From 948ce1510df750f4c18b96bdaef436a86f8bf834 Mon Sep 17 00:00:00 2001 From: icekylinx Date: Fri, 9 Oct 2026 07:11:11 +0800 Subject: [PATCH 1/7] Use stopped product-ring interchange for kappa = 7.79476e-5 --- Makefile | 10 + NOTICE | 17 + PATCHING.md | 5 +- README.md | 30 ++ SOURCES.json | 42 ++ certificates/joint-dual-kappa.json | 2 +- certificates/joint-dual-validation.json | 2 +- certificates/stopped-product-bit-axis.json | 38 ++ .../stopped-product-complex-input.json | 41 ++ certificates/stopped-product-input.json | 253 +++++++++ certificates/stopped-product-network.json | 482 ++++++++++++++++++ docs/reproducibility.md | 5 + docs/stopped-product.md | 67 +++ notes/stopped-product-assembly.tex | 108 ++++ notes/stopped-product-complex.tex | 137 +++++ notes/stopped-product-factorization.tex | 112 ++++ notes/stopped-product-interface.tex | 95 ++++ notes/stopped-product-note.tex | 76 +++ research/joint-dual/SOURCE.json | 6 +- scripts/stopped_product/README.md | 36 ++ scripts/stopped_product/__init__.py | 1 + scripts/stopped_product/complex.py | 228 +++++++++ scripts/stopped_product_network.py | 163 ++++++ scripts/stopped_product_producer.py | 92 ++++ 24 files changed, 2042 insertions(+), 6 deletions(-) create mode 100644 certificates/stopped-product-bit-axis.json create mode 100644 certificates/stopped-product-complex-input.json create mode 100644 certificates/stopped-product-input.json create mode 100644 certificates/stopped-product-network.json create mode 100644 docs/stopped-product.md create mode 100644 notes/stopped-product-assembly.tex create mode 100644 notes/stopped-product-complex.tex create mode 100644 notes/stopped-product-factorization.tex create mode 100644 notes/stopped-product-interface.tex create mode 100644 notes/stopped-product-note.tex create mode 100644 scripts/stopped_product/README.md create mode 100644 scripts/stopped_product/__init__.py create mode 100644 scripts/stopped_product/complex.py create mode 100644 scripts/stopped_product_network.py create mode 100644 scripts/stopped_product_producer.py diff --git a/Makefile b/Makefile index 84fe8290f3..e60b843993 100644 --- a/Makefile +++ b/Makefile @@ -30,6 +30,7 @@ verify-community: community-audit-check community-followup-check copied-reversed $(MAKE) climbed-48-verify verify-producers: + $(MAKE) stopped-product-verify $(MAKE) copied-centers-verify $(MAKE) structured-bulk-verify $(MAKE) endpoint-gauge-producer endpoint-gauge-certificate @@ -428,3 +429,12 @@ pair-assembly-verify: pair-assembly-producer pair-assembly-check .PHONY: verify-pair verify-pair: pair-assembly-verify python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json + +.PHONY: stopped-product-producer stopped-product-certificate stopped-product-verify +stopped-product-producer: + python3 scripts/stopped_product_producer.py + +stopped-product-certificate: + python3 scripts/stopped_product_network.py + +stopped-product-verify: stopped-product-producer stopped-product-certificate diff --git a/NOTICE b/NOTICE index b565637758..50c6d1236d 100644 --- a/NOTICE +++ b/NOTICE @@ -302,3 +302,20 @@ inherited PR #48 sources. The stacked witness in research/pair-assembly/frame uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. diff --git a/PATCHING.md b/PATCHING.md index b60f3f101b..a02e230256 100644 --- a/PATCHING.md +++ b/PATCHING.md @@ -1,6 +1,6 @@ # Applying the inherited manuscript patch -This patch is the PR #10 baseline. The current copied-center extension is +This patch is the PR #10 baseline. The PR #36 copied-center extension is presented in `notes/copied-centers-note.tex`; it is not included in this historical combined manuscript patch. @@ -30,3 +30,6 @@ alternatives for the same base. PR7 is pinned at `6725c6a17b17871a35353fd29157f4ed851bc114` for the retained producer sources. The old uniform recurrences keep their original exponents. The active consumers use `lem:batched-chunk-swap` and `prop:batched-simultaneous-layer`. + +The stopped product-ring extension is supplied separately in +`notes/stopped-product-note.tex`; it does not regenerate this historical patch. diff --git a/README.md b/README.md index 035c259b68..31aa46c2e2 100644 --- a/README.md +++ b/README.md @@ -3,6 +3,36 @@ **Community research maintained by Douglas Colkitt — conditional on the original OpenAI #109 framework.