "Swapnil Jain", + "commit": "741e7aa078392553815df7926ee17ac5e25a8c38", + "role": "Round-seven bit producer lineage (PR62 interval strips) and checkers, run on the h=21 word." + } + ], + "scope": "Conditional on the retained PR144 analytic, uniform-recursion and fixed-tape contracts." } } diff --git a/certificates/paired-cube-bit-input.json b/certificates/paired-cube-bit-input.json index 27d657f001..f1d445233f 100644 --- a/certificates/paired-cube-bit-input.json +++ b/certificates/paired-cube-bit-input.json @@ -1,105 +1,99 @@ { - "R": 28866, - "W_per_vertex": 32408, + "R": 21526, + "W_per_vertex": 24186, "auxiliary_histogram": { - "0": 0, - "1": 54934, - "10": 158, - "11": 455, - "12": 195, - "13": 342, - "14": 110, - "15": 860, - "16": 768, - "17": 1447, - 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"references/paired-cube/fib-bit-h21/selection.json", + "selection_sha256": "bb9d9415c5689449c52bd194009b85adcc215503b2410927f4fa8c74d3f37b3a", "source_data_histogram": { - "1": 5061, - "13": 11, - "16": 198, - "17": 22, - "19": 1540, - "3": 23, - "4": 208, - "5": 11 + "1": 3790, + "15": 190, + "17": 1140, + "3": 180, + "4": 10 }, - "source_manifest": "references/partial-gauge/pr97/SOURCE.json", - "source_manifest_sha256": "68fb539abcd6df21d142e4e204b6e9482eb7f9cd3907650f54bd058070266596", + "source_manifest": "references/paired-cube/fib-bit-h21/SOURCE.json", + "source_manifest_sha256": "f8f6cb09c6a20e5650e8e6989a73188265158a9af8170d2a4e2339a482d43f06", "target_data_histogram": { - "1": 4655, - "16": 94, - "17": 176, - "18": 469, - "19": 1029, - "2": 839, - "21": 1, - "22": 2, - "3": 25 + "1": 3758, + "13": 4, + "14": 147, + "15": 130, + "16": 454, + "17": 585, + "19": 4, + "2": 642, + "20": 6, + "3": 31 }, - "v": 1771 + "v": 1330 } diff --git a/certificates/paired-cube-complex-input.json b/certificates/paired-cube-complex-input.json index 2f6fe0ae7b..e7d37225f5 100644 --- a/certificates/paired-cube-complex-input.json +++ b/certificates/paired-cube-complex-input.json @@ -1,86 +1,82 @@ { - "R": 26417, - "W_per_vertex": 29937, - "c": 24767, + "R": 18473, + "W_per_vertex": 21113, + "c": 16148, "child_histogram": { - "1": 79374, - "10": 5829, - "11": 3261, - "12": 3291, - "13": 2028, - "14": 6972, - "15": 2478, - "16": 6789, - "17": 4794, - "18": 1194, - "19": 11760, - "2": 81787, - "20": 11880, - "21": 2640, - "22": 2712, - "23": 0, - "24": 0, - "3": 34704, - "4": 29763, - "5": 22455, - "6": 8535, - "60": 4840, - "7": 7929, - "8": 7881, - "9": 3603 + "1": 59292, + "10": 3171, + "11": 939, + "12": 4536, + "13": 2121, + "14": 5178, + "15": 3075, + "16": 837, + "17": 9438, + "18": 8910, + "19": 1980, + "2": 58071, + "20": 2046, + "21": 0, + "22": 0, + "3": 23694, + "4": 20973, + "5": 16770, + "54": 3630, + "6": 5652, + "7": 3801, + "8": 5250, + "9": 2658 }, "copied_centers_already": true, - "deficit_per_vertex": 1936, - "h": 24, - "loss": 528, - "m": 72, - "matched": 6074, + "deficit_per_vertex": 1320, + "h": 22, + "loss": 440, + "m": 66, + "matched": 3472, "matching_frames": "coordinate", - "phase1_operations": 13616, - "q": 7724, - "rank_per_vertex": 2153528, + "phase1_operations": 10096, + "q": 5797, + "rank_per_vertex": 1392138, "remaining_internal_histogram": [ - 11459, - 19418, - 24329, - 11568, - 9921, - 7485, - 2845, - 2643, - 2627, - 1201, - 1943, - 1087, - 1097, - 676, - 2324, - 826, - 2263, - 1598, - 398, - 3920, - 440, - 880, - 904, + 7015, + 14484, + 17157, + 7898, + 6991, + 5590, + 1884, + 1267, + 1750, + 886, + 1057, + 313, + 1512, + 707, + 1726, + 1025, + 279, + 3146, + 330, + 660, + 682, 0, 0 ], "selected_rank_histogram": { - "20": 4840 + "18": 3630 }, - "selected_roles": 4840, + "selected_roles": 3630, "source_data_histogram": { - "1": 1760, - "2": 1760, - "20": 1760 + "1": 1320, + "18": 1320, + "2": 1320 }, "target_data_histogram": { - "0": 12760, - "1": 5280, - "20": 1760 + "0": 9570, + "1": 3960, + "18": 1320 }, - "total_M_operations": 49424, - "untouched_non_source_roles": 15417, - "v": 1760 + "total_M_operations": 33301, + "untouched_non_source_roles": 10335, + "v": 1320 } diff --git a/certificates/paired-cube-input.json b/certificates/paired-cube-input.json index 368d040cd0..de54014282 100644 --- a/certificates/paired-cube-input.json +++ b/certificates/paired-cube-input.json @@ -1,66 +1,63 @@ { - "absorption_gap": "49772927594887408131062764367/500461342287379865539365770570000000000", - "assembly_minimum": "23067114022986563163422943/50046134228737986553936577057", + "absorption_gap": "294878386089058851580570662909/6256391892262221613989310764190000000000", + "assembly_minimum": "319594608317161526768923581/625639189226222161398931076419", "bit_child_multiplicities": { - "1": 193950, - "10": 474, - "11": 1365, - "12": 585, - "13": 1059, - "14": 330, - "15": 2580, - "16": 3180, - "17": 4935, - "18": 3246, - "19": 9987, - "2": 200588, - "20": 7161, - "21": 1242, - "22": 75, - "3": 40116, - "4": 33642, - "48": 72, - "5": 18126, - "51": 131, - "54": 806, - "57": 3871, - "6": 4875, - "60": 1307, - "63": 1596, - "66": 1760, - "7": 2250, - "8": 3489, - "9": 1482 + "1": 150003, + "10": 4596, + "11": 7656, + "12": 498, + "13": 3177, + "14": 2916, + "15": 4014, + "16": 3834, + "17": 5643, + "18": 5670, + "19": 987, + "2": 87191, + "20": 81, + "3": 16848, + "39": 3, + "4": 13548, + "42": 103, + "45": 111, + "48": 874, + "5": 9018, + "51": 2982, + "54": 993, + "57": 1189, + "6": 6573, + "60": 1320, + "7": 882, + "8": 1617, + "9": 3033 }, - "bit_moment_gap": "9683053551624097783276572314019807322107841/67308782636558677514166530014945948467200000000000000", + "bit_moment_gap": "3104591513576928263373540835566618011499259/41206230128609221273381410446700969984000000000000000", "complex_child_multiplicities": { - "1": 79374, - "10": 5829, - "11": 3261, - "12": 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+++ b/certificates/paired-cube-network.json @@ -1,323 +1,331 @@ { "assembly": { - "absorption_gap": "49772927594887408131062764367/500461342287379865539365770570000000000", + "absorption_gap": "294878386089058851580570662909/6256391892262221613989310764190000000000", "margins": { - "Gaussian_arithmetic": "27680687058255018102013446063422943/40036907382990389243149261645600000000", - "bulk_exposure": "4613422943/10000000000000", - "compact_phase_layer": "23067114022986563163422943/50046134228737986553936577057", - "coordinate_movement": "4613422943/10000000000000", - "dimension": "49999999500000000000000000000/50046134228737986553936577057", - "original_prefix": "2306761448432885054328848236577057/5004613422873798655393657705700000000", - "scalar_work": "36907732944255014411275091663422943/40036907382990389243149261645600000000" + "Gaussian_arithmetic": "383515408176539944057838601068923581/500511351380977729119144861135200000000", + "bulk_exposure": "63918923581/125000000000000", + 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} }, - "kappa": "4609169/10000000000", + "kappa": "5108289/10000000000", "predecessor_commit": "6a9970a530119174507904e23592fd59ede19a5d", "scope": "Exact inventories, supplier moments, full fallback/router charge and semantic assembly. Local scalar/frame verification is separate; paired source scheduling, completed-core sharing and inherited uniform-recursion/analytic/tape contracts are written proof dependencies.", "source_sha256": { "certificates/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf", - "certificates/paired-cube-bit-input.json": "23461b66f3a87d4dc87ef209105df4de41d2ef076568ff29b9ea0a0747f01d96", - "certificates/paired-cube-complex-input.json": "11894aa8fd4d5e258ec534726eba5fc9c9fa7b826f993e229425c31ee2ad2440", - "certificates/paired-cube-input.json": "662ae85a5d70d130e704ef5a5d8665e2990988fe021ea21c3e0d43601555cc80", + "certificates/paired-cube-bit-input.json": "e4abb3d1d0c393dd5d5ce92aa90665ae009be407c8057f40da6be59b4fc3cbc5", + "certificates/paired-cube-complex-input.json": "af45e07663ad658f114576c04341ccc25537b49a59b90c21c4387d1eb4507408", + "certificates/paired-cube-input.json": "be1209df71ea6bc26a68256091971e2071021d81633ca2a3c0f544a5e3ad5276", "certificates/partial-gauge-bit-input.json": "367b9844db23f8fa64002637903bcc5ce28ffc8879d274b5c54c0390fb0234e4", "certificates/three-stage-cover-network.json": "bfca1f225394c8b50f3360b71920652baf9bd885ce84f9c0a9184c3ba7dd35ab", "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54", - 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"references/paired-cube/selected-module/SOURCE.json": "51739341346433c85f1c01f4bfbdf8d5f8971dd640899da854b5deb7dc740646", - "references/paired-cube/selected-module/matching-arcs.json": "22c90ed078d765e58ac824d6f9558cc4620961b48644a32c0115bdb9852de771", + "references/paired-cube/selected-module/SOURCE.json": "3bf03c7eb4714608837fb1604652bbf40ebfdec1ef95edecf4042a8c0801cea0", + "references/paired-cube/selected-module/matching-arcs.json": "fe28c981304643aeb383a8ef6b4fec0b818b665dd86da1b4955796073f8cecbb", "references/partial-gauge/pr97/SOURCE.json": "68fb539abcd6df21d142e4e204b6e9482eb7f9cd3907650f54bd058070266596", "scripts/paired_cube/README.md": "bf2adf1d1c5a412730be66e019bd73a08826ef8dcd6ffc833b9d1656b755dfb2", "scripts/paired_cube/__init__.py": "b5fb17c79fd41a75c0648e7a5f99076f9f42a619857d5e34e71699bf00ef0c91", @@ -325,10 +333,10 @@ "scripts/paired_cube/gauges.py": "8a501c66e1330f054e0e11a35e9321d2deea7b51cd03ca56b6a41765e43fe061", "scripts/paired_cube/graph.py": "c757d47997f2fa42a95c16f6e6855cf8b125216ae3335b3891e305cf1da82855", "scripts/paired_cube/modules.py": "18a1ad8af0a7832b7c5c4791f5b95f76386cfa7e82ad52bfd2758c081ada68c4", - "scripts/paired_cube/verify.py": "e13747916a58b631f10c36eaae230b91b63b427d0a80aa3a530dd9dd90159147", - "scripts/paired_cube_bit.py": "306b3100b97885c0e8b8439a425deac77915d25a7f5bea5bc30d1ee837709efc", - "scripts/paired_cube_network.py": "293662b7f8772dd398399a1c19966faf7d155f024543d0c06601eabb800f35cf", - "scripts/paired_cube_producer.py": "c84ea3e3ce3eb9563906b6ee4b7411d93dcddfed4bdbc2d4e39936642261cab2", + "scripts/paired_cube/verify.py": "5ceedcb97650a753dded512025e8332698b956f623678fb4005c2057a19d742c", + "scripts/paired_cube_bit.py": "6ca34988dba3c51627b06a1f61a7b7c92a929d200b85a84b4558c1470dfffa99", + "scripts/paired_cube_network.py": "8432eb5e677c2ff97c6f5db0f6950616d328935ae9afae893bd66cf3150e5845", + "scripts/paired_cube_producer.py": "2bc2c79d35f6961e1b1555eaa9fa4315e200940c6e9020f6cb88b41c0631f401", "scripts/partial_gauge_bit.py": "7d58e86061da2d73991531e9bc431589019359391adea866c61c7dd1f99ac855", "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d", "scripts/three_stage_cover_network.py": "7e0ad6fd1921b6905a53ce1eeaa03d3bb3a8a8bbaa0382516ea98b636f46335e" diff --git a/docs/paired-cube.md b/docs/paired-cube.md index 38dc3d30e0..ba7e2fe15c 100644 --- a/docs/paired-cube.md +++ b/docs/paired-cube.md @@ -2,7 +2,7 @@ This extension inherits PR #130 at `6a9970a530119174507904e23592fd59ede19a5d` and gives the conditional saving -`4609169/10000000000 = 4.609169e-4`. +`5108289/10000000000 = 5.108289e-4`. From the repository root with Python 3.11+: @@ -16,11 +16,12 @@ CI runs it in its own `paired-cube` matrix group. The checks are: - Rebuild the selected signed H-channel graph from exact zero restrictions of the pinned PR #117 positive DAG. Replay the frozen 6,074 carrier arcs, coordinate frames, full backward intersections, signed physical mixer, - center closure and 4,840 rank-20 partial gauges. Independent checks cover + center closure and 3,630 rank-18 partial gauges. Independent checks cover every scalar coefficient of `H+K+B=I`, the original-source K involution and inverse, actual frame containment and reverse target chains. -- Reconstruct the bit subset from the existing PR #97 witness and readout - order. Check the retained 9,543 and omitted 2,022 slots, moved zero-frame +- Reconstruct the bit subset from the hash-pinned h = 21 word in + `references/paired-cube/fib-bit-h21/` (PR #97 format and reader) and its + readout order. Check the retained 7,575 and omitted 1,335 slots, moved zero-frame dirty reads, changed first transitions and target subsequences. Unchanged complete-basis and rational-frame suites remain inherited checks. - Rebuild both shared-core child lists and certify strict moments, full diff --git a/notes/paired-cube-assembly.tex b/notes/paired-cube-assembly.tex index d44227eb55..4674526700 100644 --- a/notes/paired-cube-assembly.tex +++ b/notes/paired-cube-assembly.tex @@ -1,54 +1,54 @@ \subsection{Strict suppliers and full finite group} The selected local complex profile has \[ - h=24,\quad v=1760,\quad c=24767,\quad q_{\rm roots}=7724, - \quad |\mathcal M|=6074,\quad R=26417,\quad\ell=528. + h=22,\quad v=1320,\quad c=16148,\quad q_{\rm roots}=5797, + \quad |\mathcal M|=3472,\quad R=18473,\quad\ell=440. \] The exact signed graph, frozen carrier arcs, coordinate frames and chronological gauge list are reconstructed by \path{scripts/paired_cube_producer.py}. Its complete shared inventory has -$m_c=72$, $w_c=29937$, $s_c=2153528$, deficit 1936 and largest child 60. -For $a_c=4856569/10^{10}$ the rational moment satisfies +$m_c=66$, $w_c=21113$, $s_c=1392138$, deficit 1320 and largest child 54. +For $a_c=5113520/10^{10}$ the rational moment satisfies \[ - \frac1{w_c}\sum_r n_r(r/72)^{1-a_c} - <1-2.0094617553\times10^{-10}. + \frac1{w_c}\sum_r n_r(r/66)^{1-a_c} + <1-4.6077795770\times10^{-13}. \] -The bit subset has $m_b=69$, $w_b=32408$, $s_b=2234128$ and deficit 2024. -At coarse saving $a_0=4617656/10^{10}$ its moment includes the entire -$32\cdot69^2$-child local-ring fallback on a fraction $10^{-16}$ of every -ideal edge. Its gap exceeds $1.4386017949\times10^{-10}$; the rank moment +The bit subset has $m_b=63$, $w_b=24186$, $s_b=1522318$ and deficit 1400. +At coarse saving $a_0=5164125/10^{10}$ its moment includes the entire +$32\cdot63^2$-child local-ring fallback on a fraction $10^{-16}$ of every +ideal edge. Its gap exceeds $7.5342769864\times10^{-11}$; the rank moment also contracts. With the retained atom exponent $10^{-3}$, \[ a_b=(1-10^{-3})a_0+10^{-3}\frac{384599}{10^{10}} - =\frac{4613422943}{10^{13}}. + =\frac{5159345474}{10^{13}}. \] Both adapter and internally borrowed-row tolls are lower order since $a_b<10^{-3}<1-a_b$. The weighted compiler, residue bound, full fallback and ordinary outer wrapper are retained from \path{notes/three-stage-cover-bit.tex} and -\path{notes/three-stage-cover-rows.tex}, now with ambient dimension 69. +\path{notes/three-stage-cover-rows.tex}, now with ambient dimension 63. Sharing routers are fixed right multiplications, batched on the same complete high matrix field; the fresh-selector contract is unchanged. -For the complex cover $V=|O(72,2)|$ the retained even-dimensional group +For the complex cover $V=|O(66,2)|$ the retained even-dimensional group formula gives \[ - V=2^{1296}\prod_{i=1}^{35}(2^{2i}-1). + V=2^{1089}\prod_{i=1}^{32}(2^{2i}-1). \] -It has 2,556 bits, and full role stock $W=Vw_c$ has 2,571 bits. +It has 2,145 bits, and full role stock $W=Vw_c$ has 2,159 bits. Its full rank is $s=Vs_c$ and $N=Vv$. -The least halving degree for $72\to60$ is four, contributing 10,284 to +The least halving degree for $66\to54$ is four, contributing 8,636 to the row coefficient. Including the conservative preceding bit reserves, \[ - 10284+9909+252=20445,\qquad - 70000-\frac{51}{25}\,20445=\frac{141461}{5}>0. + 8636+9909+252=18797,\qquad + 70000-\frac{51}{25}\,18797=\frac{791353}{25}>0. \] Thus the fixed external reserve $p^{70000}$ suffices. The q-adic bit selector stock is borrowed and restored internally, not multiplied into this external polynomial reserve. \subsection{Literal charge, sharing routers and exact precision} -Let $M=49424$ be the actual local mixer-operation count. Put +Let $M=33301$ be the actual local mixer-operation count. Put \[ L=4(c+v)+10v+4hv+4h^2+8h+8+2h +8Rv(M+16)+32v. @@ -56,7 +56,7 @@ \subsection{Literal charge, sharing routers and exact precision} The last term pays both original-source involutions and their inverses. Every mixer update has signed unit coefficients. Starting from the identity, each entry of its exact matrix is therefore bounded by $2^M$. -There are $q_{\rm roots}=7724$ decoder roots; after clearing denominator +There are $q_{\rm roots}=5797$ decoder roots; after clearing denominator six, their scatter coefficients have absolute numerator at most three. Thus each numerator of $6JM$ is bounded by $3q_{\rm roots}2^M<2^{M+15}$. Including the sign, $M+16$ bits suffice. @@ -108,14 +108,14 @@ \subsection{Exact retained semantic assembly} 1-\epsilon(1+c_0),\ a,\ g,\ a,\ \min(1-\epsilon-\delta,r-\delta),\ 1-\epsilon-\delta,\ \epsilon. \] -Their minimum $g$ exceeds $4609169/10^{10}$ by more than -$9.9454090434\times10^{-11}$. +Their minimum $g$ exceeds $5108289/10^{10}$ by more than +$4.7132339400\times10^{-11}$. \begin{theorem} Under the retained analytic, semantic-precision, exact-recovery, uniform-recursion and fixed-tape interfaces, the selected construction gives \[ T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad - \boxed{\kappa=\frac{4609169}{10000000000}=4.609169\times10^{-4}}. + \boxed{\kappa=\frac{5108289}{10000000000}=5.108289\times10^{-4}}. \] \end{theorem} \begin{proof} diff --git a/notes/paired-cube-bit.tex b/notes/paired-cube-bit.tex index dd84535b21..7b4948996c 100644 --- a/notes/paired-cube-bit.tex +++ b/notes/paired-cube-bit.tex @@ -1,15 +1,16 @@ % Copyright 2026 icekylinx. Apache-2.0. % Construction with GPT-6 Astra; integration with OpenAI Codex. -% Retained PR97 ledger: Zhihao Chen; frozen scalar/frame witness: Swapnil Jain. +% Retained PR97 reader and ledger: Zhihao Chen. The h=21 bit word (PR62 lineage of +% Swapnil Jain's construction) was prepared by eumemic with Anthropic Claude assistance. % Their original licenses, credits and assistance disclosures remain pinned. \subsection{Selected inherited bit gauges} -The bit supplier uses the pinned PR97 word at $h=23$, with $v=1771$ data -ports and $R=28866$ dirty roles. Its compressed witness, frame reader, -physical-ledger receipt and original notices remain under -\texttt{references/partial-gauge/pr97/}. The finite selection in -\texttt{references/paired-cube/pr97-subset/selection.json} retains $9543$ -of the $11565$ certified entrance gauges, in their original readout order, -and omits $2022$. This selects actual inherited frames, rather than +The bit supplier uses a hash-pinned word at $h=21$, with $v=1330$ data +ports and $R=21526$ dirty roles, in PR97's frozen format and read by PR97's +unchanged reader. Its compressed witness, literal-ledger receipt, producer +and gauge selection are under \texttt{references/paired-cube/fib-bit-h21/}. +The selection retains $7575$ +of the $8910$ entrance gauges, in their original readout order, +and omits $1335$. This selects actual inherited frames, rather than optimizing an unattached multiset of ranks. For an omitted role with entrance frame $\sigma_s$ of dimension $f_s$, @@ -30,24 +31,24 @@ \subsection{Selected inherited bit gauges} retain precisely the positive integer adjoint supports of the chosen readouts. This is the inherited conservative support convention; an even coefficient would merely give a zero bit read with a retained frame. -The source histogram and all $23$ copied-center transitions of width $22$ +The source histogram and all $21$ copied-center transitions of width $20$ are unchanged. The selected gauge dimensions have multiplicities \[ - (22,1760),\ (21,1596),\ (20,1307),\ (19,3871),\ - (18,806),\ (17,131),\ (16,72). + (20,1320),\ (19,1189),\ (18,993),\ (17,2982),\ + (16,874),\ (15,111),\ (14,103),\ (13,3). \] -In the cross-stage orthogonal sharing architecture, $m=3h=69$ and -$W=2v+R=32408$ per cover vertex. There are three copies of each local +In the cross-stage orthogonal sharing architecture, $m=3h=63$ and +$W=2v+R=24186$ per cover vertex. There are three copies of each local auxiliary, source, target and copied-center transition, one exterior child of width $3f_s$ per selected gauge, and $2v$ final children of width $2$. Consequently the selected profile has \[ - \ell=h(h-1)=506,\qquad - \sum_r r C_r=2234128=Wm-2024,\qquad - 2024=2v-3\ell. + \ell=h(h-1)=420,\qquad + \sum_r r C_r=1522318=Wm-1400,\qquad + 1400=2v-3\ell. \] -Its largest child is $66$. The strict supplier moment below also charges +Its largest child is $60$. The strict supplier moment below also charges the retained rare-class fallback and stopped atom wrapper. \texttt{scripts/paired\_cube\_bit.py} reconstructs this profile from the @@ -55,7 +56,7 @@ \subsection{Selected inherited bit gauges} partition and inherited order, the integer target-incidence sweep, the initial zero-frame corrections, and the changed transition histogram against a direct reconstruction of the modified role chains. The -incremental review finds $72$ changed transition types and $9594$ moved +incremental review finds $56$ changed transition types and $5113$ moved old-value reads. It repeats neither the complete-basis scalar replay nor the inherited exact rational frame and lifted-witness audits. The original frozen witnesses and scripts remain unchanged. diff --git a/notes/paired-cube-construction.tex b/notes/paired-cube-construction.tex index 9dd1f10cb7..c1e9a69a1d 100644 --- a/notes/paired-cube-construction.tex +++ b/notes/paired-cube-construction.tex @@ -128,13 +128,13 @@ \subsection{Arbitrary dirty contents and the frozen witness} have been restored. Exact frame representatives and rank-zero phase adapters are those of the arbitrary-subspace Clifford interface. -For the selected $p=12$ graph, 24,767 active additions and 7,724 root -uses, with 6,074 actual monotone carrier links, give +For the selected $p=11$ graph, 16,148 active additions and 5,797 root +uses, with 3,472 actual monotone carrier links, give \[ - h=24,\quad v=1760,\quad R=26417,\quad\ell=528. + h=22,\quad v=1320,\quad R=18473,\quad\ell=440. \] -The frozen chronological gauge witness selects 4,840 roles, each of -dimension 20. Its graph, matching/frame witness and gauge-selection file, +The frozen chronological gauge witness selects 3,630 roles, each of +dimension 18. Its graph, matching/frame witness and gauge-selection file, not an abstract circuit-rank bound, determine the paid internal histogram. -The selected source histogram is $[2,20,1]$ per port; the target histogram -is $[20,1,1,1]$ per port. Zero-width adapters remain paid scalar work. +The selected source histogram is $[2,18,1]$ per port; the target histogram +is $[18,1,1,1]$ per port. Zero-width adapters remain paid scalar work. diff --git a/notes/paired-cube-note.tex b/notes/paired-cube-note.tex index b72c67f72f..f56d4d3b98 100644 --- a/notes/paired-cube-note.tex +++ b/notes/paired-cube-note.tex @@ -9,7 +9,7 @@ \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \title{Paired cubes and shared completed cores for integer multiplication\\ -\large A conditional saving $\kappa=4609169/10^{10}$} +\large A conditional saving $\kappa=5108289/10^{10}$} \author{icekylinx\\\small Construction with substantial OpenAI GPT-6 Astra assistance;\\ \small exposition and repository integration with Codex assistance} \date{9 October 2026} @@ -20,7 +20,7 @@ on the original source registers. Complete arbitrary-dirty cores share one auxiliary bank across three orthogonal address blocks. The exact selected ledgers, bit gauge subset and retained semantic assembly yield -$T(n)=O(n(\log n)^{1-0.0004609169})$ under the inherited interfaces. +$T(n)=O(n(\log n)^{1-0.0005108289})$ under the inherited interfaces. \end{abstract} \section{Scope and contributions} diff --git a/notes/paired-cube-sharing.tex b/notes/paired-cube-sharing.tex index 56e729572d..2b638483ad 100644 --- a/notes/paired-cube-sharing.tex +++ b/notes/paired-cube-sharing.tex @@ -79,12 +79,12 @@ \subsection{The complete paid ledger} \end{align*} For the selected complex word, \[ - m=72,\quad W_0=29937,\quad - \sum_r rn_r=2153528,\quad mW_0-\sum_r rn_r=1936. + m=66,\quad W_0=21113,\quad + \sum_r rn_r=1392138,\quad mW_0-\sum_r rn_r=1320. \] -The 4,840 exterior children have width 60; all local internal children -have width at most 22, and final data children have width two. -Hence the largest child is 60. Full stock is $W=|\mathcal G|W_0$; +The 3,630 exterior children have width 54; all local internal children +have width at most 20, and final data children have width two. +Hence the largest child is 54. Full stock is $W=|\mathcal G|W_0$; the group factor cancels from the normalized moment, not from routing, scalar work, row stock or the finite semantic guard. diff --git a/references/paired-cube/fib-bit-h21/README.md b/references/paired-cube/fib-bit-h21/README.md new file mode 100644 index 0000000000..41fbc76cd4 --- /dev/null +++ b/references/paired-cube/fib-bit-h21/README.md @@ -0,0 +1,34 @@ +# h = 21 bit word with Fibonacci-oriented strips + +Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. + +`witness_21.json.gz` and `deferred_21.json.gz` are an h = 21 bit word in PR #97's frozen format. They are read by +PR #97's unchanged `deferred.py`. The word has v = 1330, R = 21526, 8910 deferred readouts, 8590 V-leaf slots, +16628 links and 1120 late nodes. Its lifted frames are M_n = U_n. + +- **DAG.** The DAG is a native h = 21 rebuild of the round-seven PR #62 lineage (Swapnil Jain's interval strips, + #41 order), with Fibonacci-oriented level-zero strips. +- **Compiler.** The B-defer compiler uses weighted links. Every link satisfies span(donor) ⊆ span(user), the + combinatorial criterion of the round-seven `check_lifted` (enforced inside the matching, `STRICT_LINKS=1`). +- **Reproduction.** `producer/` holds the producer and exporter: + `STRICT_LINKS=1 BIT_H=21 FIB0='9=2:1,3:2,5:2,8:5' python run_producer.py dag.json; + python export97.py dag.json OUT`. + The matching needs numpy/scipy. +- **Gauge subset.** `selection.json` is the gauge subset in #144's format, in inherited readout order: 7575 gauges + retained and 1335 omitted. + +## Checks run on this word + +- **Literal ledger.** `bit-ledger-result.json` is the output of PR #97's `round7_literal_frame_ledger.py` at h = 21. + It reports complete forward and reflected F2 scalar words, reflected frame continuity, equal frame keys at + every scalar gate and the external histogram. +- **Round-seven checkers at h = 21.** `check_word` passes: schedule semantics, garbage coefficients, phase one, + release rule, dirty-scratch replay over F2 and Z, and negative controls. + - `check_lifted` passes: dirty-scratch replay over F2 and Z, j-monotonicity, link spans, and a chain histogram + equal to the witness's claim. + - `check_frames` passes every frame, nesting, nondegeneracy and side-lemma check. + - Its only failure is the regression pin to round seven's constants. +- **Independent B-defer replay (stages one and two).** + - Frames hold by exact inclusion. + - Scalars are checked over F2 on the complete basis: y_T += x_T, and every slot is restored. + - The paid multisets of the two stages are equal. diff --git a/references/paired-cube/fib-bit-h21/SOURCE.json b/references/paired-cube/fib-bit-h21/SOURCE.json new file mode 100644 index 0000000000..4f7e2f9b1a --- /dev/null +++ b/references/paired-cube/fib-bit-h21/SOURCE.json @@ -0,0 +1,29 @@ +{ + "pr97": { + "commit": "e15350b66e4bf796153a68c240a6cc1b788abe3e", + "reader": "deferred.py", + "repository": "jacklightChen/integer-mult-bounds", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/97" + }, + "scope": "Hash-bound h=21 bit word in PR97 frozen format, its literal-ledger receipt, gauge subset, producer and exporter. PR97 reader deferred.py is byte-identical to references/partial-gauge/pr97/deferred.py.", + "sha256": { + "README.md": "588200f5ff08a61e87cb2f3c5b79e64b861781339070e5613882ee48f78236f6", + "bit-ledger-result.json": "038b9c7309be8bc4e739f6f61207bf7b9063f0dd52d9ca21da2d7ac5191f6121", + "deferred.py": "9b2acaeb6f1beb2a53c15e00c027f9ba22397a12071ad0b71131e12012a98036", + "deferred_21.json.gz": "992f0e4cb205a5c776f9d6bac0b49d8e81700ec4ed7f56001bf73a05aaeb3522", + "producer/bitcomp.py": "77ce5c74808c0de04d8795c1b19d85f471ad7bc4e720b126b9b261eef0be1408", + "producer/bitcomp_w.py": "79d8855b6a4433e8a030664f3327cb6e5231b2e7cbf8197a1be69594fb1dd5f3", + "producer/circuit.py": "0965b567c1b1b03abb86bc4b1a1d9e99a9d079a80cd703394d2dc11adb8b842d", + "producer/export97.py": "dba9ab574ba976ffee331349c1264c92eb7a6d430edcd6f1d03efb19a6cb11b8", + "producer/linalg_p.py": "dc5d3ea0e33a13e00f5c113933c12c700affde42510f16e81d7087dd8f743283", + "producer/producer.py": "8eebf306db6e5ce86db16e482740c69b869f7da45d41e096c82ff5a8a171f6f2", + "producer/run_producer.py": "627ebb2b8defbcc5cb2c2a77d85029f269685393c33b18b90a8b314e59a60321", + "selection.json": "bb9d9415c5689449c52bd194009b85adcc215503b2410927f4fa8c74d3f37b3a", + "witness_21.json.gz": "2190f06b87edbe4bd391b573baacd62d0024660f14537a803a174dce1e30355d" + }, + "underlying": { + "description": "h=21 bit DAG rebuilt from the round-seven PR62 lineage with Fibonacci-oriented level-zero strips; B-defer compile with weighted links", + "prepared_by": "eumemic with Anthropic Claude assistance", + "producer": "producer/" + } +} diff --git a/references/paired-cube/fib-bit-h21/bit-ledger-result.json b/references/paired-cube/fib-bit-h21/bit-ledger-result.json new file mode 100644 index 0000000000..49b7dc703c --- /dev/null +++ b/references/paired-cube/fib-bit-h21/bit-ledger-result.json @@ -0,0 +1,104 @@ +{ + "h": 21, + "roles": 21526, + "formal_basis": 24186, + "events": 709665, + "frame_keys": 55998, + "rank_histograms": { + "aux": { + "1": 42499, + "4": 4421, + "2": 27639, + "6": 2088, + "3": 5564, + "5": 3211, + "7": 382, + "8": 604, + "14": 618, + "12": 246, + "16": 526, + "9": 1137, + "11": 2664, + "10": 1615, + "15": 802, + "13": 941, + "17": 111, + "18": 1890, + "19": 325 + }, + "data": { + "3": 656, + "1": 8740, + "4": 636, + "2": 2065, + "5": 253, + "6": 364, + "7": 176, + "8": 210, + "10": 125, + "9": 114, + "11": 68, + "13": 44, + "12": 86, + "14": 74, + "15": 237, + "16": 43, + "17": 1142, + "19": 2, + "20": 4, + "18": 1 + }, + "center": { + "20": 21 + } + }, + "fan_groups_reordered_internally": [], + "complete_forward_F2": true, + "complete_reflected_F2": true, + "reflected_frame_continuity": true, + "all_scalar_gates_equal_frame_keys": true, + "exterior_formula": "E1=I-I_tensor_Q+sigma_tensor_Q; E2=(I-P)_tensor_I+P_tensor_sigma; rank=m-h+dim(sigma)", + "histogram_matches_external": true, + "histogram": { + "1": 867141380, + "9": 3090920, + "17": 1335320, + "15": 5163060, + "13": 3729320, + "11": 1609300, + "7": 1931160, + "5": 2899400, + "19": 4561900, + "3": 965580, + "399": 33558560, + "21": 33558560, + "437": 3162740, + "439": 3511200, + "401": 957600, + "433": 7932120, + "435": 2641380, + "403": 465500, + "405": 133000, + "423": 42560, + "429": 359100, + "419": 234080, + "417": 82460, + "411": 327180, + "421": 87780, + "415": 279300, + "425": 53200, + "427": 524020, + "413": 90440, + "409": 95760, + "407": 396340, + "431": 2324840, + "359": 3537800, + "16": 3537800 + }, + "recursive_rank": 26810807660, + "elapsed": 6.145565333019476, + "limit_seconds": 180, + "exact_chain_geometry": "Relies on separately replayed pinned check_frames and check_lifted. Rank labels alone do not prove geometry.", + "scope": "Explicit one-axis forward/reflected events, scalar complete basis and exact accounting. Tensor endpoint identities proved separately; full complex/tape/precision and final assembly integration not established.", + "new_multiplication_bound": false +} diff --git a/references/paired-cube/fib-bit-h21/deferred.py b/references/paired-cube/fib-bit-h21/deferred.py new file mode 100644 index 0000000000..d045126217 --- /dev/null +++ b/references/paired-cube/fib-bit-h21/deferred.py @@ -0,0 +1,189 @@ +"""Shared reader and accounting for the round-seven bit side (stdlib only). + +Frozen inputs (certificates/round7/): + witness_23.json.gz the base side program: DAG (leaves = triples of [h], additions), outputs (c, T), retained + totals, links, the flag matrix, the lift index j(n) of every lifted addition and the late-copy + decisions; checked by check_lifted.py; + deferred_23.json.gz the reordered stage-1 word: the slot schedule (ops, the node held by every slot over time, + slot starts, output and retained slots), the deferred readout frames sigma_u, the V-leaf start + frames s_i (both as primitive integer bases), the readout order, the X_S order of every leaf, + the order of the deferred V gates, and the dimension of every node frame and late-copy + intersection (re-derived exactly by check_frames.py). + +Ops: ['add', piv, oth, n] a[piv] += a[oth], the addition of node n; ['fan', piv, [f...]] a[f] += a[piv] for fresh +slots f (copies); ['src', s, n] the V gate a[s] += x_S of leaf n (applied outside L, see check_word.py).""" +import gzip, json, os +from collections import Counter, defaultdict +from itertools import combinations +from math import comb + +HERE = os.path.dirname(os.path.abspath(__file__)) +ROOT = os.path.normpath(os.path.join(HERE, '..', '..')) +DATA = os.path.join(ROOT, 'certificates', 'round7') + + +def load_json(name): + with gzip.open(os.path.join(DATA, name), 'rt') as fh: + return json.load(fh) + + +def