** +## Stopped product-ring extension + +The new construction contributed by **icekylinx**, extending merged +[PR #36](https://github.com/CrocSwap/integer-mult-bounds/pull/36), gives + +$$ +T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad +\kappa=\frac{194869}{2500000000}=7.79476\times10^{-5}. +$$ + +It combines a stopped product-ring bit interchange on `(23,23)` with an +all-disjoint rational-center complex network on `(24,24)`. The new generic +opposite-bank factorization pays one reversed child per projector rank; +atom adapters, ordinary leaves, endpoint copies and the exact denominator-21 +grid are included in the proof. The bound retains the original analytic +and fixed-tape hypotheses. + +[Proof source](notes/stopped-product-note.tex) · +[Exact certificate](certificates/stopped-product-network.json) · +[Incremental reproduction](docs/stopped-product.md) + +```sh +make stopped-product-verify +``` + +The maintainer-reviewed community checkpoint below remains its own result +and validation record. + +## Reviewed community checkpoint + The reviewed community witness gives $$ diff --git a/SOURCES.json b/SOURCES.json index 6096d5aff9..380b5425c2 100644 --- a/SOURCES.json +++ b/SOURCES.json @@ -234,5 +234,47 @@ } ], "continuing_analytic_dependencies": "See structured_bulk_extension.adopted and references/semantic-bulk/MANIFEST.json." + }, + "stopped_product_extension": { + "contributor": "icekylinx", + "base_commit": "56b66d58297deca1d7dd130247d720e960f77a37", + "proof_predecessor_PR": "https://github.com/CrocSwap/integer-mult-bounds/pull/36", + "proof_predecessor_commit": "11817ccacb564bb7f98789c20dc11d3fece207e3", + "predecessor_merged": true, + "archive": "integer_mult_round5_kappa_7_79476e-5_complete.zip", + "archive_sha256": "714cbffa0cccba3c18f046a63e62d6981683cb386b5d5cd09761be7b70f0b0be", + "kappa": "194869/2500000000", + "proof": "notes/stopped-product-note.tex", + "certificate": "certificates/stopped-product-network.json", + "producer": "scripts/stopped_product_producer.py", + "assistance": "Substantial OpenAI GPT-6 Astra and Codex assistance.", + "scope": "Conditional on the retained analytic and fixed-tape framework; new product-ring and exact rational-grid arguments supplied as written proofs.", + "continuing_dependencies": [ + "copied_centers_extension", + "structured_bulk_extension" + ], + "icekylinx_lineage": [ + { + "pr": 10, + "commit": "62691e395a0458ce089a1c7b5d89e74291e95e29" + }, + { + "pr": 18, + "commit": "f2ab41aebad47861caf6316282c1793e5513845e" + }, + { + "pr": 24, + "commit": "ed90fd940279c336ebc45968631bdebfb087b505" + }, + { + "pr": 32, + "commit": "0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52" + }, + { + "pr": 36, + "commit": "11817ccacb564bb7f98789c20dc11d3fece207e3" + } + ], + "curation": "Selected h23/h24 inputs, generator, exact certificate and proofs only; excludes raw graphs, research alternatives and recursive predecessor copies." } } diff --git a/certificates/joint-dual-kappa.json b/certificates/joint-dual-kappa.json index d92f653fe4..31628a32dc 100644 --- a/certificates/joint-dual-kappa.json +++ b/certificates/joint-dual-kappa.json @@ -842,7 +842,7 @@ "scripts/experiments/pin_joint_dual_sources.py": "4d31cc0e38b7902709ca5f8f714cba109760d2592346dd7f8dc0b900a2d9fe00", "scripts/experiments/verify_joint_dual.py": "7a31bba1e9c0ded32ae285df2ca9bc91ef20c330f6789fdba361876f3c7a1985" }, - "source_manifest_sha256": "fd1aab7d75753b4b55b2377f26119dae74f367b0b4fab66cba42d944b3042cc9", + "source_manifest_sha256": "db926540bbc818963af5ac78ed8949e6263afffdbbe2f05ee781ef7d3cde48f0", "sources": [ { "files": { diff --git a/certificates/joint-dual-validation.json b/certificates/joint-dual-validation.json index 99adb4cf74..b2624180c2 100644 --- a/certificates/joint-dual-validation.json +++ b/certificates/joint-dual-validation.json @@ -226,7 +226,7 @@ } }, "bit_saving": "2382370177/50000000000000", - "certificate_sha256": "2ed658f05365b28825e24a6e7bac9fc9cc015d5a5d63d9579f4ac6e0640ae559", + "certificate_sha256": "b8263db0d04aabb98a31965a40c198667709bd6a6c7f98df2990baf523bcd075", "kappa": "4764513337/100000000000000", "margins": 7, "producer_words_regenerated_and_matched": true, diff --git a/certificates/stopped-product-bit-axis.json b/certificates/stopped-product-bit-axis.json new file mode 100644 index 0000000000..5824891de9 --- /dev/null +++ b/certificates/stopped-product-bit-axis.json @@ -0,0 +1,38 @@ +{ + "h": 23, + "v": 1771, + "c": 34764, + "q": 5336, + "baseline_R": 40100, + "matching": 1324, + "R": 38776, + "loss": 506, + "histogram": [ + 9840, + 38409, + 32471, + 8898, + 9754, + 2116, + 5737, + 1725, + 4145, + 1547, + 3128, + 1551, + 2893, + 1925, + 2841, + 2450, + 2327, + 3096, + 2344, + 3628, + 9435, + 2110, + 23, + 23 + ], + "label_source": "positive", + "description": "Retained-total aligned triple producer, base-two recursion, original maximum carrier matching, and compatible positive labels." +} diff --git a/certificates/stopped-product-complex-input.json b/certificates/stopped-product-complex-input.json new file mode 100644 index 0000000000..7b1d99c518 --- /dev/null +++ b/certificates/stopped-product-complex-input.json @@ -0,0 +1,41 @@ +{ + "h": 24, + "v": 2024, + "c": 45764, + "q": 8120, + "baseline_R": 53884, + "matched": 8966, + "R": 44918, + "orientation_changes": 7338, + "rank_sum": 1079136, + "loss": 552, + "histogram": [ + 8930, + 49042, + 30844, + 15972, + 11883, + 8272, + 6399, + 4356, + 6682, + 2263, + 5109, + 1808, + 5317, + 1733, + 5391, + 1757, + 4908, + 3290, + 6233, + 4363, + 4056, + 264, + 564, + 24, + 24 + ], + "central_disjoint": 24, + "center_denominator": 21 +} diff --git