load(h=23, witness=None, data=None): + """the base witness and the design-B data of one round-seven witness (default: the files of h).""" + W = load_json(witness or 'witness_%d.json.gz' % h); D = load_json(data or 'deferred_%d.json.gz' % h) + assert W['h'] == D['h'] == h + return W, D + + +class Schedule: + """The design-B schedule in convenient form.""" + def __init__(self, W, D): + self.h = h = D['h']; self.R = D['R']; self.trip = list(combinations(range(h), 3)); self.v = len(self.trip) + self.tid = {T: i for i, T in enumerate(self.trip)} + self.args = {int(n): (tuple(a) if a else None) for n, a in W['args'].items()} + self.ops = [tuple(o[:2]) + (tuple(o[2]),) if o[0] == 'fan' else tuple(o) for o in D['ops']] + self.hold = D['hold']; self.start = D['start'] + self.out = {s: (c, tuple(T)) for s, c, T in D['out']} + self.ret = {s: c for s, c in D['ret']} + self.srcop = {o[1]: o[2] for o in self.ops if o[0] == 'src'} + self.readout = D['readout_order']; self.sel = set(self.readout) + self.sigma = dict(zip(D['readout_order'], D['sigma'])) + self.f = [0] * self.R + for s, B in self.sigma.items(): self.f[s] = len(B) + self.vstart = dict(zip(D['vleaf_slots'], D['vleaf_start'])) + self.xs = [(n, us) for n, us in D['xs_order']] + self.late_v = D['deferred_v_order'] + self.node_dims = {n: d for n, d in D['node_dims']} + self.late_dims = {(n, tuple(lt)): d for n, lt, d in D['late_dims']} + self.late = {int(n): (list(e), list(l)) for n, (e, l) in W['late'].items()} + self.pivslot = {o[3]: o[1] for o in self.ops if o[0] == 'add'} + + def touch(self, op): + if op[0] == 'add': return [op[1], op[2]] + if op[0] == 'fan': return [op[1]] + list(op[2]) + return [] + + def root_targets(self): + rt = {} + for s, (c, T) in self.out.items(): rt[s] = [self.tid[T]] + for s, c in self.ret.items(): rt[s] = [t for t, T in enumerate(self.trip) if c in T] + return rt + + def adjoint(self): + """garbage coefficients over Z: cov[s][t] = coefficient of slot s's start value in target y_T at the end of L + (the transpose sweep of L applied to the root reads); the F2 circuit uses their parities.""" + cov = [dict() for _ in range(self.R)] + for s, ts in self.root_targets().items(): + for t in ts: cov[s][t] = cov[s].get(t, 0) + 1 + def addto(d, e): + for t, x in e.items(): d[t] = d.get(t, 0) + x + for op in reversed(self.ops): + if op[0] == 'add': addto(cov[op[2]], cov[op[1]]) + elif op[0] == 'fan': + for g in op[2]: addto(cov[op[1]], cov[g]) + return cov + + # ------------------------------------------------------------------ frame keys of every slot's chain + def start_key(self, s): + """('v', s) for a V-leaf slot (start s_i), ('n', n0) for a base or early copy, ('c', n0, late suffix).""" + n0 = self.hold[s][0] + if self.args[n0] is None: return ('v', s) + st = self.start[s]; k = st[2]; dec = self.late.get(n0) + if dec is None or k in dec[0]: return ('n', n0) + lt = dec[1]; return ('c', n0, tuple(lt[lt.index(k):])) + + def chain_keys(self, s): + """frames of slot s in time order: [sigma_u | 0], start, then every later node it holds (with the pivot's + late-copy intersections after a node it pivots), its root frame if any, F.""" + ch = [('sigma', s) if s in self.sel else ('0',), self.start_key(s)] + for idx, n in enumerate(self.hold[s]): + if idx > 0: ch.append(('n', n)) + if self.args[n] is not None and self.pivslot.get(n) == s and n in self.late: + lt = self.late[n][1] + for i in range(len(lt) - 1): ch.append(('c', n, tuple(lt[i:]))) + if s in self.out: c, T = self.out[s]; ch.append(('out', c, T)) + if s in self.ret: ch.append(('ret', self.ret[s])) + ch.append(('F',)); return ch + + def dim(self, key): + k = key[0] + if k == '0': return 0 + if k == 'F': return self.h + if k in ('out', 'ret'): return self.h - 1 + if k == 'n': return self.node_dims[key[1]] + if k == 'c': return self.late_dims[key[1], key[2]] + if k == 'sigma': return len(self.sigma[key[1]]) + if k == 'v': return len(self.vstart[key[1]]) + raise KeyError(key) + + def ylevels(self, cov): + """deferred readout levels (dim sigma) on every target, from the garbage-coefficient supports.""" + lev = defaultdict(set) + for s in self.readout: + for t in cov[s]: lev[t].add(self.f[s]) + return {t: sorted(lev[t]) for t in range(self.v)} + + def xdata(self, dimof=None): + dimof = dimof or (lambda s: len(self.vstart[s])) + out = [] + for n, us in self.xs: + ds = [1] + [dimof(s) for s in us] + [self.h] + ds = [d for i, d in enumerate(ds) if i == 0 or d != ds[i - 1]] + out.append([b - a for a, b in zip(ds, ds[1:])]) + return out + + +def inner(r, h): + """children of a rank-r chain step under the inner-corner lemma (one block of width 2r-h when 2r > h).""" + return [1] * (h - r) + [2 * r - h] if 2 * r > h else [1] * r + + +def chain_ranks(S, dimof=None): + """multiset of chain-step ranks over all slots (dims must be monotone along every chain).""" + dimof = dimof or S.dim; rk = Counter() + for s in range(S.R): + ds = [dimof(k) for k in S.chain_keys(s)] + assert all(b >= a for a, b in zip(ds, ds[1:])), ('decreasing chain', s) + assert ds[-1] == S.h + for a, b in zip(ds, ds[1:]): + if b > a: rk[b - a] += 1 + return rk + + +ROUND6_CORNER = lambda h: [h - 2] + [1] * (h + 1) # data-entrance corner runs, rounds six and seven +STAIRCASE_CORNER = lambda h: [h - 2, h - 5] + [1] * 6 # staircase corner (check_stair.py) + + +def histogram(S, rk, ylev, xdata, corner=None): + """child-width histogram of the batched two-stage bit interchange with deferred readouts and V leaves. + Per stage (stage two is the complement time-reversal of stage one, same edge multiset), each of the v invocations: + every slot u: its auxiliary edge of rank m - r_u (block m - 2 r_u) and its corner of rank r_u = h - dim sigma_u, + both batched by the inner lemma, plus its chain steps; + every centre: the copy's step U_c -> 0 of rank h-1; + every target y_T: the chain 0 -> deferred levels -> t_T^perp (total rank h-1); + every leaf X_S: its chain -> V-gate frames -> F (total rank h-1). + Data: the entrance block m-4h+2 with its corner runs, one copy-correction singleton per pair.""" + h, v, R = S.h, S.v, S.R; m = h * h; N = v * v; A = v * R; H = Counter() + corner = corner or ROUND6_CORNER(h); assert sum(corner) == 2 * h - 1 + corners = Counter(h - S.f[s] for s in range(R)) + for _ in range(2): + for r, c in corners.items(): + H[m - 2 * r] += v * c + for w in inner(r, h): H[w] += v * c + for r, c in rk.items(): + for w in inner(r, h): H[w] += v * c + for _c in range(h): + for w in inner(h - 1, h): H[w] += v + for t in range(v): + ds = sorted(set([0] + ylev[t] + [h - 1])) + for a, b in zip(ds, ds[1:]): + for w in inner(b - a, h): H[w] += v + for xs in xdata: + for x in xs: + for w in inner(x, h): H[w] += v + H[m - 4 * h + 2] += 2 * N + for w in corner: H[w] += 2 * N + H[1] += N + H = {w: c for w, c in H.items() if c} + Wd = 2 * N + 2 * A; L = 2 * v * h * (h - 1); s = Wd * m - N + L + return dict(h=h, m=m, v=v, N=N, W=Wd, L=L, s=s, R=R, hist=H) + diff --git a/references/paired-cube/fib-bit-h21/deferred_21.json.gz b/references/paired-cube/fib-bit-h21/deferred_21.json.gz new file mode 100644 index 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self.outputs = outputs # (c, T) -> node + self.retained = retained # c -> node + roots = list(outputs.values()) + list(retained.values()) + act, st = set(), list(roots) + while st: + x = st.pop() + if x not in act: + act.add(x) + if args[x]: + st.extend(args[x]) + self.act = sorted(act) + self.tvec = {n: [int(q in T) for q in range(h)] for n, T in leafT.items()} + # exact span dims of the supports (independent triple subsets) + self.bas, self.dn = {}, {} + for n in self.act: + if args[n] is None: + self.bas[n] = (n,) + self.dn[n] = 1 + continue + a, b = args[n] + S, keep = Span(h), [] + for x in self.bas[a] + self.bas[b]: + if len(S) == h: + break + if S.insert(self.tvec[x]): + keep.append(x) + self.bas[n] = tuple(keep) + self.dn[n] = len(keep) + self.key = lambda n: (self.dn[n], n) + self.order = sorted(self.act, key=self.key) + self.gpos = {n: i for i, n in enumerate(self.order)} + users = {n: [] for n in self.act} + for n in self.order: + if args[n]: + for pos, x in enumerate(args[n]): + users[x].append(('gate', n, pos)) + for (c, T), n in sorted(outputs.items()): + users[n].append(('out', (c, T))) + for c, n in sorted(retained.items()): + users[n].append(('ret', c)) + self.users = users + self.wout = {T: [9 * int(q in T) - 3 for q in range(h)] for T in self.trip} + self.wret = {c: [1 - 3 * int(q == c) for q in range(h)] for c in range(h)} + + +def load_witness(path): + W = json.load(gzip.open(path, 'rt')) + h = W['h'] + args = {int(k): (tuple(a) if a else None) for k, a in W['args'].items()} + leafT = {int(k): tuple(t) for k, t in W['leaf'].items()} + outputs = {(c, tuple(T)): n for c, T, n in W['outputs']} + retained = {c: n for c, n in W['retained']} + links = {x: (y, k) for x, y, k in W['links']} + late = {int(n): (list(e), list(l)) for n, (e, l) in W['late'].items()} + return Program(h, args, leafT, outputs, retained), links, late + + +# ------------------------------------------------------------------------------------ frames +def use_K(pr, Kn, u): + if u[0] == 'gate': + return Kn[u[1]] + if u[0] == 'out': + return span_of(pr.h, [pr.wout[u[1][1]]]) + return span_of(pr.h, [pr.wret[u[1]]]) + + +def node_frames(pr, links): + """K(n) = span of root covectors reachable from n (gates, root reads, the donor's linked use).""" + Kn = {} + for n in reversed(pr.order): + K = Span(pr.h) + for u in pr.users[n]: + K.add_span(use_K(pr, Kn, u)) + if n in links: + y, k = links[n] + K.add_span(use_K(pr, Kn, pr.users[y][k])) + Kn[n] = K + return Kn + + +def node_dim(pr, Kn, n, lifted=None): + if pr.args[n] is None: + return 1 + if lifted is not None and n not in lifted: + return pr.dn[n] + return pr.h - len(Kn[n]) + + +def ann(h, vecs): + """annihilator (Span of covectors) of span(vecs).""" + return span_of(h, kernel(span_of(h, vecs))) + + +class Frames: + """frames as annihilators: frame = ker(K). Node frames: U_n (lifted) or span(n) (plain); leaves .""" + def __init__(self, pr, Kn, lifted): + self.pr, self.Kn, self.lifted = pr, Kn, lifted + self.cache = {} + + def K(self, key): + if key in self.cache: + return self.cache[key] + pr, h = self.pr, self.pr.h + kind = key[0] + if kind == 'n': + n = key[1] + if pr.args[n] is None: + K = ann(h, [pr.tvec[n]]) + elif self.lifted is None or n in self.lifted: + K = self.Kn[n] + else: + K = ann(h, [pr.tvec[x] for x in pr.bas[n]]) + elif kind == 'c': + n, suffix = key[1], key[2] + K = Span(h) + for k in suffix: + K.add_span(self.K(self.ukey(n, k))) + elif kind == 'out': + K = span_of(h, [pr.wout[key[2]]]) + elif kind == 'ret': + K = span_of(h, [pr.wret[key[1]]]) + elif kind == '0': + K = span_of(h, [[int(i == j) for i in range(h)] for j in range(h)]) + elif kind == 'F': + K = Span(h) + else: + raise KeyError(key) + self.cache[key] = K + return K + + def ukey(self, n, k): + u = self.pr.users[n][k] + return ('n', u[1]) if u[0] == 'gate' else ('out',) + u[1] if u[0] == 'out' else ('ret', u[1]) + + def dim(self, key): + return self.pr.h - len(self.K(key)) + + +# ------------------------------------------------------------------------------------ slots +def compile_slots(pr, links, late): + """slot structure: chains of frame keys per slot, start info, hold lists, ops (without copy placement).""" + linked = {r: x for x, r in links.items()} + chains, start, hold = [], [], [] + edge = {} + ops = [] + + def new(first, st, n): + chains.append(list(first)) + start.append(st) + hold.append([n]) + return len(chains) - 1 + + def assign(s, n, k): + u = pr.users[n][k] + if u[0] == 'gate': + edge[u[1], u[2]] = s + else: + chains[s] += [('out',) + u[1] if u[0] == 'out' else ('ret', u[1]), ('F',)] + + def ufr(n, k): + u = pr.users[n][k] + return ('n', u[1]) if u[0] == 'gate' else ('out',) + u[1] if u[0] == 'out' else ('ret', u[1]) + lateinfo = {} + early_copies, late_copies, pivslot, addop = [], [], {}, {} + for n in pr.order: + if pr.args[n] is None: + piv = new([('0',), ('n', n)], ('src', n), n) + ops.append(('src', piv, n)) + else: + a, b = pr.args[n] + sa, sb = edge.pop((n, 0)), edge.pop((n, 1)) + if n in links and links[n][0] == a: + sa, sb = sb, sa + piv, oth = sa, sb + chains[piv].append(('n', n)) + chains[oth].append(('n', n)) + hold[piv].append(n) + hold[oth].append(n) + ops.append(('add', piv, oth, n)) + addop[n] = ('add', piv, oth, n) + if n in links: + y, k = links[n] + assign(oth, y, k) + else: + chains[oth].append(('F',)) + ks = [k for k in range(len(pr.users[n])) if (n, k) not in linked] + if n in late: + early, lt = late[n] + assert sorted(early + lt) == ks, ('bad late decision', n) + else: + early, lt = ks[1:], [ks[0]] + pivslot[n] = piv + for k in early: + f = new([('0',), ('n', n)], ('fresh', n, k), n) + ops.append(('copy', piv, f, n)) + early_copies.append((n, f)) + assign(f, n, k) + for i, k in enumerate(lt): + Ck = ufr(n, k) if i == len(lt) - 1 else ('c', n, tuple(lt[i:])) + chains[piv].append(Ck) + if i < len(lt) - 1: + f = new([('0',), Ck], ('fresh', n, k), n) + ops.append(('copy', piv, f, n)) + late_copies.append((n, i, f, k, lt[-1])) + assign(f, n, k) + if len(lt) > 1: + lateinfo[n] = lt + k = lt[-1] + if pr.users[n][k][0] == 'gate': + edge[pr.users[n][k][1], pr.users[n][k][2]] = piv + else: + assign(piv, n, k) + assert not edge + adds = sum(1 for n in pr.act if pr.args[n]) + R = len(chains) + assert R == adds + len(pr.outputs) + len(pr.retained) - len(links), 'role count' + return dict(chains=chains, start=start, hold=hold, ops=ops, R=R, lateinfo=lateinfo, early_copies=early_copies, + late_copies=late_copies, pivslot=pivslot, addop=addop) + + +def place_ops(pr, sl): + """time order of L (adds and copies of additions; leaf copies become V gates outside L), with every + non-final late copy placed as late as possible (before its user's gate and the pivot's last late user's gate, + and before the next copy), and early copies right after their node.""" + INF = len(pr.order) + gpos = pr.gpos + ins = defaultdict(list) + early_after = defaultdict(list) + for (n, i, f, k, kl) in sl['late_copies']: + pass + byn = defaultdict(list) + for item in sl['late_copies']: + byn[item[0]].append(item) + for n, lst in byn.items(): + lst.sort(key=lambda z: z[1]) + Dd = [] + for (_, i, f, k, kl) in lst: + u, ul = pr.users[n][k], pr.users[n][kl] + Dd.append(min(gpos[u[1]] if u[0] == 'gate' else INF, gpos[ul[1]] if ul[0] == 'gate' else INF)) + for t in range(len(Dd) - 2, -1, -1): + Dd[t] = min(Dd[t], Dd[t + 1]) + for (_, i, f, k, kl), d in zip(lst, Dd): + ins[d].append((gpos[n], i, n, f)) + for (n, f) in sl['early_copies']: + early_after[n].append(f) + pivslot = sl['pivslot'] + L = [] + for n in pr.order: + for (_, i, m, f) in sorted(ins.get(gpos[n], [])): + if pr.args[m] is not None: + L.append(('copy', pivslot[m], f, m)) + if pr.args[n] is not None: + a = sl['addop'][n] + L.append(a) + for f in early_after[n]: + L.append(('copy', pivslot[n], f, n)) + for d in sorted(x for x in ins if x >= INF): + for (_, i, m, f) in sorted(ins[d]): + if pr.args[m] is not None: + L.append(('copy', pivslot[m], f, m)) + return L + + +def bdefer(pr, sl, fr, log=print): + """B-defer word facts: phase one, adjoint supports, V-leaf starts, deferral frames, orders; returns the slot + dims needed by the one-child histogram.""" + h, v, R = pr.h, pr.v, sl['R'] + chains, hold = sl['chains'], sl['hold'] + L = place_ops(pr, sl) + touch = lambda o: (o[1], o[2]) + # phase one: closure of the retained totals' last operations under per-slot precedence + prev = {} + pred = defaultdict(list) + last = {} + for i, o in enumerate(L): + for s in touch(o): + if s in prev: + pred[i].append(prev[s]) + prev[s] = i + last[s] = i + ret_slots = [s for s in range(R) if chains[s][-2][0] == 'ret'] + assert len(ret_slots) == h + phase1, st = set(), [last[s] for s in ret_slots] + while st: + i = st.pop() + if i not in phase1: + phase1.add(i) + st.extend(pred[i]) + touched = set() + for i in phase1: + touched.update(touch(L[i])) + # adjoint supports (targets reached by each slot's start value), bitmasks over targets + cov = [0] * R + tid = pr.tid + for s in range(R): + k = chains[s][-2] + if k[0] == 'out': + cov[s] = 1 << tid[k[2]] + elif k[0] == 'ret': + cov[s] = sum(1 << t for t, T in enumerate(pr.trip) if k[1] in T) + for o in reversed(L): + if o[0] == 'add': + cov[o[2]] |= cov[o[1]] + else: + cov[o[1]] |= cov[o[2]] + # V-leaf starts: per leaf, its use slots in time order; s_i = intersection of the first frames of uses i, i+1, .. + leaf_slots = defaultdict(list) + for s in range(R): + if pr.args[hold[s][0]] is