a/certificates/stopped-product-input.json b/certificates/stopped-product-input.json new file mode 100644 index 0000000000..f0a910a495 --- /dev/null +++ b/certificates/stopped-product-input.json @@ -0,0 +1,253 @@ +{ + "bit": { + "dimensions": [ + 23, + 23 + ], + "m": 529, + "N": 3136441, + "W": 143617474, + "L": 1792252, + "total_rank": 75972299557, + "deficit": 1344189, + "maxchild": 506, + "child_multiplicities": { + "1": 139262585, + "2": 115012282, + "3": 31516716, + "4": 34548668, + "5": 7494872, + "6": 20320454, + "7": 6109950, + "8": 14681590, + "9": 5479474, + "10": 11079376, + "11": 5493642, + "12": 10247006, + "13": 6818350, + "14": 10062822, + "15": 8677900, + "16": 8242234, + "17": 10966032, + "18": 8302448, + "19": 12850376, + "20": 33418770, + "21": 7473620, + "22": 12627230, + "484": 6272882, + "506": 137344592 + } + }, + "complex": { + "dimensions": [ + 24, + 24 + ], + "m": 576, + "N": 4096576, + "B1": 90914032, + "B2": 90914032, + "W": 190021216, + "L": 2234496, + "total_rank": 109450358336, + "deficit": 1862080, + "child_multiplicities": { + "552": 181828064, + "529": 8193152, + "1": 202715744, + "2": 124856512, + "3": 64654656, + "4": 48102384, + "5": 33485056, + "6": 25903152, + "7": 17633088, + "8": 27048736, + "9": 9160624, + "10": 20681232, + "11": 7318784, + "12": 21523216, + "13": 7015184, + "14": 21822768, + "15": 7112336, + "16": 19867584, + "17": 13317920, + "18": 25231184, + "19": 17661424, + "20": 16418688, + "21": 1068672, + "22": 2283072, + "23": 16483456 + }, + "maxchild": 552, + "copied_histogram": [ + 8930, + 49066, + 30844, + 15972, + 11883, + 8272, + 6399, + 4356, + 6682, + 2263, + 5109, + 1808, + 5317, + 1733, + 5391, + 1757, + 4908, + 3290, + 6233, + 4363, + 4056, + 264, + 564, + 24, + 0 + ] + }, + "bit_moment_gap": "5833629405069796335513229037/13595148940731587639987765177686687744", + "complex_moment_gap": "5499421901694541095908997425024101371546537414283732387206104389099738183215366564793192567257041780652609318673168302647523216560182242981533611801155442603608986943408777543208667066118724847925169249370145237707441178592436788856344246441565482324551821454604550454953780270300756671351666361036963486701477553679079126088067165335949185500960812006586245961913848693714754073033035419679174118868763905107326417918471742975833959733450001524553321932789312500612407132407690299/41230077325513267360846956938521502341474073689326505257121676970478810391277326276471865083362032190646188250982499628351612283105589897175543987487125650452330304348151388045812369968133964037865011250349179368669257862504666828211703334554008512518414563221340357395437053315115874615168412042904680012697363239611038021437069048505672439008745508864584512067644825937731293242352557278635159598633861792145775836588122497044363982384099548431927704944786606529202786560000000000000000000", + "finite_bridge": { + "bit_coarse": { + "m": 529, + "W": 143617474, + "maxchild": 506, + "halving_degree": 16, + "wire_bits": 28 + }, + "ordinary_leaf_row_degree": 252, + "complex": { + "m": 576, + "W": 190021216, + "s": 109450358336, + "maxchild": 552, + "halving_degree": 17, + "wire_bits": 28, + "scalar_terms": [ + { + "h": 24, + "v": 2024, + "c": 45764, + "invocations": 2024, + "local_group_upper": 408200, + "copied_center_extra_groups": 48 + }, + { + "h": 24, + "v": 2024, + "c": 45764, + "invocations": 2024, + "local_group_upper": 408200, + "copied_center_extra_groups": 48 + } + ], + "scalar_group_upper": 1656684480 + }, + "semantic": { + "E": 403063477262941121443761178688, + "literal_charge": 119639333593035096270287748, + "strict_literal_gap": 402943837929348086347490890940, + "B": 403063477262941121553211537024, + "C0": 2994465792675104952757349965746759652008778122322142627817848832, + "C1": 1, + "induction_gap": 18943983431358232713000942240128, + "fixed_odd_divisor": 21, + "exact_grid": "One common dyadic grid times the fixed odd divisor to K=G*(D_complex+1); no child rounding" + }, + "rows": { + "coefficient": 1176, + "degree": 4000, + "suffix_slope": 16000, + "degree_gap": "40024/25", + "contract": "W_complex^D_complex * W_coarse^D_coarse * W_old^D_old; one preceding prefix and one padding; sequential reuse" + } + }, + "assembly": { + "parameters": { + "actual_bit_saving": "803380799/10000000000000", + "a_bit": "1948995551/25000000000000", + "a_complex": "1949/25000000", + "tau": "24998051004449/25000000000000", + "sigma": "24998051/25000000", + "eta": "1/100000000", + "beta": "1/1000000", + "q": "97449775601004449/1250000000000000000000", + "c": "9744977657550220501004449/125000000000000000000000000000", + "epsilon": "124999998750000000000000000000/125019489955217650665401004449", + "lambda_": "2499805100446848995551/2500000000000000000000", + "lambda_prime": "1249902550224398995551/1250000000000000000000", + "alpha_squared_power": "14618091340150667350000000/125019489955217650665401004449", + "delta": "1/800000000", + "C0": 2994465792675104952757349965746759652008778122322142627817848832, + "C1": 