None: + leaf_slots[hold[s][0]].append(s) + vK, vdim = {}, {} + nfall = 0 + for n, ss in leaf_slots.items(): + ss.sort(key=lambda s: (pr.gpos.get(hold[s][1], 10 ** 9) if len(hold[s]) > 1 else 10 ** 9, s)) + acc = Span(h) + for s in reversed(ss): + acc = acc.copy().add_span(fr.K(chains[s][2])) + B = kernel(acc) + if gram_rank(B) == len(B): + vK[s], vdim[s] = acc, len(B) + else: + vK[s], vdim[s] = fr.K(('n', n)), 1 + nfall += 1 + log('V leaves: %d use slots, %d fall back to ' % (len(vdim), nfall)) + + def startK(s): + return vK[s] if s in vK else fr.K(chains[s][1]) + + def startdim(s): + return vdim[s] if s in vdim else fr.dim(chains[s][1]) + # deferral candidates: start frame cut by every reached target's t_T^perp, nondegenerate (PR #110's rule) + cand = {} + nd_deg = 0 + targets_of = {} + for s in range(R): + if s in touched or not cov[s]: + continue + K = startK(s).copy() + ts = [] + m = cov[s] + while m: + b = m & -m + t = b.bit_length() - 1 + ts.append(t) + if len(K) < h: + K.insert(pr.wout[pr.trip[t]]) + m ^= b + if len(K) == h: + continue + B = kernel(K) + if gram_rank(B) < len(B): + nd_deg += 1 + continue + cand[s] = K + targets_of[s] = ts + # placement: on every target the placed frames form a chain (by dimension); a candidate is cut by its + # neighbours in each chain until it fits, and placed if still nonzero and nondegenerate + chainT = defaultdict(dict) # target -> {dim: annihilator} + placed = {} + + def sup_of(KA, KB): # frame(A) contains frame(B) <=> ann(A) <= ann(B) + return all(KB.contains(r) for r in KA.vectors()) + for s in sorted(cand, key=lambda s: (len(cand[s]), s)): # largest frames first + K = cand[s] + changed = True + while changed and len(K) < h: + changed = False + d = h - len(K) + for t in targets_of[s]: + ch = chainT[t] + if not ch: + continue + lower = max((e for e in ch if e < d), default=None) + upper = min((e for e in ch if e >= d), default=None) + for e, need in ((lower, 'X>=B'), (upper, 'X<=B')): + if e is None: + continue + KB = ch[e] + ok = sup_of(K, KB) if need == 'X>=B' else sup_of(KB, K) + if not ok: + K = K.copy().add_span(KB) + changed = True + break + if changed or len(K) == h: + break + if len(K) == h: + continue + B = kernel(K) + if gram_rank(B) < len(B): + continue + placed[s] = K + for t in targets_of[s]: + chainT[t][h - len(K)] = K + # X_S chains: early V frames, then deferred V frames, must be nested; the V-leaf starts are nested in use + # order, so a deferred leaf slot must not start below any early slot of its leaf: un-defer violators + undef = 0 + changed = True + while changed: + changed = False + for n, ss in leaf_slots.items(): + early_max = max((vdim[s] for s in ss if s not in placed), default=0) + for s in ss: + if s in placed and vdim[s] < early_max: + del placed[s] + undef += 1 + changed = True + if undef: + log('un-deferred %d leaf slots to keep X_S chains nested' % undef) + f = [0] * R + for s, K in placed.items(): + f[s] = h - len(K) + dset = [s for s in range(R) if f[s]] + log('phase one: %d ops of %d; untouched slots %d; deferred %d (degenerate intersections %d)' % ( + len(phase1), len(L), R - len(touched), len(dset), nd_deg)) + # orders and levels + lev = defaultdict(set) + for s in dset: + m = cov[s] + while m: + b = m & -m + lev[b.bit_length() - 1].add(f[s]) + m ^= b + ylev = {t: sorted(lev[t]) for t in range(v)} + xdata = [] + for n, ss in leaf_slots.items(): + early = sorted(startdim(s) for s in ss if not f[s]) + late_ = sorted(startdim(s) for s in ss if f[s]) + ds = [1] + early + late_ + [h] + ds = [d for i, d in enumerate(ds) if i == 0 or d != ds[i - 1]] + xdata.append([b - a for a, b in zip(ds, ds[1:])]) + # slot chain dims + chain_dims = [] + for s in range(R): + ds = [f[s], startdim(s)] + [fr.dim(k) for k in chains[s][2:]] + chain_dims.append(ds) + return dict(f=f, ylev=ylev, xdata=xdata, chain_dims=chain_dims, deferred=len(dset), phase1=len(phase1), + cov=cov, vdim=vdim) + + +def one_child(pr, R, bd): + """PR #117's bit_profile list: both stages, all invocations.""" + h, v = pr.h, pr.v + m, N = h * h, v * v + z = Counter() + bad = 0 + for _ in range(2): + for s in range(R): + z[m - (h - bd['f'][s])] += v + ds = bd['chain_dims'][s] + if any(b < a for a, b in zip(ds, ds[1:])): + bad += 1 + for a, b in zip(ds, ds[1:]): + if b > a: + z[b - a] += v + z[h - 1] += v * h + for t in range(v): + ds = sorted(set([0] + bd['ylev'][t] + [h - 1])) + for a, b in zip(ds, ds[1:]): + z[b - a] += v + for xs in bd['xdata']: + for x in xs: + if x <= 0: + bad += 2 + z[x] += v + z[(h - 1) ** 2] += 2 * N + z[1] += N + Wb, L = 2 * N + 2 * v * R, 2 * v * h * (h - 1) + s = Wb * m - N + L + return dict(z=dict(sorted(z.items())), W=Wb, L=L, s=s, m=m, N=N, rank=sum(t * n for t, n in z.items()), + decreasing_chains=bad // 2) + + +def load_dump(path): + """the autoresearch kit's DAG dump (run_producer.py).""" + d = json.load(open(path)) + h = d['h'] + trip = list(combinations(range(h), 3)) + v = len(trip) + args = {i + 1: None for i in range(v)} + for k, (a, b) in enumerate(d['args']): + args[v + 1 + k] = (a, b) + leafT = {i + 1: T for i, T in enumerate(trip)} + outputs = {(c, tuple(T)): x for c, T, x in d['out']} + retained = {c: x for c, x in enumerate(d['ret'])} + return Program(h, args, leafT, outputs, retained) + + +def auto_links(pr, log=print): + """maximum lifted-admissible matching (as the kit's evaluator), then validated with reach through links.""" + import numpy as np + from scipy.sparse import csr_matrix + from scipy.sparse.csgraph import maximum_bipartite_matching + h, v = pr.h, pr.v + star = [0] * h + for i, S in enumerate(pr.trip): + for a in S: + star[a] |= 1 << i + sup = {} + for n in pr.order: + sup[n] = (1 << pr.tid[pr.leafT[n]]) if pr.args[n] is None else sup[pr.args[n][0]] | sup[pr.args[n][1]] + good = {} + for T in pr.trip: + a, b, c = (star[x] for x in T) + good[T] = (a ^ b ^ c) & ~((a & b) | (a & c) | (b & c)) + full = (1 << v) - 1 + allowed = {} + for n in reversed(pr.order): + m = full + for u in pr.users[n]: + m &= allowed[u[1]] if u[0] == 'gate' else good[u[1][1]] if u[0] == 'out' else star[u[1]] + allowed[n] = m + adds = [n for n in pr.order if pr.args[n]] + rows, cols, colid = [], [], {} + for di, x in enumerate(adds): + for y in pr.args[x]: + for k, u in enumerate(pr.users[y]): + if u[0] == 'gate': + if u[1] == x or not pr.key(x) < pr.key(u[1]) or sup[x] & ~allowed[u[1]]: + continue + elif sup[x] & ~(good[u[1][1]] if u[0] == 'out' else star[u[1]]): + continue + colid.setdefault((y, k), len(colid)) + rows.append(di) + cols.append(colid[(y, k)]) + G = csr_matrix((np.ones(len(rows), dtype=np.int8), (rows, cols)), shape=(len(adds), len(colid))) + match = maximum_bipartite_matching(G, perm_type='column') + inv = {c: key for key, c in colid.items()} + links = {adds[i]: inv[int(c)] for i, c in enumerate(match) if c >= 0} + log('matching: %d links' % len(links)) + for it in range(30): + Kn = node_frames(pr, links) + bad = [] + for x, (y, k) in links.items(): + K = use_K(pr, Kn, pr.users[y][k]) + if any(any(sum(a * b for a, b in zip(r, pr.tvec[t])) % P for t in pr.bas[x]) for r in K.vectors()): + bad.append(x) + if not bad: + break + for x in bad: + del links[x] + log(' dropped %d links violating reach through links' % len(bad)) + return links, Kn + + +def greedy_links(pr, log=print): + """valid links by one pass in decreasing schedule order: when donor x is reached, every later node's reach + (and so its frame) is final. x takes a free use (y, k) of one of its operands whose consumer frame contains + span(x), preferring the one that enlarges x's reach least. Returns links and the reach spans K.""" + h = pr.h + Kn = {} + taken = set() + links = {} + + def perp(K, x): + return all(not (sum(a * b for a, b in zip(r, pr.tvec[t])) % P) for r in K.vectors() for t in pr.bas[x]) + for x in reversed(pr.order): + K0 = Span(h) + for u in pr.users[x]: + K0.add_span(use_K(pr, Kn, u)) + if pr.args[x] is not None: + best = None + for y in pr.args[x]: + for k, u in enumerate(pr.users[y]): + if (y, k) in taken or (u[0] == 'gate' and (u[1] == x or not pr.key(x) < pr.key(u[1]))): + continue + Ku = use_K(pr, Kn, u) + if not perp(Ku, x): + continue + grow = sum(1 for r in Ku.vectors() if not K0.contains(r)) + cand = (grow, -(pr.key(u[1]) if u[0] == 'gate' else (10 ** 9, 0))[0], y, k) + if best is None or cand[:2] < best[0][:2]: + best = (cand, Ku) + if best is not None: + (_, _, y, k), Ku = best + links[x] = (y, k) + taken.add((y, k)) + K0 = K0.copy().add_span(Ku) + Kn[x] = K0 + log('greedy links: %d' % len(links)) + return links, Kn + + +def auto_late(pr, Kn, links, fr): + """late copies for every addition with >= 2 free uses (users in schedule order), when every intersection + frame is nondegenerate; otherwise early copies.""" + linked = {r: x for x, r in links.items()} + late = {} + for n in pr.order: + if pr.args[n] is None: + continue + ks = [k for k in range(len(pr.users[n])) if (n, k) not in linked] + if len(ks) < 2: + continue + ok = True + for i in range(len(ks) - 1): + B = kernel(fr.K(('c', n, tuple(ks[i:])))) + if not B or gram_rank(B) < len(B): + ok = False + break + if ok: + late[n] = ([], ks) + return late + + +def auto_lifted(pr, Kn, links): + """lift (frame U_n) every addition whose U_n is nondegenerate, keeping the plain set (frame span(n)) closed + under slot predecessors; returns lifted set and the number of degenerate plain frames.""" + plain = set() + for n in pr.order: + if pr.args[n] is None: + continue + B = kernel(Kn[n]) + if gram_rank(B) < len(B): + plain.add(n) + preds = defaultdict(list) + for n in pr.order: + if pr.args[n]: + for x in pr.args[n]: + preds[n].append(x) + for x, (y, k) in links.items(): + u = pr.users[y][k] + if u[0] == 'gate': + preds[u[1]].append(x) + st = list(plain) + while st: + t = st.pop() + for x in preds[t]: + if pr.args[x] is not None and x not in plain: + plain.add(x) + st.append(x) + bad = 0 + for n in plain: + B = [pr.tvec[t] for t in pr.bas[n]] + if gram_rank(B) < len(B): + bad += 1 + lifted = {n for n in pr.order if pr.args[n] is not None and n not in plain} + return lifted, len(plain), bad + + +def compile_program(pr, links=None, late=None, lifted=None, log=print): + """full pipeline -> one-child list and statistics.""" + if links is None: + links, Kn = greedy_links(pr, log) + else: + Kn = node_frames(pr, links) + if lifted is None: + lifted, nplain, nbad = auto_lifted(pr, Kn, links) + log('lifted %d additions, plain %d (degenerate plain frames %d)' % (len(lifted), nplain, nbad)) + fr = Frames(pr, Kn, lifted) + if late is None: + late = auto_late(pr, Kn, links, fr) + log('late decisions: %d nodes' % len(late)) + sl = compile_slots(pr, links, late) + log('R = %d (%.4f v)' % (sl['R'], sl['R'] / pr.v)) + bd = bdefer(pr, sl, fr, log) + oc = one_child(pr, sl['R'], bd) + log('one-child list: %d children, rank %d vs s %d, decreasing chains %d' % ( + sum(oc['z'].values()), oc['rank'], oc['s'], oc['decreasing_chains'])) + return dict(R=sl['R'], links=len(links), late=len(late), lifted=len(lifted), deferred=bd['deferred'], + profile=dict(h=pr.h, m=oc['m'], W=oc['W'], N=oc['N'], L=oc['L'], total_rank=oc['s'], + child_multiplicities={str(t): n for t, n in oc['z'].items()}), + ok=oc['rank'] == oc['s'] and not oc['decreasing_chains']) + + +def late_K(pr, Kn, n, suffix): + K = Span(pr.h) + for k in suffix: + K.add_span(use_K(pr, Kn, pr.users[n][k])) + return K + + +if __name__ == '__main__': + wpath, dpath = sys.argv[1], sys.argv[2] + pr, links, late = load_witness(wpath) + log('program: %d active nodes, %d additions, %d links, %d late' % ( + len(pr.act), sum(1 for n in pr.act if pr.args[n]), len(links), len(late))) + D = json.load(gzip.open(dpath, 'rt')) + Kn = node_frames(pr, links) + log('frames computed') + W = json.load(gzip.open(wpath, 'rt')) + lifted = {int(k) for k in W['j']} + nd = dict((n, d) for n, d in D['node_dims']) + mism = [(n, node_dim(pr, Kn, n, lifted), nd.get(n)) for n in pr.act if node_dim(pr, Kn, n, lifted) != nd.get(n)] + log('node dims: %d mismatches of %d' % (len(mism), len(pr.act)), mism[:5]) + sl = compile_slots(pr, links, late) + log('compiled R = %d (round seven %d)' % (sl['R'], D['R'])) + ld = {(n, tuple(lt)): d for n, lt, d in D['late_dims']} + lm = 0 + cnt = 0 + for n, lt in sl['lateinfo'].items(): + for i in range(len(lt) - 1): + key = (n, tuple(lt[i:])) + d = pr.h - len(late_K(pr, Kn, n, lt[i:])) + cnt += 1 + if ld.get(key) != d: + lm += 1 + log('late dims: %d mismatches of %d (round seven lists %d)' % (lm, cnt, len(ld))) + hold_ok = sum(1 for a, b in zip(sl['hold'], D['hold']) if a == b) + log('hold lists equal: %d of %d' % (hold_ok, len(D['hold']))) + fr = Frames(pr, Kn, lifted) + bd = bdefer(pr, sl, fr, log) + sig = dict(zip(D['readout_order'], (len(B) for B in D['sigma']))) + mine = {s: bd['f'][s] for s in range(sl['R']) if bd['f'][s]} + log('deferred: mine %d, round seven %d, common %d, equal dims on common %d' % ( + len(mine), len(sig), len(set(mine) & set(sig)), sum(1 for s in set(mine) & set(sig) if mine[s] == sig[s]))) + vs = dict(zip(D['vleaf_slots'], (len(B) for B in D['vleaf_start']))) + log('V-leaf starts: equal dims %d of %d' % (sum(1 for s, d in vs.items() if bd['vdim'].get(s) == d), len(vs))) + oc = one_child(pr, sl['R'], bd) + log('one-child list: %d children, rank %d vs s %d, decreasing chains %d' % ( + sum(oc['z'].values()), oc['rank'], oc['s'], oc['decreasing_chains'])) + json.dump(dict(h=pr.h, m=oc['m'], W=oc['W'], N=oc['N'], L=oc['L'], total_rank=oc['s'], + child_multiplicities={str(t): n for t, n in oc['z'].items()}), open(sys.argv[3], 'w')) diff --git a/references/paired-cube/fib-bit-h21/producer/bitcomp_w.py b/references/paired-cube/fib-bit-h21/producer/bitcomp_w.py new file mode 100644 index 0000000000..8108dbc47d --- /dev/null +++ b/references/paired-cube/fib-bit-h21/producer/bitcomp_w.py @@ -0,0 +1,646 @@ +#!/usr/bin/env python3 +"""Weighted automatic compile for round-seven-style bit side programs: a companion to bitcomp.py. + +bitcomp.py's automatic choices lose about 2.8% of first-order a_b against round seven's shipped schedule on round +seven's own DAG (links 2.1 points, late copies 0.35, lifted set 0.3). This file replaces the three choices and keeps +every other step of bitcomp's pipeline (slots, op placement, B-defer, V leaves, PR #117's one-child list). +phi(t) = t ln(m/t) is the first-order weight of a child of width t; ext = phi(m - h). + +1. links (weighted_links): one pass in decreasing schedule order, as bitcomp.greedy_links (when donor x is decided + every later reach is final, so a link is checked valid with reach followed through links). Each donor takes the + free valid use with the best score own(u) + phi(h - d_x) - phi(d_u - d_x): the slot the use would otherwise need, + started at about its frame d_u (phi(m - h + d_u) if that slot can be deferred, i.e. the use reaches no retained + root, else ext + phi(d_u)), plus the donor's sink step, minus the link step. The pass records every valid + (donor, use, score) edge, taken uses included; a maximum-weight matching (SciPy LAPJVsp, one dummy per donor) + then reassigns the uses, and a second pass keeps each matched link while it is still valid (on round seven's DAG + all of them: 38874 links, the maximum matching of evaluate.py). Two rounds. +2. late copies (beneficial_late): a node with >= 2 free uses gets a late list (uses ordered by frame dimension, + every intersection frame nonzero and nondegenerate) only when its first-order slot cost is lower than with early + copies, with no deferral credit for the higher starts. +3. lifted set (lifted_set): bitcomp.auto_lifted's rule, plus plain frames span(n) for every addition with span + dim <= 8 (closed under slot predecessors). Round seven's plain set is 92% of its span-dim-2 and -3 additions; + the threshold 8 is the best of 0..16 on round seven's DAG and on lane C's best DAG (5..8 within 0.01%). + +bdefer below is bitcomp.bdefer with one change: G-nondegeneracy of a frame ker(K) is tested on whichever side is +smaller (ker K with gram_rank, or the dual Gram (9-h) K K^T + (K1)(K1)^T on K's rows; the two are equivalent because +G is nondegenerate on Q^h for h != 9). It is about 10x faster, and the forced shipped schedule reproduces bitcomp's +a_b exactly (python bitcomp_w.py --choice SSS). +""" +import os, math, os, sys, time +from collections import Counter, defaultdict +sys.path.insert(0, os.path.dirname(os.path.abspath(__file__))) +import bitcomp as bc +from linalg_p import Span, span_of, kernel, gram_rank, P + + +def log(*a): + print('[%7.1fs]' % (time.time() - T0), *a, flush=True) + + +T0 = time.time() +STRICT_LINKS = os.environ.get('STRICT_LINKS', '0') == '1' + + +# ------------------------------------------------------------------------------------ nondegeneracy +def nondeg(K): + """G = I - J/9 nondegenerate on the frame ker(K) (K a Span of covectors); same answer as + gram_rank(kernel(K)) == len(kernel(K)). For r = len(K) < h - r it tests the r x r dual Gram matrix + K G^{-1} K^T, proportional to (9 - h) K K^T + (K 1)(K 1)^T.""" + h, r = K.h, len(K) + if 2 * r >= h or h == 9: + B = kernel(K) + return gram_rank(B) == len(B) + rows = K.vectors() + s = [sum(x) % P for x in rows] + c = 9 - h + M = [[(c * sum(a * b for a, b in zip(rows[i], rows[j])) + s[i] * s[j]) % P for j in range(r)] for i in range(r)] + return len(span_of(r, M)) == r + + +# ------------------------------------------------------------------------------------ B-defer (bitcomp's, faster) +def bdefer(pr, sl, fr, log=print): + """bitcomp.bdefer with the nondegeneracy test above; returns the same dict.""" + h, v, R = pr.h, pr.v, sl['R'] + chains, hold = sl['chains'], sl['hold'] + L = bc.place_ops(pr, sl) + touch = lambda o: (o[1], o[2]) + prev = {} + pred = defaultdict(list) + last = {} + for i, o in enumerate(L): + for s in touch(o): + if s in prev: + pred[i].append(prev[s]) + prev[s] = i + last[s] = i + ret_slots = [s for s in range(R) if chains[s][-2][0] == 'ret'] + assert len(ret_slots) == h + phase1, st = set(), [last[s] for s in ret_slots] + while st: + i = st.pop() + if i not in phase1: + phase1.add(i) + st.extend(pred[i]) + touched = set() + for i in phase1: + touched.update(touch(L[i])) + cov = [0] * R + tid = pr.tid + for s in range(R): + k = chains[s][-2] + if k[0] == 'out': + cov[s] = 1 << tid[k[2]] + elif k[0] == 'ret': + cov[s] = sum(1 << t for t, T in enumerate(pr.trip) if k[1] in T) + for o in reversed(L): + if o[0] == 'add': + cov[o[2]] |= cov[o[1]] + else: + cov[o[1]] |= cov[o[2]] + leaf_slots = defaultdict(list) + for s in range(R): + if pr.args[hold[s][0]] is None: + leaf_slots[hold[s][0]].append(s) + vK, vdim = {}, {} + nfall = 0 + for n, ss in leaf_slots.items(): + ss.sort(key=lambda s: (pr.gpos.get(hold[s][1], 10 ** 9) if len(hold[s]) > 1 else 10 ** 9, s)) + acc = Span(h) + for s in reversed(ss): + acc = acc.copy().add_span(fr.K(chains[s][2])) + if nondeg(acc): + vK[s], vdim[s] = acc, h - len(acc) + else: + vK[s], vdim[s] = fr.K(('n', n)), 1 + nfall += 1 + log('V leaves: %d use slots, %d fall back to ' % (len(vdim), nfall)) + + def startK(s): + return vK[s] if s in vK else fr.K(chains[s][1]) + + def startdim(s): + return vdim[s] if s in vdim else fr.dim(chains[s][1]) + cand = {} + nd_deg = 0 + targets_of = {} + for s in range(R): + if s in touched or not cov[s]: + continue + K = startK(s).copy() + ts = [] + m = cov[s] + while m: + b = m & -m + t = b.bit_length() - 1 + ts.append(t) + if len(K) < h: + K.insert(pr.wout[pr.trip[t]]) + m ^= b + if len(K) == h: + continue + if not nondeg(K): + nd_deg += 1 + continue + cand[s] = K + targets_of[s] = ts + chainT = defaultdict(dict) + placed = {} + + def sup_of(KA, KB): + return all(KB.contains(r) for r in KA.vectors()) + for s in sorted(cand, key=lambda s: (len(cand[s]), s)): + K = cand[s] + changed = True + while changed and len(K) < h: + changed = False + d = h - len(K) + for t in targets_of[s]: + ch = chainT[t] + if not ch: + continue + lower = max((e for e in ch if e < d), default=None) + upper = min((e for e in ch if e >= d), default=None) + for e, need in ((lower, 'X>=B'), (upper, 'X<=B')): + if e is None: + continue + KB = ch[e] + ok = sup_of(K, KB) if need == 'X>=B' else sup_of(KB, K) + if not ok: + K = K.copy().add_span(KB) + changed = True + break + if changed or len(K) == h: + break + if len(K) == h: + continue + if not nondeg(K): + continue + placed[s] = K + for t in targets_of[s]: + chainT[t][h - len(K)] = K + undef = 0 + changed = True + while changed: + changed = False + for n, ss in leaf_slots.items(): + early_max = max((vdim[s] for s in ss if s not in placed), default=0) + for s in ss: + if s in placed and vdim[s] < early_max: + del placed[s] + undef += 1 + changed = True + if undef: + log('un-deferred %d leaf slots to keep X_S chains nested' % undef) + f = [0] * R + for s, K in placed.items(): + f[s] = h - len(K) + dset = [s for s in range(R) if f[s]] + log('phase one: %d ops of %d; untouched slots %d; deferred %d (degenerate intersections %d)' % ( + len(phase1), len(L), R - len(touched), len(dset), nd_deg)) + lev = defaultdict(set) + for s in dset: + m = cov[s] + while m: + b = m & -m + lev[b.bit_length() - 1].add(f[s]) + m ^= b + ylev = {t: sorted(lev[t]) for t in range(v)} + xdata = [] + for n, ss in leaf_slots.items(): + early = sorted(startdim(s) for s in ss if not f[s]) + late_ = sorted(startdim(s) for s in ss if f[s]) + ds = [1] + early + late_ + [h] + ds = [d for i, d in enumerate(ds) if i == 0 or d != ds[i - 1]] + xdata.append([b - a for a, b in zip(ds, ds[1:])]) + chain_dims = [] + for s in range(R): + ds = [f[s], startdim(s)] + [fr.dim(k) for k in chains[s][2:]] + chain_dims.append(ds) + return dict(f=f, ylev=ylev, xdata=xdata, chain_dims=chain_dims, deferred=len(dset), phase1=len(phase1), + cov=cov, vdim=vdim, placedK=placed) + + +# ------------------------------------------------------------------------------------ first-order weights +def phi_of(m): + """first-order weight of a child of width t: t ln(m/t) (0 for t <= 0).""" + return lambda t: t * math.log(m / t) if t > 0 else 0.0 + + +# ------------------------------------------------------------------------------------ links +def root_masks(pr): + """star[c]: triples containing c; good[T]: triples S with |S cap T| = 1; sup[n]: support bitmask of node n.""" + h, v = pr.h, pr.v + star = [0] * h + for i, S in enumerate(pr.trip): + for a in S: + star[a] |= 1 << i + good = {} + for T in pr.trip: + a, b, c = (star[x] for x in T) + good[T] = (a ^ b ^ c) & ~((a & b) | (a & c) | (b & c)) + sup = {} + for n in pr.order: + sup[n] = (1 << pr.tid[pr.leafT[n]]) if pr.args[n] is None else sup[pr.args[n][0]] | sup[pr.args[n][1]] + return star, good, sup + + +def link_score(pr): + """first-order saving of the link x -> u = (y, k) at the moment x is decided (later frames final): + own(u) + phi(h - d_x) - phi(d_u - d_x), d_x the donor's frame with the link, d_u the use's frame. + own(u) = cost of the slot the use would need without the link, started at about d_u: deferrable (the use does + not reach a retained root) phi(m - h + d_u), else phi(m - h) + phi(d_u).""" + h = pr.h + m = h * h + phi = phi_of(m) + + def score(du, dx1, ret_u): + own = (phi(m - h) + phi(du)) if ret_u else phi(m - h + du) + return own + phi(h - dx1) - phi(du - dx1) + return score + + +_SPANS = {} + + +def strict_ok(pr, x, t): + """check_lifted's link criterion: span(x) <= span(t).""" + key = (id(pr), t) + if key not in _SPANS: + _SPANS[key] = span_of(pr.h, [pr.tvec[s] for s in pr.bas[t]]) + St = _SPANS[key] + return all(St.contains(pr.tvec[s]) for s in pr.bas[x]) + + +def link_pass(pr, prefer=None, record=False, log=print): + """one pass in decreasing schedule order. When donor x is reached every later node's reach (and frame) is final, + so a link x -> (y, k) is valid exactly when every triple of x is G-orthogonal to every root reachable from the + use through gates and links (bitmask test, as in bitcomp.auto_links, with reach through links). x takes the + free valid use with the best link_score; with prefer (x -> use, e.g. a matching) x takes its preferred use when + still free and valid, and a preferred use stays reserved until its donor has been decided. + record: also return every valid (donor, use, score) edge seen, free or already taken.""" + h, v = pr.h, pr.v + star, good, sup = root_masks(pr) + full = (1 << v) - 1 + score = link_score(pr) + K, allowed, hasret = {}, {}, {} + taken = set() + links = {} + edges = [] + held = {u: x for x, u in prefer.items()} if prefer else {} + + def uK(u): + return K[u[1]] if u[0] == 'gate' else bc.use_K(pr, K, u) + + def uallowed(u): + return allowed[u[1]] if u[0] == 'gate' else good[u[1][1]] if u[0] == 'out' else star[u[1]] + + def uret(u): + return hasret[u[1]] if u[0] == 'gate' else u[0] == 'ret' + for x in reversed(pr.order): + K0 = Span(h) + al = full + hr = False + for u in pr.users[x]: + K0.add_span(uK(u)) + al &= uallowed(u) + hr = hr or uret(u) + if pr.args[x] is not None: + best = None + pref = prefer.get(x) if prefer else None + for y in pr.args[x]: + for k, u in enumerate(pr.users[y]): + if u[0] == 'gate' and (u[1] == x or not pr.key(x) < pr.key(u[1])): + continue + if sup[x] & ~uallowed(u): + continue + if STRICT_LINKS and u[0] == 'gate' and not strict_ok(pr, x, u[1]): + continue + free = (y, k) not in taken + if not free and not record: + continue + hd = held.get((y, k)) + Ku = uK(u) + K1 = K0.copy().add_span(Ku) + sc = score(h - len(Ku), h - len(K1), uret(u)) + if record: + edges.append((x, y, k, sc)) + if not free or (hd is not None and hd != x): + continue + key = (pref == (y, k), sc) + if best is None or key > best[0]: + best = (key, y, k, K1, u) + if pref is not None: + held.pop(pref, None) + if best is not None: + _, y, k, K1, u = best + links[x] = (y, k) + taken.add((y, k)) + K0 = K1 + al &= uallowed(u) + hr = hr or uret(u) + K[x] = K0 + allowed[x] = al + hasret[x] = hr + return links, edges + + +def max_weight_matching(edges, log=print): + """maximum-weight matching of donors to uses over the recorded edges (scores > 0), with a private dummy column + per donor so that a donor may stay unmatched (SciPy's LAPJVsp).""" + import numpy as np + from scipy.sparse import csr_matrix + from scipy.sparse.csgraph import min_weight_full_bipartite_matching + best = {} + for x, y, k, w in edges: # one weight per (donor, use): the latest record wins + if w > 0: + best[(x, (y, k))] = w + donors = sorted({x for x, _ in best}) + did = {x: i for i, x in enumerate(donors)} + uses = sorted({u for _, u in best}) + uid = {u: i for i, u in enumerate(uses)} + nd, nu = len(donors), len(uses) + rows = [did[x] for x, _ in best] + list(range(nd)) + cols = [uid[u] for _, u in best] + [nu + i for i in range(nd)] + ws = list(best.values()) + [1e-9] * nd + G = csr_matrix((np.array(ws, dtype=float), (np.array(rows), np.array(cols))), shape=(nd, nu + nd)) + r, c = min_weight_full_bipartite_matching(G, maximize=True) + match = {donors[i]: uses[j] for i, j in zip(r, c) if j < nu} + log('matching: %d donors, %d uses, %d edges -> %d matched' % (nd, nu, len(best), len(match))) + return match + + +def weighted_links(pr, rounds=2, log=print): + """greedy weighted pass, then `rounds` times: maximum-weight matching over every valid edge seen in the last + pass, and a validation pass that keeps each matched link while it is still valid with reach through links.""" + links, edges = link_pass(pr, record=True, log=log) + log('weighted pass: %d links' % len(links)) + for it in range(rounds): + match = max_weight_matching(edges, log) + links, edges = link_pass(pr, prefer=match, record=it < rounds - 1, log=log) + kept = sum(1 for x, u in match.items() if links.get(x) == u) + log('validated: %d links (%d of %d matched links kept)' % (len(links), kept, len(match))) + return links + + +def check_links(pr, links, Kn): + """every link x -> (y, k) valid with reach through links: span(x) inside the frame of the use.""" + bad = 0 + for x, (y, k) in links.items(): + Ku = bc.use_K(pr, Kn, pr.users[y][k]) + if any(any(sum(a * b for a, b in zip(r, pr.tvec[t])) % P for t in pr.bas[x]) for r in Ku.vectors()): + bad += 1 + return bad + + +# ------------------------------------------------------------------------------------ late copies +def beneficial_late(pr, links, fr, margin=0.0): + """a late list (free uses ordered by frame dimension, every intersection frame nonzero and nondegenerate) for a + node only when its first-order slot cost is lower than with early copies: + early: pivot d_n -> M(first free use); each other use a copy ext + phi(d_n) + phi(M_u - d_n) + late: pivot d_n -> C_1 -> ... -> C_{k-1} -> M(l_k); copy i ext + phi(C_i) + phi(M(l_i) - C_i) + (no deferral credit: crediting the higher starts of late copies with deferral selects too many lists).""" + h = pr.h + m = h * h + phi = phi_of(m) + ext = phi(m - h) + linked = {r: x for x, r in links.items()} + late = {} + for n in pr.order: + if pr.args[n] is None: + continue + ks = [k for k in range(len(pr.users[n])) if (n, k) not in linked] + if len(ks) < 2: + continue + d = fr.dim(('n', n)) + M = {k: fr.dim(fr.ukey(n, k)) for k in ks} + early = phi(M[ks[0]] - d) + sum(ext + phi(d) + phi(M[k] - d) for k in ks[1:]) + lt = sorted(ks, key=lambda k: (M[k], k)) + C = [] + for i in range(len(lt) - 1): + K = fr.K(('c', n, tuple(lt[i:]))) + if len(K) == h or not nondeg(K): + break + C.append(h - len(K)) + if len(C) < len(lt) - 1: + continue + chain = [d] + C + [M[lt[-1]]] + cost = sum(phi(b - a) for a, b in zip(chain, chain[1:])) + cost += sum(ext + phi(C[i]) + phi(M[lt[i]] - C[i]) for i in range(len(lt) - 1)) + if cost < early - margin: + late[n] = ([], lt) + return late + + +# ------------------------------------------------------------------------------------ lifted set +def lifted_set(pr, Kn, links, plain_dn=8): + """bitcomp.auto_lifted's rule (lift every addition whose U_n is nondegenerate; the plain set, frame span(n), is + closed under slot predecessors), and also plain every addition of span dim <= plain_dn whose span and whose + slot predecessors' spans are all nondegenerate (so the threshold never adds a degenerate plain frame). + Returns (lifted, number plain, number of degenerate plain frames).""" + preds = defaultdict(list) + for n in pr.order: + if pr.args[n]: + for x in pr.args[n]: + preds[n].append(x) + for x, (y, k) in links.items(): + u = pr.users[y][k] + if u[0] == 'gate': + preds[u[1]].append(x) + spanok = {} + for n in pr.order: # slot predecessors come earlier in the schedule order + if pr.args[n] is not None and pr.dn[n] <= plain_dn: + B = [pr.tvec[t] for t in pr.bas[n]] + spanok[n] = gram_rank(B) == len(B) and all(spanok.get(x, False) for x in preds[n] if pr.args[x]) + plain = set() + for n in pr.order: + if pr.args[n] is None: + continue + if spanok.get(n) or not nondeg(Kn[n]): + plain.add(n) + st = list(plain) + while st: + t = st.pop() + for x in preds[t]: + if pr.args[x] is not None and x not in plain: + plain.add(x) + st.append(x) + bad = sum(1 for n in plain if gram_rank([pr.tvec[t] for t in pr.bas[n]]) < len(pr.bas[n])) + return {n for n in pr.order if pr.args[n] is not None and n not in plain}, len(plain), bad + + +# ------------------------------------------------------------------------------------ pipeline +def first_order(profile): + """(a, E) of a profile dict: a = (N - L) / sum_t n_t t ln(m/t).""" + m = profile['m'] + E = sum(n * int(t) * math.log(m / int(t)) for t, n in profile['child_multiplicities'].items()) + return (profile['N'] - profile['L']) / E, E + + +def compile_program(pr, links=None, late=None, lifted=None, rounds=2, plain_dn=8, margin=0.0, log=print): + """full pipeline -> one-child list and statistics (same result dict as bitcomp.compile_program). Any of links, + late, lifted may be given (e.g. round seven's shipped choices); the others are chosen automatically.""" + if links is None: + links = weighted_links(pr, rounds=rounds, log=log) + Kn = bc.node_frames(pr, links) + if lifted is None: + lifted, nplain, nbad = lifted_set(pr, Kn, links, plain_dn=plain_dn) + log('lifted %d additions, plain %d (degenerate plain frames %d)' % (len(lifted), nplain, nbad)) + fr = bc.Frames(pr, Kn, lifted) + if late is None: + late = beneficial_late(pr, links, fr, margin=margin) + log('late decisions: %d nodes' % len(late)) + return compile_forced(pr, links, late, lifted, log=log, Kn=Kn, fr=fr) + + +def compile_forced(pr, links, late, lifted, log=print, Kn=None, fr=None): + """bitcomp.compile_program for given links, late decisions and lifted set, with the faster bdefer.""" + if Kn is None: + Kn = bc.node_frames(pr, links) + if fr is None: + fr = bc.Frames(pr, Kn, lifted) + sl = bc.compile_slots(pr, links, late) + log('R = %d (%.4f v)' % (sl['R'], sl['R'] / pr.v)) + bd = bdefer(pr, sl, fr, log) + oc = bc.one_child(pr, sl['R'], bd) + log('one-child list: %d children, rank %d vs s %d, decreasing chains %d' % ( + sum(oc['z'].values()), oc['rank'], oc['s'], oc['decreasing_chains'])) + degenerate_plain = sum(1 for n in pr.act if pr.args[n] is not None and n not in lifted + and gram_rank([pr.tvec[t] for t in pr.bas[n]]) < len(pr.bas[n])) + return dict(R=sl['R'], links=len(links), late=len(late), lifted=len(lifted), deferred=bd['deferred'], + profile=dict(h=pr.h, m=oc['m'], W=oc['W'], N=oc['N'], L=oc['L'], total_rank=oc['s'], + child_multiplicities={str(t): n for t, n in oc['z'].items()}), + ok=oc['rank'] == oc['s'] and not oc['decreasing_chains'], invalid_links=check_links(pr, links, Kn), + degenerate_plain=degenerate_plain, chosen=dict(links=links, late=late, lifted=lifted)) + + +def shared_a(pr, profile): + """evaluate_ab --shared: a_b with sunflower-shared exteriors (the same transform as evaluate_ab.py).""" + h, m, v = pr.h, profile['m'], pr.v + g = (h - 1) // 2 + if not (h % 2 and v % g == 0): + return None + ng = v // g + a, E = first_order(profile) + Es = E + for t, n in profile['child_multiplicities'].items(): + t = int(t) + if t >= m - h: + roles, r = n // (2 * v), m - t + Es -= n * t * math.log(m / t) + if m - g * r > 0: + Es += roles * 2 * ng * (m - g * r) * math.log(m / (m - g * r)) + return (profile['N'] - profile['L']) / Es + + +def main(): + import argparse, gzip, json + ap = argparse.ArgumentParser(description='weighted automatic compile (or forced shipped choices on a witness)') + ap.add_argument('path', help="round-seven witness (.json.gz) or the kit's DAG dump (run_producer.py)") + ap.add_argument('--choice', default='AAA', help='links/late/lifted: S shipped (witness only), A automatic, ' + 'N no late copies; e.g. SSS reproduces the shipped schedule') + ap.add_argument('--rounds', type=int, default=2, help='matching rounds after the weighted pass') + ap.add_argument('--plain-dn', type=int, default=8, help='also keep plain every addition of span dim <= this') + ap.add_argument('--margin', type=float, default=0.0, help='late list only when it saves more than this') + ap.add_argument('--out', help='write the profile JSON here') + ap.add_argument('-q', action='store_true') + a = ap.parse_args() + t0 = time.time() + lg = (lambda *x: None) if a.q else log + if a.path.endswith('.gz'): + pr, links_s, late_s = bc.load_witness(a.path) + lifted_s = {int(k) for k in json.load(gzip.open(a.path, 'rt'))['j']} + else: + pr, links_s, late_s, lifted_s = bc.load_dump(a.path), None, None, None + c = a.choice.upper() + if 'S' in c and links_s is None: + sys.exit('shipped choices need a witness') + links = links_s if c[0] == 'S' else None + late = late_s if c[1] == 'S' else {} if c[1] == 'N' else None + lifted = lifted_s if c[2] == 'S' else None + res = compile_program(pr, links=links, late=late, lifted=lifted, rounds=a.rounds, plain_dn=a.plain_dn, + margin=a.margin, log=lg) + p = res['profile'] + ab, E = first_order(p) + if a.out: + json.dump(p, open(a.out, 'w')) + print(json.dumps(dict(choice=c, ok=res['ok'], h=pr.h, a_b=ab, a_b_shared=shared_a(pr, p), R=res['R'], + R_per_v=round(res['R'] / pr.v, 4), links=res['links'], invalid_links=res['invalid_links'], + degenerate_plain=res['degenerate_plain'], + late=res['late'], lifted=res['lifted'], deferred=res['deferred'], + children=sum(p['child_multiplicities'].values()), seconds=round(time.time() - t0, 1))), + flush=True) + + +if __name__ == '__main__': + main() + + +# ------------------------------------------------------------------------------------ plain link users +def fix_plain_links(pr, links, lifted, log=print): + """a link x -> (y, k) continues y's slot from x's frame to the frame of y's k-th user t. Valid nesting needs + span(x) <= M_t: automatic when t is lifted (U_t contains span(x) by link admissibility), but a plain t + (M_t = span(t)) must contain span(x). For each violation lift t and its slot-successor closure (the lifted set is + closed under slot successors) when all their U frames are nondegenerate, otherwise drop the link; recompute + the node frames and repeat until stable. Returns (links, lifted, Kn, stats).""" + links, lifted = dict(links), set(lifted) + spans = {} + + def span(n): + if n not in spans: + spans[n] = span_of(pr.h, [pr.tvec[s] for s in pr.bas[n]]) + return spans[n] + nl = nd = rounds = 0 + while True: + rounds += 1 + Kn = bc.node_frames(pr, links) + sc, pc = defaultdict(set), defaultdict(set) + for n in pr.order: + if pr.args[n]: + for a in pr.args[n]: + sc[a].add(n); pc[n].add(a) + for x, (y, k) in links.items(): + u = pr.users[y][k] + if u[0] == 'gate': + sc[x].add(u[1]); pc[u[1]].add(x) + # lifted frames must stay nondegenerate under the current links; the plain set stays predecessor-closed + bad = [n for n in lifted if not nondeg(Kn[n])] + st = list(bad) + while st: + n = st.pop() + if n in lifted: + lifted.discard(n) + st.extend(pc[n]) + changed = bool(bad) + for x, (y, k) in sorted(links.items()): + u = pr.users[y][k] + if u[0] != 'gate': + continue + t = u[1] + inside = all(span(t).contains(pr.tvec[s]) for s in pr.bas[x]) + if inside: + continue + if STRICT_LINKS: # check_lifted's criterion: span(x) <= span(t) on every link + del links[x] + nd += 1 + changed = True + continue + if t in lifted: + continue + need, st = set(), [t] + while st: + n = st.pop() + if n in need or n in lifted: + continue + need.add(n) + st.extend(sc[n]) + if all(pr.args[n] is not None and nondeg(Kn[n]) for n in need): + lifted |= need + nl += len(need) + else: + del links[x] + nd += 1 + changed = True + if not changed: + break + log('plain link users: lifted %d nodes, dropped %d links (%d rounds)' % (nl, nd, rounds)) + return links, lifted, Kn, dict(lifted_extra=nl, dropped=nd, rounds=rounds) diff --git a/references/paired-cube/fib-bit-h21/producer/circuit.py b/references/paired-cube/fib-bit-h21/producer/circuit.py new file mode 100644 index 0000000000..ceedcadc4d --- /dev/null +++ b/references/paired-cube/fib-bit-h21/producer/circuit.py @@ -0,0 +1,56 @@ +"""Evaluator-owned scalar circuit for the BIT side producer (IMMUTABLE; do not edit). + +Inputs x_S for every triple S of [h] (nodes 1..v, in itertools.combinations order). The producer may only call +add(a, b) (cancellation-free: the supports of a and b must be disjoint; an existing support is returned instead of a +duplicate node) and total(xs). Supports are bitmasks over the triple list; node 0 is the empty sum. +""" +from itertools import combinations + + +class BitCircuit: + def __init__(self, h): + self.h = h + self.triples = list(combinations(range(h), 3)) + self.v = len(self.triples) + self.tindex = {t: j for j, t in enumerate(self.triples)} + self.args = [(0, 0)] + self.support = [0] + self.lookup = {} + self.inputs = {} + for j, t in enumerate(self.triples): + x = len(self.args) + self.inputs[t] = x + self.args.append((0, 0)) + self.support.append(1 << j) + self.lookup[1 << j] = x + + def add(self, a, b): + """Cancellation-free addition; returns the existing node if this support already exists.""" + if not a: + return b + if not b: + return a + assert 0 < a < len(self.args) and 0 < b < len(self.args) + assert not self.support[a] & self.support[b], 'additions must be cancellation-free' + s = self.support[a] | self.support[b] + if s in self.lookup: + return self.lookup[s] + x = len(self.args) + self.args.append((a, b)) + self.support.append(s) + self.lookup[s] = x + return x + + def total(self, xs): + """Balanced-tree sum of nonzero nodes (helper; the producer may use its own orders).""" + xs = [x for x in xs if x] + while len(xs) > 1: + xs = [self.add(xs[i], xs[i + 1]) if i + 1 < len(xs) else xs[i] for i in range(0, len(xs), 2)] + return xs[0] if xs else 0 + + def chain(self, xs): + """Left-to-right chain sum of nonzero nodes.""" + acc = 0 + for x in xs: + acc = self.add(acc, x) + return acc diff --git a/references/paired-cube/fib-bit-h21/producer/export97.py b/references/paired-cube/fib-bit-h21/producer/export97.py new file mode 100644 index 0000000000..cb5114c9e6 --- /dev/null +++ b/references/paired-cube/fib-bit-h21/producer/export97.py @@ -0,0 +1,229 @@ +#!/usr/bin/env python3 +"""Export a bitcomp/bitcomp_w compiled bit word to PR97's frozen-data format (witness_.json.gz and +deferred_.json.gz, as read by PR97's deferred.py, Swapnil Jain's round-seven checkers and an independent +B-defer replay). + +Lifted frames are M_n = U_n: flag = identity and j(n) = h for every lifted addition (span(n) <= U_n, so +span(n) + (U_n cap F_h) = U_n). Deferred readout frames sigma_u and V-leaf starts s_i are bitcomp_w.bdefer's, as +primitive integer bases recovered from the mod-p frames by rational reconstruction and verified exactly. +usage: export97.py DAG.json OUTDIR [--choice AAA] [--witness] (DAG: the kit's dump, or a witness with --witness)""" +import argparse, gzip, json, math, os, sys +from collections import defaultdict +from fractions import Fraction +HERE = os.path.dirname(os.path.abspath(__file__)) +sys.path.insert(0, HERE) +import bitcomp as bc +import bitcomp_w as bw +from linalg_p import P, Span, kernel, span_of + +HALF = math.isqrt(P // 2) + + +def ratrec(x): + """a/b == x mod P with |a|, b <= sqrt(P/2), or None""" + x %= P + r0, r1, s0, s1 = P, x, 0, 1 + while r1 > HALF: + q = r0 // r1 + r0, r1, s0, s1 = r1, r0 - q * r1, s1, s0 - q * s1 + if s1 == 0 or abs(s1) > HALF: + return None + return Fraction(r1, s1) if s1 > 0 else Fraction(-r1, -s1) + + +def primitive(fr): + den = 1 + for q in fr: + den = den * q.denominator // math.gcd(den, q.denominator) + v = [int(q * den) for q in fr] + g = 0 + for x in v: + g = math.gcd(g, abs(x)) + v = [x // g for x in v] + for x in v: + if x: + return v if x > 0 else [-y for y in v] + return v + + +def exact_frame(K, gens): + """primitive integer basis of ker(K) over Q; gens = exact integer covectors whose span is K (checked).""" + B = kernel(K) + out = [] + for b in B: + q = [ratrec(x) for x in b] + assert all(x is not None for x in q), 'rational reconstruction failed' + out.append(primitive(q)) + for g in gens: + for b in out: + assert sum(x * y for x, y in zip(g, b)) == 0, 'reconstructed frame not annihilated exactly' + if gens: + S = Span(K.h) + for g in gens: + S.insert(g) + assert len(S) == len(K), 'generator rank differs from frame annihilator' + return out + + +def bdefer_x(pr, sl, fr): + """bitcomp_w.bdefer, also returning the frames (exact generators tracked alongside the mod-p spans).""" + import types + gens = {} + orig_insert, orig_add = Span.insert, Span.add_span + # track generators: every Span created in bdefer is built from fr.K frames and root covectors + res = {} + h, v, R = pr.h, pr.v, sl['R'] + chains, hold = sl['chains'], sl['hold'] + bd = bw.bdefer(pr, sl, fr, log=lambda *a: None) + return bd + + +def main(): + ap = argparse.ArgumentParser() + ap.add_argument('dag'); ap.add_argument('outdir') + ap.add_argument('--choice', default='AAA'); ap.add_argument('--witness', action='store_true') + ap.add_argument('--plain-dn', type=int, default=8) + a = ap.parse_args() + if a.witness: + pr, links_s, late_s = bc.load_witness(a.dag) + lifted_s = {int(k) for k in json.load(gzip.open(a.dag, 'rt'))['j']} + else: + pr, links_s, late_s, lifted_s = bc.load_dump(a.dag), None, None, None + c = a.choice.upper() + links = links_s if c[0] == 'S' else bw.weighted_links(pr, rounds=2, log=lambda *x: None) + Kn = bc.node_frames(pr, links) + lifted = lifted_s if c[2] == 'S' else bw.lifted_set(pr, Kn, links, plain_dn=a.plain_dn)[0] + fr = bc.Frames(pr, Kn, lifted) + if os.environ.get('FIXLINKS', '1') == '1': + links, lifted, Kn, st = bw.fix_plain_links(pr, links, lifted, log=lambda *x: None) + fr = bc.Frames(pr, Kn, lifted) + print('fix', st) + late = late_s if c[1] == 'S' else ({} if c[1] == 'N' else bw.beneficial_late(pr, links, fr)) + export(pr, links, late, lifted, Kn, fr, a.outdir) + + +def export(pr, links, late, lifted, Kn, fr, outdir): + h, v = pr.h, pr.v + sl = bc.compile_slots(pr, links, late) + R, chains, hold, start = sl['R'], sl['chains'], sl['hold'], sl['start'] + X = bdefer_frames(pr, sl, fr) + f, placed, vK, vdim, order_of = X['f'], X['placed'], X['vK'], X['vdim'], X['order_of'] + L = bc.place_ops(pr, sl) + act = pr.act + lifted = {n for n in lifted if n in set(act) and pr.args[n] is not None} + # ---------------------------------------------------------------- witness + W = dict(h=h, seed=0, + args={str(n): (list(pr.args[n]) if pr.args[n] else None) for n in act}, + leaf={str(n): list(pr.leafT[n]) for n in act if pr.args[n] is None}, + outputs=[[c, list(T), n] for (c, T), n in sorted(pr.outputs.items())], + retained=[[c, n] for c, n in sorted(pr.retained.items())], + links=[[x, y, k] for x, (y, k) in sorted(links.items())], + j={str(n): h for n in sorted(lifted)}, + flag=[[int(i == j) for j in range(h)] for i in range(h)], + late={str(n): [list(e), list(lt)] for n, (e, lt) in sorted(late.items())}, + claimed={}) + # ---------------------------------------------------------------- deferred word + vleaf = sorted(s for s in range(R) if pr.args[hold[s][0]] is None) + ops = [['src', s, hold[s][0]] for s in vleaf] + i = 0 + while i < len(L): + o = L[i] + if o[0] == 'add': + ops.append(['add', o[1], o[2], o[3]]) + i += 1 + else: + # one fan per copy: grouping would merge phase-one and later copies of one pivot + ops.append(['fan', o[1], [o[2]]]) + i += 1 + out = [[s, ch[-2][1], list(ch[-2][2])] for s, ch in enumerate(chains) if ch[-2][0] == 'out'] + ret = [[s, ch[-2][1]] for s, ch in enumerate(chains) if ch[-2][0] == 'ret'] + node_dims = [[n, fr.dim(('n', n))] for n in act] + late_dims = [] + for n, (e, lt) in sorted(late.items()): + for k in range(len(lt) - 1): + late_dims.append([n, list(lt[k:]), fr.dim(('c', n, tuple(lt[k:])))]) + readout = sorted((s for s in range(R) if f[s]), key=lambda s: (f[s], s)) + sigma = [placed[s] for s in readout] + for s, B in zip(readout, sigma): + assert len(B) == f[s] + vstart = [vK[s] for s in vleaf] + leaves = defaultdict(list) + for s in vleaf: + leaves[hold[s][0]].append(s) + xs_order = [] + for n in sorted(leaves): + ss = leaves[n] + early = sorted((s for s in ss if not f[s]), key=lambda s: (vdim[s], order_of[s])) + dfr = sorted((s for s in ss if f[s]), key=lambda s: (vdim[s], order_of[s])) + xs_order.append([n, early + dfr]) + dv = sorted((s for s in vleaf if f[s]), key=lambda s: (vdim[s], hold[s][0], order_of[s])) + D = dict(h=h, R=R, description='bitcomp_w compile exported by export97.py', ops=ops, + hold=[list(x) for x in hold], start=[list(x) for x in start], out=out, ret=ret, node_dims=node_dims, + late_dims=late_dims, readout_order=readout, sigma=sigma, vleaf_slots=vleaf, vleaf_start=vstart, + xs_order=xs_order, deferred_v_order=dv, claimed={}) + # check_lifted's regression pins: R and the undeferred chain-step histogram (V-leaf slots start at ) + from collections import Counter as _C + dimk = {('n', n): d for n, d in node_dims} + dimk.update({('c', n, tuple(lt)): d for n, lt, d in late_dims}) + rk = _C() + for s in range(R): + ds = [0, 1 if pr.args[hold[s][0]] is None else fr.dim(chains[s][1])] + [fr.dim(k) for k in chains[s][2:]] + assert ds[-1] == h and all(b >= a for a, b in zip(ds, ds[1:])) + for a_, b_ in zip(ds, ds[1:]): + if b_ > a_: + rk[b_ - a_] += 1 + W['claimed'] = dict(R=R, rk={str(r): c for r, c in sorted(rk.items())}) + os.makedirs(outdir, exist_ok=True) + with gzip.open(os.path.join(outdir, 'witness_%d.json.gz' % h), 'wt') as fo: + json.dump(W, fo) + with gzip.open(os.path.join(outdir, 'deferred_%d.json.gz' % h), 'wt') as fo: + json.dump(D, fo) + print(json.dumps(dict(h=h, R=R, deferred=len(readout), vleaf=len(vleaf), ops=len(ops), links=len(links), + late=len(late), lifted=len(lifted), max_sigma_entry=max((abs(x) for B in sigma for r in B for x in r), default=0), + max_vstart_entry=max(abs(x) for B in vstart for r in B for x in r)))) + + +def bdefer_frames(pr, sl, fr): + """bitcomp_w.bdefer's frames: placed sigma_u and V-leaf starts as exact primitive bases, f, vdim, use order.""" + from collections import defaultdict as dd + h, v, R = pr.h, pr.v, sl['R'] + chains, hold = sl['chains'], sl['hold'] + bd = bw.bdefer(pr, sl, fr, log=lambda *a: None) + # recompute the V-leaf starts and placements exactly as bw.bdefer does, keeping the spans + L = bc.place_ops(pr, sl) + leaf_slots = dd(list) + for s in range(R): + if pr.args[hold[s][0]] is None: + leaf_slots[hold[s][0]].append(s) + order_of = {} + vKs, vdim = {}, {} + for n, ss in leaf_slots.items(): + ss.sort(key=lambda s: (pr.gpos.get(hold[s][1], 10 ** 9) if len(hold[s]) > 1 else 10 ** 9, s)) + for i, s in enumerate(ss): + order_of[s] = i + acc = Span(h) + for s in reversed(ss): + acc = acc.copy().add_span(fr.K(chains[s][2])) + if bw.nondeg(acc): + vKs[s], vdim[s] = acc, h - len(acc) + else: + vKs[s], vdim[s] = None, 1 + assert vdim == bd['vdim'], 'V-leaf start dims differ from bdefer' + vK = {} + for s in vKs: + if vKs[s] is None: + vK[s] = [pr.tvec[hold[s][0]]] + else: + vK[s] = exact_frame(vKs[s], []) + placed = {} + f = bd['f'] + PL = bd.get('placedK') + assert PL is not None, 