1, + "kappa": "194869/2500000000" + }, + "strict_constraints": { + "bit_positive": "1948995551/25000000000000", + "complex_above_bit": "4449/25000000000000", + "complex_below_one_over32": "779301/25000000", + "beta_positive": "1/1000000", + "beta_below_one": "999999/1000000", + "leaf_saving_above_bit": "1/10000000000", + "q_positive": "97449775601004449/1250000000000000000000", + "q_below_internal": "1948995551/1250000000000000000000", + "q_below_leaf": "126948995551/1250000000000000000000", + "c_positive": "9744977657550220501004449/125000000000000000000000000000", + "c_below_one": "124990255022342449779498995551/125000000000000000000000000000", + "q_below_reservations": "97449775601004449/125000000000000000000000000000", + "lambda_above_tau": "1948995551/2500000000000000000000", + "lambda_above_sigma": "446848995551/2500000000000000000000", + "lambda_above_internal": "1948995551/2500000000000000000000", + "lambda_prime_above_lambda": "1948995551/2500000000000000000000", + "compact_leaf": "126948995551/1250000000000000000000", + "compact_reservations": "97449775601004449/125000000000000000000000000000", + "lambda_prime_below_one": "97449775601004449/1250000000000000000000", + "epsilon_positive": "124999998750000000000000000000/125019489955217650665401004449", + "epsilon_below_one": "19491205217650665401004449/125019489955217650665401004449", + "guard_width": "19491205217650665401004449/125019489955217650665401004449", + "K_geometry": "974622765755022147550220501004449/12501948995521765066540100444900000000", + "K_dominates_log": "974497756010044392550224398995551/12501948995521765066540100444900000000", + "record_suffix": "19491205217650665401004449/125019489955217650665401004449", + "phase_local": "15592839154630577103152893798995551/100015591964174120532320803559200000000", + "phase_boundary": "11694348052630578662349334598995551/100015591964174120532320803559200000000", + "gamma_sublinear": "4873113877499998051004449/125019489955217650665401004449", + "cell_above_band": "124995125636122500001948995551/250038979910435301330802008898", + "prime_interval_packing": "19491205217650665401004449/125019489955217650665401004449", + "alpha_positive": "14618091340150667350000000/125019489955217650665401004449", + "alpha_below_one": "125004871863877499998051004449/125019489955217650665401004449", + "alpha_below_one_fourth": "124961017589857047996001004449/500077959820870602661604017796", + "delta_positive": "1/800000000", + "delta_below_one_eighth": "99999999/800000000", + "short_record_fallback": "3124756306320288991609616461252697967793601/3125487248880441266635025111225000000000000", + "small_field_exposure": "9746227754999996102008898/125019489955217650665401004449", + "artificial_boundary": "700128635079475474301789581367398995551/100015591964174120532320803559200000000", + "literal_scalar_guard": "402943837929348086347490890940", + "row_product_gap": "40024/25", + "original_prefix_above_kappa": "786538948061330309871047284761/78137181222011031665875627780625000000", + "coordinate_movement_above_kappa": "305551/25000000000000", + "compact_phase_layer_above_kappa": "20668543364879972849164027819/312548724888044126663502511122500000000", + "bulk_exposure_above_kappa": "305551/25000000000000", + "Gaussian_arithmetic_above_kappa": "97459317411097999618605138287111327/2500389799104353013308020088980000000000", + "scalar_work_above_kappa": "194921594961097960638694118287111327/2500389799104353013308020088980000000000", + "dimension_above_kappa": "312475634452011916691632483971664027819/312548724888044126663502511122500000000" + }, + "margins": { + "original_prefix": "974622765755022147550220501004449/12501948995521765066540100444900000000", + "coordinate_movement": "1948995551/25000000000000", + "compact_phase_layer": "9744977462650669298995551/125019489955217650665401004449", + "bulk_exposure": "1948995551/25000000000000", + "Gaussian_arithmetic": "11694348052630578662349334598995551/100015591964174120532320803559200000000", + "scalar_work": "15592839154630577103152893798995551/100015591964174120532320803559200000000", + "dimension": "124999998750000000000000000000/125019489955217650665401004449" + }, + "minimum_margin": "9744977462650669298995551/125019489955217650665401004449", + "absorption_gap": "20668543364879972849164027819/312548724888044126663502511122500000000", + "recurrence": { + "internal": "24998051004449/25000000000000", + "leaf": "24998051001949/25000000000000", + "reservations": "124990255022342449779498995551/125000000000000000000000000000" + } + } +} diff --git a/certificates/stopped-product-network.json b/certificates/stopped-product-network.json new file mode 100644 index 0000000000..998a8a7ea2 --- /dev/null +++ b/certificates/stopped-product-network.json @@ -0,0 +1,482 @@ +{ + "assembly": { + "absorption_gap": "20668543364879972849164027819/312548724888044126663502511122500000000", + "margins": { + "Gaussian_arithmetic": "11694348052630578662349334598995551/100015591964174120532320803559200000000", + "bulk_exposure": "1948995551/25000000000000", + "compact_phase_layer": "9744977462650669298995551/125019489955217650665401004449", + "coordinate_movement": "1948995551/25000000000000", + "dimension": "124999998750000000000000000000/125019489955217650665401004449", + "original_prefix": "974622765755022147550220501004449/12501948995521765066540100444900000000", + "scalar_work": "15592839154630577103152893798995551/100015591964174120532320803559200000000" + }, + "minimum_margin": "9744977462650669298995551/125019489955217650665401004449", + "parameters": { + "C0": 2994465792675104952757349965746759652008778122322142627817848832, + "C1": 1, + "a_bit": "1948995551/25000000000000", + "a_complex": 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403063477262941121443761178688, + "exact_grid": "One common dyadic grid times the fixed odd divisor to K=G*(D_complex+1); no child rounding", + "fixed_odd_divisor": 21, + "induction_gap": 18943983431358232713000942240128, + "literal_charge": 119639333593035096270287748, + "strict_literal_gap": 402943837929348086347490890940 + } + }, + "kappa": "194869/2500000000", + "proof_predecessor_commit": "11817ccacb564bb7f98789c20dc11d3fece207e3", + "scope": "Exact finite moments, stopped savings and assembly; the new complex producer is checked separately. Opposite-bank factorization, atom streaming, ordinary conversion, common exact grid and retained analytic/tape interfaces are written proof dependencies.", + "source_sha256": { + "certificates/copied-centers-bit-axes.json": "ed307cef595091b11ba8f8e6ff11302ad8db190227a2fbf34c232fd680206254", + "certificates/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf", + "certificates/stopped-product-bit-axis.json": "52f493a0019b7e4ce69a4c26bd3d35af5d3397461126abc4be44d1430ae8930d", + "certificates/stopped-product-complex-input.json": "5bcf00402bbfb768bd2fc0935f32ad329ee0780a3dfe5827bb010831d7909c4d", + "certificates/stopped-product-input.json": "8185c7bf8c307728f32484c5972af9a1b948ac5d0838e02f85c86cb438060417", + "notes/stopped-product-assembly.tex": "1c3c7147851f30f1ff97679cfcda157b1cbe2655b8766e34f1345f20c630eaec", + "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "notes/stopped-product-factorization.tex": "70d5a4405e1be9c7b6cfb326bb4ffdf88e5585d1fb3d16c7bb5ad62ac421fae3", + "notes/stopped-product-interface.tex": "454a8f3924afc26e575b2a8cec6d0860397cb7f2dc431f3ba63fb8a7142cc96b", + "notes/stopped-product-note.tex": "486d14c599f4c2551c019f3358898f72e6ecafeb04ad590726ea69ed987fe025", + "scripts/copied_centers/physical.py": "837345d1f8753eab0e70f105b1d1bb0db965b993da037b1825ddef3672609d7d", + "scripts/copied_centers_network.py": "409ebfbd8a41c4c4d089aa0949fcf5a949415dc26f57440ffd48b7bd8881e6a9", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/stopped_product/README.md": "6c1805dda45b01ed0ef420c674ec2cd0048fb9d7a1b015ab6cd837067fe66176", + "scripts/stopped_product/__init__.py": "7b794c22bccc00bb6ae8ba4d3379f469570565bbcb1a86090699133b8cf1b7d3", + "scripts/stopped_product/complex.py": "407650d56dceb5cb09d74928658cebed1bb42f4d7e28ca9e3fd36eea075f1ad0", + "scripts/stopped_product_network.py": "a8baaa87dd7679db4f2dd1a18a720397ee6f443262ad04fa26cf51b39909b74c", + "scripts/stopped_product_producer.py": "2c5c71399136ebcfebb8e5277317d5f334eb8df5716ad287391d0996fcc1492c", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d" + }, + "status": "Conditional stopped product-ring multiplication witness" +} diff --git a/docs/reproducibility.md b/docs/reproducibility.md index e48f4190cd..7b966039e0 100644 --- a/docs/reproducibility.md +++ b/docs/reproducibility.md @@ -1,5 +1,10 @@ # Reproducing the result +For the new stopped product-ring extension, run `make stopped-product-verify`. +Its [incremental reproduction guide](stopped-product.md) covers the h24 +rational-center producer, new moments, stopping parameters and assembly. +The community checkpoint and historical targets below retain their own scope. + The selected release is documented in the [joint-frame community review](research/community-round2-review.md) and [current status](research/current-status.md), with the [selected parameter certificate](../research/matrix-exponent-synthesis/candidate/arithmetic.json). diff --git a/docs/stopped-product.md b/docs/stopped-product.md new file mode 100644 index 0000000000..5bc1cbc88e --- /dev/null +++ b/docs/stopped-product.md @@ -0,0 +1,67 @@ +# Stopped product-ring reproduction + +The extension gives the conditional saving `194869/2500000000 = 7.79476e-5`. +It starts from merged PR #36 and is submitted on upstream main at +`56b66d58297deca1d7dd130247d720e960f77a37`. + +From the repository root, with Python 3.11+, Make and a C++17 compiler: + +```sh +make stopped-product-verify +``` + +The incremental checks: + +- Match the unchanged positive-label h23 bit producer to its verified + copied-center input, preserving the same matching and histogram. +- Rebuild