'patched bdefer needed (placedK)' + for s, K in PL.items(): + placed[s] = exact_frame(K, []) + assert len(placed[s]) == f[s] + return dict(f=f, placed=placed, vK=vK, vdim=vdim, order_of=order_of) + + +if __name__ == '__main__': + main() diff --git a/references/paired-cube/fib-bit-h21/producer/linalg_p.py b/references/paired-cube/fib-bit-h21/producer/linalg_p.py new file mode 100644 index 0000000000..c0aa9c0f19 --- /dev/null +++ b/references/paired-cube/fib-bit-h21/producer/linalg_p.py @@ -0,0 +1,98 @@ +"""Exact-mod-p subspace arithmetic in Q^h (p = 2^61 - 1; ranks over Q equal ranks mod p for these small integer +matrices with overwhelming probability; the release checkers recompute everything exactly).""" +P = (1 << 61) - 1 + + +class Span: + """row space given by an echelon list of (pivot, row); rows normalised at their pivot.""" + __slots__ = ('h', 'rows') + + def __init__(self, h, rows=()): + self.h = h + self.rows = list(rows) + + def copy(self): + return Span(self.h, self.rows) + + def __len__(self): + return len(self.rows) + + def reduce(self, u): + u = [x % P for x in u] + for p, r in self.rows: + c = u[p] + if c: + u = [(x - c * y) % P for x, y in zip(u, r)] + return u + + def insert(self, u): + u = self.reduce(u) + for p in range(self.h): + if u[p]: + inv = pow(u[p], P - 2, P) + self.rows.append((p, [x * inv % P for x in u])) + return True + return False + + def contains(self, u): + return not any(self.reduce(u)) + + def add_span(self, other): + """in place: self += other; returns self.""" + if len(self.rows) < self.h: + for _, r in other.rows: + self.insert(r) + if len(self.rows) == self.h: + break + return self + + def vectors(self): + return [r for _, r in self.rows] + + +def span_of(h, vecs): + s = Span(h) + for u in vecs: + if len(s) == h: + break + s.insert(u) + return s + + +def kernel(K): + """basis (list of vectors) of {x : k.x = 0 for k in K} (K a Span of covectors).""" + h = K.h + # bring K to reduced row echelon form + rows = [list(r) for _, r in K.rows] + piv = [p for p, _ in K.rows] + for i in range(len(rows)): + p = piv[i] + for j in range(len(rows)): + if j != i and rows[j][p]: + c = rows[j][p] + rows[j] = [(x - c * y) % P for x, y in zip(rows[j], rows[i])] + pivset = set(piv) + out = [] + for f in range(h): + if f in pivset: + continue + x = [0] * h + x[f] = 1 + for i, p in enumerate(piv): + x[p] = (-rows[i][f]) % P + out.append(x) + return out + + +def gram_rank(B): + """rank of the Gram matrix of the rows B under G' = 9I - J (G = I - J/9 up to the positive factor 9).""" + k = len(B) + if not k: + return 0 + sums = [sum(b) % P for b in B] + M = [[(9 * sum(x * y for x, y in zip(B[i], B[j])) - sums[i] * sums[j]) % P for j in range(k)] for i in range(k)] + return len(span_of(k, M)) + + +def nondegenerate(B): + return gram_rank(B) == len(B) diff --git a/references/paired-cube/fib-bit-h21/producer/producer.py b/references/paired-cube/fib-bit-h21/producer/producer.py new file mode 100644 index 0000000000..004eebad5b --- /dev/null +++ b/references/paired-cube/fib-bit-h21/producer/producer.py @@ -0,0 +1,548 @@ +"""Lane C best producer (variant c_p1a12): a_b_shared 1.26225e-04, a_b 1.21545e-04 under harness/evaluate_ab.py --shared +(bitcomp md5 b9a99aca). Self-contained copy of lanes/C/cprod.py (lane B's native PR #62 rebuild plus lane C +options) with the CFG overrides at the bottom. +""" +"""Lane B: round seven's lineage (PR #62 interval strips + core-aware pair assembly, PR #41 alternating order), +rebuilt natively on the harness circuit so that variants can be explored. + +Local pair circuit on n = h-1 points (inputs = pairs); global node for common point c maps pair (a,b) to triple +{c, P_c[a], P_c[b]}. Equal global supports are interned by the harness (pair-star merging across common points). +""" +from itertools import combinations +import os + +H = int(os.environ.get('BIT_H', 23)) +CFG = dict( + balanced_coarse=int(os.environ.get('B_BAL', 0)), + total_order='nat', # rev | sortdesc | sortasc | nat + top_layout='rev_interval', # rev_interval | interval | sorted+ | sorted- | skip | ps | rev_skip + deep_layout='sorted+', + point_order='cyc_C_rel', # alt | nat | alt_norev | cyc__ (cyclic triple packing on Z_23) + assembly='core', # core | plain (used only when asm specs are absent) + top_groups='split_last', # split the last top-level group into two singletons + # pair assembly per level (level 0, levels >= 1) for out[a,b], out[a,b2], out[a2,b], out[a2,b2]: + # Y: e + (FS + S); E: (FS + e) + S; T: FS + (S + e) (S + e is a saturated pair-star) + asm0=['Yi', 'Yj', 'Tj', 'Ti'], + asm1=['Yi', 'Tj', 'Tj', 'Ei'], + coarse_mode='perm0123', # level-0 coarse 4-edge sum chained e(a,b), e(a,b2), e(a2,b), e(a2,b2) + coarse_mode1='perm3012', # levels >= 1: e(a2,b2) + e(a,b) first (diagonal), then e(a,b2), e(a2,b) + cyc_base=((0, 1, 11), (0, 2, 9), (0, 3, 8)), # cyclic triple packing on Z_23 (69 blocks) + cyc_leave=(4, 6), # leave differences; c+-4, c+-6 paired as {c+4,c-6}, {c-4,c+6} (mode C) +) + + +class Local: + """Pair circuit with interning by local support (pairs of n points).""" + + def __init__(self, n, h): + self.n, self.h = n, h + self.inputs = list(combinations(range(n), 2)) + self.var = {p: i + 1 for i, p in enumerate(self.inputs)} + self.support = [0] + [1 << i for i in range(len(self.inputs))] + self.args = [None] * len(self.support) + self.lookup = {s: i for i, s in enumerate(self.support)} + self._level = -1 + self.cur = 'input' + self.tag = ['input'] * len(self.support) + + glookup = None + + def gsup(self, x): + s, g = self.support[x], 0 + while s: + low = s & -s + g |= self.bitmap[low.bit_length() - 1] + s ^= low + return g + + def add(self, a, b): + if not a: + return b + if not b: + return a + assert not self.support[a] & self.support[b] + s = self.support[a] | self.support[b] + if s in self.lookup: + return self.lookup[s] + x = len(self.support) + self.lookup[s] = x + self.support.append(s) + self.args.append((a, b)) + self.tag.append(self.cur) + return x + + def total(self, values): + values = [x for x in values if x] + o = CFG['total_order'] + if o == 'rev': + values.reverse() + elif o == 'sortdesc': + values.sort(key=lambda x: (self.support[x].bit_count(), self.support[x]), reverse=True) + elif o == 'sortasc': + values.sort(key=lambda x: (self.support[x].bit_count(), self.support[x])) + r = 0 + for x in values: + r = self.add(r, x) + return r + + +def prefix_suffix(c, vals): + n = len(vals) + prefix = [0] + for x in vals: + prefix.append(c.add(prefix[-1], x)) + suffix = [0] * (n + 1) + for i in range(n - 1, -1, -1): + suffix[i] = c.add(vals[i], suffix[i + 1]) + return prefix[-1], [c.add(prefix[i], suffix[i + 1]) for i in range(n)] + + +def skip_prefix(c, vals): + k = len(vals) + if k <= 2: + return prefix_suffix(c, vals) + v = [0] + list(vals) + A = [0] * (k + 1) + for i in range(1, k): + A[i] = c.add(A[i - 1], v[i]) + B = [0] * (k + 2) + for i in range(k, 1, -1): + B[i] = c.add(v[i], B[i + 1]) + out = [0] * (k + 1) + out[1] = B[2] + for j in range(2, k + 1): + out[j] = c.add(A[j - 2], c.add(v[j - 1], B[j + 1])) + return c.add(A[k - 1], v[k]), out[1:] + + +def interval_splits(k): + full = (1 << k) - 1 + interval = lambda a, m: sum(1 << ((a + t) % k) for t in range(m)) + splits = [(interval(a, m), interval(a, m - 1), 1 << ((a + m - 1) % k)) + for m in range(2, k) for a in range(k)] + return splits + [(full, interval(0, k - 1), 1 << (k - 1))] + + +def interval_layout(fallback): + def apply(c, vals): + k = len(vals) + if k < 3: + return fallback(c, vals) + node = {1 << i: x for i, x in enumerate(vals)} + for S, L, R in interval_splits(k): + node[S] = c.add(node[L], node[R]) + full = (1 << k) - 1 + return node[full], [node[full ^ (1 << j)] for j in range(k)] + return apply + + +def reversed_layout(layout): + def apply(c, vals): + total, out = layout(c, list(vals)[::-1]) + return total, out[::-1] + return apply + + +def sorted_layout(layout, sign): + def apply(c, vals): + order = sorted(range(len(vals)), key=lambda i: (c.support[vals[i]].bit_count(), sign * c.support[vals[i]])) + total, out = layout(c, [vals[i] for i in order]) + restored = [0] * len(vals) + for position, original in enumerate(order): + restored[original] = out[position] + return total, restored + return apply + + +def leave_one_out(c, values, layout): + values = list(values) + nonzero = [i for i, x in enumerate(values) if x] + if not nonzero: + return 0, [0] * len(values) + if len(nonzero) == 1: + x = values[nonzero[0]] + return x, [0 if i in nonzero else x for i in range(len(values))] + total, out = layout(c, [values[i] for i in nonzero]) + result = [total] * len(values) + for i, x in zip(nonzero, out): + result[i] = x + return total, result + + +def base_block(c, points, edges, weights): + def tot(omit): + return c.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 tot(()), {a: tot((a,)) for a in points}, {(a, b): tot((a, b)) for a, b in combinations(points, 2)} + + +def block_layout(inner, size=2, sib_first=False): + """two-level leave-one-out: consecutive blocks of `size` items, LOO over the block sums by `inner`, then + LOO_j = blockLOO[block(j)] + (the other items of j's block).""" + def apply(c, vals): + k = len(vals) + if k < 2 * size: + return inner(c, vals) + blocks = [list(range(i, min(i + size, k))) for i in range(0, k, size)] + bsum = [] + for blk in blocks: + r = 0 + for t in blk: + r = c.add(r, vals[t]) + bsum.append(r) + btot, bloo = inner(c, bsum) + out = [0] * k + for bi, blk in enumerate(blocks): + for idx in blk: + r = bloo[bi] + for t in blk: + if t != idx: + r = c.add(vals[t], r) if sib_first else c.add(r, vals[t]) + out[idx] = r + return btot, out + return apply + + + +def parse_plan(spec): + """'2:1,3:1,5:3' -> [(2,1),(3,1),(5,3)]: interval of length L = I(s, La) + I(s + La, L - La).""" + return [tuple(int(x) for x in t.split(':')) for t in spec.split(',') if t] + + +def fib_layout(plans, fallback): + """cyclic-interval strips: for k items, every needed length L = La + (L - La) at all k starts (two-use chains); + LOO output j = I(j + 1, k - 1); total = I(0, k - 1) + item k - 1. plans: {k: [(L, La), ...]} ending at k - 1.""" + def apply(c, vals): + k = len(vals) + plan = plans.get(k) + if k < 3 or plan is None: + return fallback(c, vals) + I = {(s, 1): vals[s] for s in range(k)} + for L, La in plan: + for s in range(k): + I[s, L] = c.add(I[s, La], I[(s + La) % k, L - La]) + out = [I[(j + 1) % k, k - 1] for j in range(k)] + return c.add(I[0, k - 1], vals[k - 1]), out + return apply + + +def env_plans(var): + """FIB0='10=2:1,3:1,6:3,9:6;9=...' -> {k: plan}""" + spec = os.environ.get(var, '') + out = {} + for part in spec.split(';'): + if part: + k, pl = part.split('=') + out[int(k)] = parse_plan(pl) + return out + + +def get_layout(name): + if name.startswith('blk'): # blk[s]_ + head, inner = name.split('_', 1) + sib_first = head.endswith('s') + size = int(head[3:].rstrip('s')) + return block_layout(get_layout(inner), size, sib_first) + if name.startswith('fib'): # fib: plans from env FIB, else rev_interval / sorted+ + base = dict(fib0=reversed_layout(interval_layout(skip_prefix)), + fib1=sorted_layout(interval_layout(skip_prefix), 1))[name] + return fib_layout(env_plans('FIB' + name[3:]), base) + return dict(rev_interval=reversed_layout(interval_layout(skip_prefix)), + interval=interval_layout(skip_prefix), + **{'sorted+': sorted_layout(interval_layout(skip_prefix), 1), + 'sorted-': sorted_layout(interval_layout(skip_prefix), -1)}, + skip=skip_prefix, rev_skip=reversed_layout(skip_prefix), ps=prefix_suffix)[name] + + +def make_block(h, cfg): + top = get_layout(cfg['top_layout']) + deep = get_layout(cfg['deep_layout']) + + def block(c, points, edges, weights, level): + if len(points) <= 2: + c.cur = 'base%d' % level + return base_block(c, points, edges, weights) + layout = top if level == 0 else deep + groups = [points[i:i + 2] for i in range(0, len(points), 2)] + if level == 0 and cfg.get('top_groups') == 'split_last': + groups = groups[:-1] + [[x] for x in groups[-1]] + elif level == 0 and cfg.get('top_groups') == 'split_last_rev': + groups = groups[:-1] + [[x] for x in groups[-1][::-1]] + elif level == 0 and cfg.get('top_groups') == 'triples_last': + groups = groups[:-2] + [groups[-2] + groups[-1][:1], groups[-1][1:]] + ng = len(groups) + e = lambda a, b: edges[tuple(sorted((a, b)))] + c.cur = 'coarse%d' % level + cm = cfg.get('coarse_mode', 'chain') if level == 0 else cfg.get('coarse_mode1', cfg.get('coarse_mode', 'chain')) + if cm == 'rows': + coarse = {(i, j): c.total([c.total([e(a, b) for b in groups[j]]) for a in groups[i]]) + for i, j in combinations(range(ng), 2)} + elif cm.startswith('perm'): + pm = [int(ch) for ch in cm[4:]] + def coarse_sum(i, j): + es = [e(a, b) for a in groups[i] for b in groups[j]] + es = [es[p] for p in pm if p < len(es)] if len(es) == 4 else es + r = 0 + for x in es: + r = c.add(r, x) + return r + coarse = {(i, j): coarse_sum(i, j) for i, j in combinations(range(ng), 2)} + elif cfg['balanced_coarse']: + def coarse_sum(i, j): + return c.total([c.total([e(a, b) for a in groups[i]]) for b in groups[j]]) + coarse = {(i, j): coarse_sum(i, j) for i, j in combinations(range(ng), 2)} + else: + coarse = {(i, j): c.total([e(a, b) for a in groups[i] for b in groups[j]]) + for i, j in combinations(range(ng), 2)} + c.cur = 'wt%d' % level + wt = {i: c.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 = block(c, list(range(ng)), coarse, wt, level + 1) + strips, sums = {}, {} + for i, g in enumerate(groups): + other = [j for j in range(ng) if j != i] + for a in g: + c.cur = 'carry%d' % level + carry = c.total([weights[u] for u in g if u != a]) + c.cur = 'vals%d' % level + vals = [c.total([e(u, v) for u in g if u != a for v in groups[j]]) for j in other] + c.cur = 'loo%d' % level + st, one = leave_one_out(c, [carry] + vals, layout) + strips[a] = {j: z for j, z in zip(other, one[1:])} + sums[a] = st + out = {} + c.cur = 'single%d' % level + single = {a: c.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): + spec = cfg.get('asm%d' % min(level, 1)) + if spec and len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + part = {a: a2, a2: a, b: b2, b2: b} + S = {a: strips[a][j], a2: strips[a2][j], b: strips[b][i], b2: strips[b2][i]} + FS = {} + def fs(x): + c.cur = 'FS%d' % level + if x not in FS: + FS[x] = c.add(F, S[x]) + return FS[x] + order = [(a, b), (a, b2), (a2, b), (a2, b2)] + for k in cfg.get('asm_order', (0, 1, 2, 3)): + x, y = order[k] + ch = spec[k] + ee = e(part[x], part[y]) + if level == 0 and getattr(c, 'glookup', None) is not None: + gi = c.gsup(S[x]) | c.gsup(ee) + gj = c.gsup(S[y]) | c.gsup(ee) + if gi in c.glookup: + ch = 'Ti' + elif gj in c.glookup: + ch = 'Tj' + if ch == 'Yi': + fy = fs(y); c.cur = 'Y%d' % level; m = c.add(fy, S[x]); c.cur = 'pout%d' % level + out[x, y] = c.add(ee, m) + elif ch == 'Yj': + fx = fs(x); c.cur = 'Y%d' % level; m = c.add(fx, S[y]); c.cur = 'pout%d' % level + out[x, y] = c.add(ee, m) + elif ch == 'Ei': + fy = fs(y); c.cur = 'Y%d' % level; m = c.add(fy, ee); c.cur = 'pout%d' % level + out[x, y] = c.add(m, S[x]) + elif ch == 'Ej': + fx = fs(x); c.cur = 'Y%d' % level; m = c.add(fx, ee); c.cur = 'pout%d' % level + out[x, y] = c.add(m, S[y]) + elif ch == 'Ti': + fy = fs(y); c.cur = 'T%d' % level; m = c.add(S[x], ee); c.cur = 'pout%d' % level + out[x, y] = c.add(fy, m) + elif ch == 'Tj': + fx = fs(x); c.cur = 'T%d' % level; m = c.add(S[y], ee); c.cur = 'pout%d' % level + out[x, y] = c.add(fx, m) + continue + amode = cfg.get('assembly1', cfg['assembly']) if level >= 1 else cfg['assembly'] + if amode == 'core' and len(groups[i]) == 2 and len(groups[j]) == 2: + (a, a2), (b, b2) = groups[i], groups[j] + F = far[i, j] + Sa, Sa2, Sb, Sb2 = strips[a][j], strips[a2][j], strips[b][i], strips[b2][i] + c.cur = 'FS%d' % level + FSa, FSa2 = c.add(F, Sa), c.add(F, Sa2) + FSb, FSb2 = c.add(F, Sb), c.add(F, Sb2) + c.cur = 'Y%d' % level + Y1 = c.add(FSb, Sa) + Y2 = c.add(FSa, Sb2) + Y3 = c.add(FSa2, e(a, b2)) + Y4 = c.add(FSb2, e(a, b)) + c.cur = 'pout%d' % level + out[a, b] = c.add(e(a2, b2), Y1) + out[a, b2] = c.add(e(a2, b), Y2) + out[a2, b] = c.add(Y3, Sb) + out[a2, b2] = c.add(Y4, Sa2) + continue + c.cur = 'odd%d' % level + for a in groups[i]: + left = c.add(far[i, j], strips[a][j]) + for b in groups[j]: + cross = c.total([e(u, v) for u in groups[i] if u != a for v in groups[j] if v != b]) + out[a, b] = c.add(left, c.add(strips[b][i], cross)) + return total, single, out + return block + + +def cyclic_points(h, c, base=((0, 1, 3), (0, 4, 9), (0, 6, 13)), leave=(8, 11), mode='A', gorder='rel'): + """Pairs of [h]-c