only the new h24 all-disjoint complex producer with aligned pair + stars, exact rational center decoding, support and binary-frame checks, + then reproduce every matching count and histogram entry. +- Reconstruct both child lists and strict rational moments; derive the + stopped ordinary-bit saving and check that the atom-adapter toll is lower. +- Check the denominator-21 semantic charge, product row stock `p^4000`, + seven assembly margins and all 47 strict constraints. + +Intermediate DAGs and the matcher executable are temporary. To retain them: + +```sh +python3 scripts/stopped_product_producer.py --work-dir /tmp/stopped-product-producers +``` + +For arithmetic alone, use `make stopped-product-certificate`. The inherited +`make verify-producers` also includes this target; the full `make verify` +retains the community and historical checks. Those unchanged suites are +not part of this round's local incremental validation. + +The [proof](../notes/stopped-product-note.tex) is supplied as LaTeX source; +no PDF is generated. Its common-basis factorization, atom streaming and +stopping argument, outer ordinary conversion and shared exact rational +grid are written proofs. Finite checks verify the selected scalar data and +arithmetic, not the complete all-size theorem. + +[SOURCES.json](../SOURCES.json) and [NOTICE](../NOTICE) preserve contribution +credits and source pins. Existing two-stage, ordinary-leaf and semantic +proof dependencies remain in `references/copied-centers/` and +`references/semantic-bulk/`. Research alternatives, raw binary DAGs and +recursive predecessor copies are excluded from this submission. + +## Shared source bindings before submission + +The inherited `research/joint-dual/SOURCE.json` also binds the repository's +`Makefile`, `README.md` and `NOTICE`. Adding a verification target or editing +those documents therefore affects the joint-frame check even when its +mathematical construction is unchanged. + +After reviewing such source changes, refresh the manifest and regenerate +its dependent certificate and validation receipt: + +```sh +python3 scripts/experiments/pin_joint_dual_sources.py +make verify-joint +``` + +Include `research/joint-dual/SOURCE.json`, `certificates/joint-dual-kappa.json` +and `certificates/joint-dual-validation.json` in the same submission. Check +that their changes are the expected source bindings, then rerun the affected +check against the staged artifacts and require a clean diff. CI verifies +the committed bindings; it does not refresh them automatically. diff --git a/notes/stopped-product-assembly.tex b/notes/stopped-product-assembly.tex new file mode 100644 index 0000000000..3932d3ade5 --- /dev/null +++ b/notes/stopped-product-assembly.tex @@ -0,0 +1,108 @@ +\subsection{Simultaneous row reserves} +Use a conservative global width bound $e$ for every adapter and child. +For each recursive family $j$, the least integer $t_j$ with +$m_j^{t_j}>2r_j^{t_j}$ gives depth at most +$t_j\lceil\log_2\max(2,e)\rceil$ plus a fixed constant. +The new coarse bit family has $(t_j,\operatorname{bitlength}W_j)=(16,28)$, +the ordinary leaf family $(9,28)$, and the complex family $(17,28)$. +The required reserve is the product of all three stocks: +\[ + Q=W_c^{D_c}W_b^{D_b}W_{\rm old}^{D_{\rm old}}. +\] +After the complex and coarse divisions, the old stock remains available +to every peeled-atom or stopped-leaf call. Sequential copies and outer +ordinary wrappers reuse restored rows; they introduce no independent +row factor. The combined coefficient is +\[ + 16\cdot28+9\cdot28+17\cdot28=1176, + \qquad4000-\frac{51}{25}\,1176=\frac{40024}{25}>0. +\] +Thus the retained logarithmic comparison, for eventual $e\le Cp$, +supplies a sufficient $p^{4000}$ stock including the fixed constants. +Use one physically preceding transformed prefix and one complete-row +padding, as in \path{notes/structured-bulk-assembly.tex}. Complete +spectators and parked fields are preserved by every descendant. +The suffix condition +$b_{\rm in}^{1-\epsilon}>16000(\log_2b_{\rm in}+8)$ is eventual +for every fixed $\epsilon<1$. + +\subsection{Analytic transfer and selected parameters} +The retained analytic proof map in +\path{notes/structured-bulk-assembly.tex} supplies the active-masked +arbitrary-source router with paid repair scans, the rounded phase-cell +inverse, persistent bulk halos with original period cuts, sequential +overlap tapes and factor pages, prime packing and exact recovery. +The new ordinary bit primitive has precisely the arbitrary-width, +complete-spectator and restored-row contract consumed by that router. +The new complex primitive supplies the exact completed tensor contract +on one common grid. Its outer grid conversions add only logarithmic +work. The changed finite implementations therefore meet the same +analytic interfaces, including the full bulk bound +\[ + O\!