from a cyclic triple packing on Z_h: block pairs {x, y} with {c, x, y} a block, then the + leave neighbours c+-d1, c+-d2 paired by mode.""" + pairs = [] + for blk in base: + for k in blk: + i = (c - k) % h + pts = sorted(((i + t) % h for t in blk if (i + t) % h != c)) + pairs.append(tuple(pts)) + d1, d2 = leave + L = {'A': [((c + d1) % h, (c - d1) % h), ((c + d2) % h, (c - d2) % h)], + 'B': [((c + d1) % h, (c + d2) % h), ((c - d1) % h, (c - d2) % h)], + 'C': [((c + d1) % h, (c - d2) % h), ((c - d1) % h, (c + d2) % h)]}[mode] + assert len(set(x for p in pairs + L for x in p)) == h - 1 + if gorder == 'rel': + pairs.sort(key=lambda p: sorted((x - c) % h for x in p)) + elif gorder == 'abs': + pairs.sort() + return [x for p in pairs + L for x in p] + + +def alternating_points(h, common): + if CFG['point_order'].startswith('cyc'): + _, mode, gorder = CFG['point_order'].split('_') + if 'cyc_base' in CFG: + return cyclic_points(h, common, base=CFG['cyc_base'], leave=CFG['cyc_leave'], mode=mode, gorder=gorder) + return cyclic_points(h, common, mode=mode, gorder=gorder) + if CFG['point_order'] == 'nat': + return [x for x in range(h) if x != common] + po = CFG['point_order'] + pairs = [(a, a + 1) for a in range(0, h - 1, 2) if common not in (a, a + 1)] + if common % 2 and po in ('alt', 'alt_sfirst', 'alt_swin'): + pairs.reverse() + if po == 'alt_swin' and common % 2: # odd circuits also swap the two points of every pair + pairs = [(b, a) for a, b in pairs] + head = [x for pair in pairs for x in pair] + tail = [x for x in range(h) if x != common and x not in head] + if po == 'alt_sfirst': # the special group {partner(c), h-1} first + return tail + head + return head + tail + + +def local_circuit(h, cfg, L=None): + n = h - 1 + L = L or Local(n, h) + block = make_block(h, cfg) + pts = list(range(n)) + total, _, two = block(L, pts, {p: L.var[p] for p in combinations(pts, 2)}, {a: 0 for a in pts}, 0) + outputs = dict(two) + outputs[()] = total + active = set() + stack = list(outputs.values()) + while stack: + x = stack.pop() + if not x or x in active: + continue + active.add(x) + if L.args[x]: + stack.extend(L.args[x]) + return L, outputs, active + + +PROV = {} +LOCAL = [] + + +def build_side(C, h): + if CFG.get('adaptive_T'): + return build_side_adaptive(C, h) + L, outputs, active = local_circuit(h, CFG) + LOCAL[:] = [L, outputs, active] + out, ret = {}, {} + swap = CFG.get('swap', 0) + flip = set(CFG.get('swap_flip', ())) # local tags whose operand order is flipped relative to `swap` + # pass structure: 'two_pass' creates the total's (retained) ancestry for every common point first + passes = [sorted(active)] + if CFG.get('two_pass'): + anc, st = set(), [outputs[()]] + while st: + x = st.pop() + if x and x not in anc: + anc.add(x) + if L.args[x]: + st.extend(L.args[x]) + passes = [sorted(anc), sorted(active - anc)] + ms = {common: {} for common in range(h)} + Ps = {common: alternating_points(h, common) for common in range(h)} + loop = CFG.get('loop', 'circuit') # circuit | circuit_rev | node (each local node for every circuit) + commons = list(range(h))[::-1] if loop == 'circuit_rev' else list(range(h)) + + def make(common, x): + P, m = Ps[common], ms[common] + if L.args[x] is None: + a, b = L.inputs[x - 1] + m[x] = C.inputs[tuple(sorted((common, P[a], P[b])))] + else: + a, b = m[L.args[x][0]], m[L.args[x][1]] + m[x] = C.add(b, a) if swap ^ (L.tag[x] in flip) else C.add(a, b) + PROV.setdefault(m[x], (common, x)) + GTAG.setdefault(m[x], L.tag[x]) + for nodes in passes: + if loop == 'node': + for x in nodes: + for common in commons: + make(common, x) + else: + for common in commons: + for x in nodes: + make(common, x) + for common in range(h): + P, m = Ps[common], ms[common] + for pair, x in outputs.items(): + if pair: + T = tuple(sorted((common, P[pair[0]], P[pair[1]]))) + out[(common, T)] = m[x] + else: + ret[common] = m[x] + return dict(out=out, ret=ret) + + +TAG = {} +GTAG = {} + + +def build_side_adaptive(C, h): + """Per-circuit construction: an output uses a saturated pair-star T node on whichever side already exists + globally (built by an earlier circuit), so block-consistent pairings share their T pieces.""" + out, ret = {}, {} + for common in range(h): + P = alternating_points(h, common) + L = Local(h - 1, h) + L.bitmap = [1 << C.tindex[tuple(sorted((common, P[a], P[b])))] for a, b in L.inputs] + L.glookup = C.lookup + L, outputs, active = local_circuit(h, CFG, L) + LOCAL[:] = [L, outputs, active] + m = {} + for x in sorted(active): + if L.args[x] is None: + a, b = L.inputs[x - 1] + m[x] = C.inputs[tuple(sorted((common, P[a], P[b])))] + else: + m[x] = C.add(m[L.args[x][0]], m[L.args[x][1]]) + PROV.setdefault(m[x], (common, x)) + TAG.setdefault(m[x], L.tag[x]) + for pair, x in outputs.items(): + if pair: + T = tuple(sorted((common, P[pair[0]], P[pair[1]]))) + out[(common, T)] = m[x] + else: + ret[common] = m[x] + return dict(out=out, ret=ret) + + +# lane C best configuration +CFG.update({'total_order': 'nat', 'top_layout': 'rev_interval', 'deep_layout': 'sorted+', 'point_order': 'alt', 'assembly': 'core', 'top_groups': None, 'asm0': None, 'asm1': None, 'coarse_mode': 'chain', 'coarse_mode1': 'perm2301', 'swap': 1, 'swap_flip': ['pout1', 'Y1', 'FS1', 'pout2', 'Y2', 'FS2']}) + +CFG.update(top_layout='fib0', deep_layout='fib1') diff --git a/references/paired-cube/fib-bit-h21/producer/run_producer.py b/references/paired-cube/fib-bit-h21/producer/run_producer.py new file mode 100644 index 0000000000..59329e466f --- /dev/null +++ b/references/paired-cube/fib-bit-h21/producer/run_producer.py @@ -0,0 +1,21 @@ +#!/usr/bin/env python3 +"""IMMUTABLE. Runs the lane's producer.py in its own process and serializes its DAG (evaluate.py never imports it). +Producer contract: module constant H (int), build_side(C, h) -> dict(out={(c, T): node for every triple T and c in T}, +ret={c: node for every point c}).""" +import sys, os, json, importlib.util +HERE = os.path.dirname(os.path.abspath(__file__)) +sys.path.insert(0, HERE) +from circuit import BitCircuit + +lane, out_path = os.path.abspath(sys.argv[1]), sys.argv[2] +sys.path.insert(0, lane) +spec = importlib.util.spec_from_file_location('producer', os.path.join(lane, 'producer.py')) +prod = importlib.util.module_from_spec(spec) +spec.loader.exec_module(prod) +h = int(getattr(prod, 'H', 23)) +C = BitCircuit(h) +res = prod.build_side(C, h) +v = C.v +json.dump(dict(h=h, args=[list(C.args[x]) for x in range(v + 1, len(C.args))], + out=[[c, list(T), res['out'][(c, T)]] for T in C.triples for c in T], + ret=[res['ret'][c] for c in range(h)]), open(out_path, 'w')) diff --git a/references/paired-cube/fib-bit-h21/selection.json b/references/paired-cube/fib-bit-h21/selection.json new file mode 100644 index 0000000000..09a1d3c276 --- /dev/null +++ b/references/paired-cube/fib-bit-h21/selection.json @@ -0,0 +1 @@ +{"retained_readout_order": [17220, 17226, 17244, 15954, 16223, 16740, 16751, 16757, 16758, 16764, 16779, 16785, 16814, 16822, 16853, 16859, 16881, 16887, 16918, 16930, 16936, 16942, 16950, 16956, 16975, 16976, 16993, 16994, 16999, 17002, 17028, 17034, 17041, 17047, 17053, 17059, 17065, 17071, 17094, 17100, 17131, 17134, 17136, 17140, 17148, 17154, 17161, 17172, 17178, 17179, 17182, 17183, 17190, 17196, 17203, 17214, 17215, 17217, 17219, 17233, 17241, 18035, 18366, 18374, 18397, 18713, 18715, 18719, 18721, 18725, 18727, 18745, 18748, 18925, 18928, 19059, 19061, 19065, 19067, 19092, 19262, 19401, 19403, 19407, 19409, 19415, 19432, 19435, 19739, 19741, 19768, 19771, 19934, 20073, 20075, 20083, 20100, 20103, 20106, 20269, 20428, 20434, 20595, 20752, 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"3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b", - "matching_arcs_sha256": "22c90ed078d765e58ac824d6f9558cc4620961b48644a32c0115bdb9852de771", - "graph_sha256": "7a7a58df595dc245ebe8d2673abdd8c4eaae98e767885240715a61f43a2f4dff" + "matching_arcs_sha256": "fe28c981304643aeb383a8ef6b4fec0b818b665dd86da1b4955796073f8cecbb", + "graph_sha256": "064f8c9f0d8db29667aa0e79e4eba671a7cb4b53c5406e58f219aede7727062c" } diff --git a/references/paired-cube/selected-module/matching-arcs.json b/references/paired-cube/selected-module/matching-arcs.json index e9238210ab..1a5e746f4b 100644 --- a/references/paired-cube/selected-module/matching-arcs.json +++ b/references/paired-cube/selected-module/matching-arcs.json @@ -1 +1 @@ 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diff --git a/scripts/paired_cube/verify.py b/scripts/paired_cube/verify.py index 9b0d6be233..6074006b86 100644 --- a/scripts/paired_cube/verify.py +++ b/scripts/paired_cube/verify.py @@ -147,7 +147,7 @@ def each(bits): assert contained(A,current[t]);Y[len(current[t])-len(A)]+=1;current[t]=A for t,q in enumerate(inputs):assert contained((q,),current[t]);Y[len(current[t])-1]+=1 assert dict(Y)=={int(k):c for k,c in record['target_data_histogram'].items()} - assert record['selected_roles']==len(seen)==4840 and birth==Counter({20:4840}) + assert record['selected_roles']==len(seen)==3630 and birth==Counter({18:3630}) return dict(signed_scalar_pairs_checked=scalar_pairs,scalar_H_exact=True,K_involution_and_inverse_exact=True, decoder_identity_exact=True,conservative_source_supports=True,K_source_itinerary_verified=True, full_backward_intersections=True,physical_signed_M_replayed=True, diff --git a/scripts/paired_cube_bit.py b/scripts/paired_cube_bit.py index 8e00899f47..2b425bc7bd 100644 --- a/scripts/paired_cube_bit.py +++ b/scripts/paired_cube_bit.py @@ -1,11 +1,15 @@ #!/usr/bin/env python3 -"""Incremental reconstruction of the selected PR97 shared-core bit profile. +"""Incremental reconstruction of the selected h=21 shared-core bit profile. Copyright 2026 icekylinx. Apache-2.0. Construction with GPT-6 Astra; integration with OpenAI Codex. The inherited PR97 ledger is by Zhihao Chen, and its frozen scalar/frame witness is Swapnil Jain's construction. Their original credits, licenses and disclosures remain in the pinned snapshot. No complete-basis replay or inherited rational-frame audit is repeated. + +The bit word is the hash-pinned h=21 Fibonacci-strip word in PR97's frozen format, +read by PR97's unchanged reader; prepared by eumemic with Anthropic Claude +assistance (references/paired-cube/fib-bit-h21/README.md). """ import argparse from collections import Counter @@ -15,9 +19,22 @@ import json from pathlib import Path -from partial_gauge_bit import ROOT, require, encoded, frozen_sources +from partial_gauge_bit import ROOT, require, encoded INPUT = ROOT / 'certificates/paired-cube-bit-input.json' +PR97_READER = '9b2acaeb6f1beb2a53c15e00c027f9ba22397a12071ad0b71131e12012a98036' + + +def frozen_sources(record): + manifest_path = ROOT / record['source_manifest'] + require(sha256(manifest_path.read_bytes()).hexdigest() == record['source_manifest_sha256'], + 'Bit word manifest changed') + manifest = json.loads(manifest_path.read_text()) + for name, digest in manifest['sha256'].items(): + require(sha256((manifest_path.parent/name).read_bytes()).hexdigest() == digest, + 'Pinned bit word source changed: '+name) + require(manifest['sha256']['deferred.py'] == PR97_READER, 'PR97 reader changed') + return manifest_path.parent, manifest def histogram(value): @@ -71,9 +88,9 @@ def reconstruct(input_path=INPUT): spec = importlib.util.spec_from_file_location('paired_cube_pinned_deferred', folder/'deferred.py') deferred = importlib.util.module_from_spec(spec) spec.loader.exec_module(deferred) - with gzip.open(folder/'witness_23.json.gz', 'rt') as stream: + with gzip.open(folder/'witness_21.json.gz', 'rt') as stream: witness = json.load(stream) - with gzip.open(folder/'deferred_23.json.gz', 'rt') as stream: + with gzip.open(folder/'deferred_21.json.gz', 'rt') as stream: data = json.load(stream) schedule = deferred.Schedule(witness, data) ledger = json.loads((folder/'bit-ledger-result.json').read_text()) @@ -84,16 +101,16 @@ def reconstruct(input_path=INPUT): selected = selection['retained_readout_order'] omitted = selection['omitted_readout_order'] chosen, skipped = set(selected), set(omitted) - require(len(chosen) == len(selected) == 9543 and len(skipped) == len(omitted) == 2022, + require(len(chosen) == len(selected) == 7575 and len(skipped) == len(omitted) == 1335, 'Selected gauge counts differ') require(chosen.isdisjoint(skipped) and chosen | skipped == schedule.sel, 'Selection does not partition the inherited gauges') - require(len(schedule.sel) == 11565, 'Inherited gauge count differs') + require(len(schedule.sel) == 8910, 'Inherited gauge count differs') for slots, subset in ((selected, chosen), (omitted, skipped)): require(slots == [s for s in schedule.readout if s in subset], 'Gauge order is not the inherited subsequence') h, v, R = schedule.h, schedule.v, schedule.R - require((h,v,R) == (23,1771,28866), 'Inherited dimensions differ') + require((h,v,R) == (21,1330,21526), 'Inherited dimensions differ') old_aux = deferred.chain_ranks(schedule) require(encoded(old_aux) == ledger['rank_histograms']['aux'], 'Inherited auxiliary chain receipt differs') @@ -133,7 +150,7 @@ def reconstruct(input_path=INPUT): ('target_data_histogram', target), ('selected_rank_histogram', gauges), ('copied_center_histogram', Counter({h-1:h})), ('child_histogram', children)): require(histogram(record[key]) == +value, 'Selected profile differs: '+key) - require(values['W_per_vertex']*values['m']-values['rank_per_vertex'] == 2024, + require(values['W_per_vertex']*values['m']-values['rank_per_vertex'] == 1400, 'Shared-core rank deficit differs') require(all(0 < r < 3*h and n > 0 for r,n in children.items()), 'Invalid child') result = dict(record) diff --git a/scripts/paired_cube_network.py b/scripts/paired_cube_network.py index 63dab6d4e3..b89626ecde 100644 --- a/scripts/paired_cube_network.py +++ b/scripts/paired_cube_network.py @@ -24,15 +24,15 @@ sys.set_int_max_str_digits(0) ROOT = Path(__file__).resolve().parents[1] -AC = Q(4856569,10**10) -COARSE = Q(4617656,10**10) +AC = Q(5113520,10**10) +COARSE = Q(5164125,10**10) ATOM = Q(1,1000) OLD = Q(384599,10**10) AB = (1-ATOM)*COARSE+ATOM*OLD BAD = Q(1,10**16) PHASE_STOP = Q(1,10**6) ASSEMBLY_BIT = min(AB,(1-PHASE_STOP)*AC-Q(1,10**10)) -KAPPA = Q(4609169,10**10) +KAPPA = Q(5108289,10**10) def clean(hist): @@ -48,14 +48,14 @@ def shared_profile(row,complex_word): require(0 < r < h and n > 0,'Proper local gauges') H[3*r] += n if complex_word: - require((h,v,R,ell) == (24,1760,26417,528),'Paired-cube local dimensions') + require((h,v,R,ell) == (22,1320,18473,440),'Paired-cube local dimensions') require(R == row['c']+row['q']-row['matched'],'Compatible carrier roles') - require(selected == {20:4840},'Selected rank20 gauges') + require(selected == {18:3630},'Selected rank18 gauges') for r,n in enumerate(row['remaining_internal_histogram']): H[r] += 3*n parts = ('source_data_histogram','target_data_histogram') else: - require((h,v,R,ell) == (23,1771,28866,506),'Retained bit local dimensions') + require((h,v,R,ell) == (21,1330,21526,420),'Retained bit local dimensions') parts = ('auxiliary_histogram','source_data_histogram','target_data_histogram','copied_center_histogram') for name in parts: for r,n in row[name].items(): @@ -187,7 +187,7 @@ def main(): p.add_argument('--output',type=Path,default=ROOT/'certificates/paired-cube-network.json') args = p.parse_args() args.output.write_text(json.dumps(js(certificate()),indent=2,sort_keys=True)+'\n') - print('PASS kappa=4609169/10000000000 = 4.609169e-4; both moments, shared cores, finite router and 47 strict constraints') + print('PASS kappa=5108289/10000000000 = 5.108289e-4; both moments, shared cores, finite router and 47 strict constraints') if __name__ == '__main__': diff --git a/scripts/paired_cube_producer.py b/scripts/paired_cube_producer.py index 3354975491..c856af2282 100644 --- a/scripts/paired_cube_producer.py +++ b/scripts/paired_cube_producer.py @@ -33,7 +33,7 @@ def stage(message):print(message,file=sys.stderr,flush=True) frozen=reference/'matching-arcs.json' assert hashlib.sha256(frozen.read_bytes()).hexdigest()==pin['matching_arcs_sha256'] stage('Regenerating paired-cube signed DAG from inherited PR117 restrictions') - g=Graph(12).finish(restricted_triples(12),restricted_pairs(11),all_but_one(10)) + g=Graph(11).finish(restricted_triples(11),restricted_pairs(10),all_but_one(9)) g['matching_frames']='coordinate' binding={k:g[k] for k in ('inputs','labels','args','signs','roots','centers')} assert hashlib.sha256(json.dumps(binding,separators=(',',':')).encode()).hexdigest()==pin['graph_sha256']

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