\left(Tp\left[p^\tau\operatorname{polylog}p+ + d\operatorname{polylog}p+dp^\delta+w_G^2p^\delta+ + dw_G^2p^\delta/L\right]\right)+n^{o(1)}, +\] +where $L=2^{\lceil8\log_2p\rceil}$, Gaussian band width +$w_G^2=O(p^{1-r})$, and normalization retains $\epsilon+r<1$. +Here $w_G$ is unrelated to the address atom width. + +Use the proved ordinary bit saving $a_b=803380799/10^{13}$ and complex +saving $b=1949/25000000$. To instantiate the retained assembly, weaken +the bit parameter explicitly to +\[ + \beta=10^{-6},\qquad + a=(1-\beta)b-10^{-10}=\frac{1948995551}{25000000000000}6.6129027953\times10^{-11}>0. +\] +The strict gaps absorb fixed logarithms, including the common-grid +conversions. The stopped atom recurrence supplies the ordinary +interchange interface, the rational-center construction supplies the +exact complex interface, and the product stock supports all nested +recursions. The unchanged analytic transfer then proves the stated +bound, with its constructive setup, descriptor and catalogue domination, +prime-existence and exact-recovery thresholds retained as eventual +conditions. +\end{proof} diff --git a/notes/stopped-product-complex.tex b/notes/stopped-product-complex.tex new file mode 100644 index 0000000000..4a9037137c --- /dev/null +++ b/notes/stopped-product-complex.tex @@ -0,0 +1,137 @@ +\subsection{All-disjoint retained centers} +Use two factors $h=24$. For triple inputs write $G=\sum_TX_T$, +$T_i=\sum_{T\ni i}X_T$, and retain all $A_i=G-T_i$. +Each input triple avoids exactly 21 points, so +\[ + \sum_{i=1}^{24}A_i=21G,\qquad G=\frac1{21}\sum_i A_i. +\] +For a target triple $S$ the central correction is +\[ + G-\frac12\sum_{i\in S}A_i + =\frac{\sum_{i\in S}T_i-G}{2}. +\] +An input triple meeting $S$ in $j$ points has central coefficient +$(j-1)/2$. Adding half the disjoint sum and subtracting half the +intersection-two sum leaves coefficient one exactly when $j=3$. +The scalar source-to-scatter transfer is therefore the identity. +The transparent old-value subtraction and new-value addition use this +identity only on fresh contributions and restore arbitrary old values. + +The base-two paired exclusion and aligned pair-star producer retains +nested binary labels: common-pair supports have their orthonormal triple +span, other ordinary sums have their coordinate cover. Each retained +$A_i$ has the nondegenerate coordinate hyperplane excluding $i$, +of dimension 23. Hence all copied-center arguments and general +nondegenerate binary residuals of the preceding proof apply. The +selected local counts are +\[ + v=2024,\quad c_h=45764,\quad q_h=8120,\quad + |\mathcal M|=8966,\quad R=44918,\quad\ell=552. +\] +The old internal histogram, starting at rank zero, is +\begin{small}\begin{align*} +[&8930,49042,30844,15972,11883,8272,6399,4356,6682,2263,\\ + &5109,1808,5317,1733,5391,1757,4908,3290,6233,4363,\\ + &4056,264,564,24,24]. +\end{align*}\end{small} +It has rank mass $24R+2\ell$. Replace 24 rank-24 original transitions +by 24 rank-one transitions; all rank-23 copied transforms remain. +The new mass is $24R+\ell$. + +\subsection{Physical endpoints and strict complex moment} +The copied-center two-stage complex contract in +\path{notes/copied-centers-complex.tex} is unchanged by the scalar +center decoding. For the tensor triple line $U$, let +$T=C_U$, $F=C_I$, $E=C_{U^\perp}=FT^{-1}$. +The two data outputs are $A=-Fy$ and $B=FT^{-2}x+Ey$. +Add $T^{-1}$ applied to a copy of $A$ into $B$, paying one rank-one +child per data pair. The inherited input/output $Z$ phases and +$i^{9f}$ scalar normalize $FT^{-2}$ to $F$; sign and bank corrections +complete the exact tensor $C$. Auxiliary source/sink operators remain +$C_{D_0}$ and $FC_{D_0}$ in the second stage. Every original role +therefore returns the exact selected-axis tensor operation on arbitrary +inputs. This algebraic statement holds over $\mathbb Q(i)$ as well as +over Gaussian dyadics. + +With $m_c=576$, $N_c=v^2=4096576$, $B_c=vR=90914032$, put +\[ + W_c=2N_c+2B_c=190021216,\quad L_c=2v\ell=2234496, +\] +\[ + s_c=W_cm_c-N_c+L_c=109450358336,\qquad N_c-L_c=1862080. +\] +The complete list is $2B_c$ width-552 auxiliary exteriors, +$2N_c$ width-529 data macros, $2vH'_r$ width-$r$ internal children, +$4N_c$ width-23 data fronts, and $N_c$ width-one endpoint copies. +These disjoint classes include both kinds of paid copies and sum to +$s_c$. All binary residuals, including alternating forms, use the retained +one-child Gauss normal form with paid bit adapters and unit phases. +At $a_c=1949/25000000$ the exact rational enclosure gives +\[ + \sum_r\frac{n_r}{W_c}(r/m_c)^{1-a_c} + <1-1.3338373969\times10^{-10}. +\] + +\subsection{One exact odd-denominator grid} +The only new odd divisor is 21. Let $d$ bound the root axis count, +$D$ bound its maximum complex recursion depth, and $G_0$ bound the +number of grouped scalar operations per node. Choose +\[ + K=G_0(D+1),\qquad \text{common grid }2^{-P}21^{-K}. +\] +Root inputs and arbitrary dirty auxiliaries start Gaussian dyadic. +Multiply their integer numerators by $21^K$ once at the outer boundary. +Every local coefficient contains at most one factor 21 in its denominator, +so a local finite program adds at most $G_0$ to the odd-denominator +exponent. A completed $u$-axis child has Gaussian-dyadic coefficients +and therefore preserves its input's existing odd-denominator exponent; +it adds no new odd factor. Only the active chain of unfinished calls +can accumulate new factors. Its length is at most $D+1$, proving that +all intermediates lie on the common grid and every local division by +21 is an exact integer division of its encoded numerator. + +This divisibility claim uses the root dyadic-input invariant, not an +assumption about arbitrary numerators on the finest grid. Internal values +may have odd denominators. They are neither rounded nor re-encoded when +a child returns. At the completed outer return the operator is the exact +Gaussian-dyadic tensor on root dyadic inputs, so the final numerators +are divisible by $21^K$; exact unscaling restores dyadic encoding. + +Since the largest child is $552<576$, $D=O(\log d)$ and +$K=O(\log d)$ with fixed constants. Constant-divisor long division +is linear in numerator length. Initial and final scaling by $K$ +successive constant multiplications/divisions cost $O(V\log d)$ and +occur only at the outer boundary. The extra numerator length is +$O(\log d)$, preserving the retained $O(p)$ word bound. This overhead +is subordinate to the positive-power complex layer bound. + +For explicit semantic constants use +\[ + g_h=4(c_h+v)+10v+4hv+4h^2+8h+8=408200, +\] +\[ + G_0=N_c+2v(g_h+2h)=1656684480, +\] +where endpoint additions and copied-center scalar work are included. +The complete child contributes at most $u$ binary denominator bits +and row-norm factor $2^u$, with no additional odd exponent. A local +21-division contributes fewer than five denominator-height bits, +covered by the fixed scalar charge. Set +\[ +\begin{aligned} + E_0&=64(W_c+m_c+G_0+1)^3=403063477262941121443761178688,\\ + \mathcal E&=2G_0W_c^2+8s_c+4W_c+4+32m_c\\ + &=1196393335930350962702877484.2909639537\times10^{-10}. +\] +It uses the retained 24-term positive atanh-series logarithm enclosure, +its geometric tail, range reduction and upward rational exponential +bound. Also $\mu_1=s_b/(W_bm_b)<1$. These are the two gaps used below. diff --git a/notes/stopped-product-interface.tex b/notes/stopped-product-interface.tex new file mode 100644 index 0000000000..20c44ce486 --- /dev/null +++ b/notes/stopped-product-interface.tex @@ -0,0 +1,95 @@ +\subsection{Paid atom adapters and remainders} +Expand each fixed lower-triangular formal factor into unit scalings and +additions from earlier to later formal fields. Execute intrabank targets +in descending formal-field order, so earlier controls still have their +required original values. Every atom update reads only physically earlier +controls. In a cross-bank shear the update is +\[ + D_{i,t}\leftarrow D_{i,t}+k_{ij}H_{j,f-1-t}. +\] +Even with the reversed source index, the source lies in the earlier head +bank. The retained ordered-affine streaming primitive applies to each +ordinary width-$w$ atom update, costing $O(V)$ per pass. +There are $O(f)$ passes per fixed matrix and thus $O(Vn)$ per finite +node. The reversed control is an indexed earlier atom, not a reversed +field operation. Atom loops use binary descriptors on a fixed tape set; +all inactive digits remain complete spectators. The inherited parking +schedule never scans through parked ancestors, and polynomial descriptor +work is absorbed by the complete stream volume. + +For $n=m_bf+\delta$, $0\le\deltaa_b$, the paid adapter term is strictly lower order. +All bounded widths use the old interface. Numerical padding of a binary +chunk range to the least suitable radix-$q$ range has volume factor +below $q^2$; it preserves numerical order and is removed after the +completed ordinary wrapper, whose endpoint is ordinary interchange. + +If external rows are unavailable, use the inherited ordinary high-digit +borrowing construction from \path{notes/batched-bit-rows.tex}. +Borrow $O(\log e)$ high digits, exchange and join them into a preceding +row field, pad that field once, act on the body, and separate the high +parts. It applies literally to the completed ordinary wrapper; no claim +about borrowed high positions is made for an unwrapped reversed call. +Single-digit moves cost $O(V\log e)$, and small widths use the old +algorithm. Atom indices and rational coefficients are finitely specified; +the algorithm uses the same fixed tape set and complete spectator ranges. diff --git a/notes/stopped-product-note.tex b/notes/stopped-product-note.tex new file mode 100644 index 0000000000..a8b23254c8 --- /dev/null +++ b/notes/stopped-product-note.tex @@ -0,0 +1,76 @@ +\documentclass[11pt]{article} +\usepackage[margin=1in]{geometry} +\usepackage[T1]{fontenc} +\usepackage{lmodern,amsmath,amssymb,amsthm,mathtools,booktabs,longtable,microtype} +\usepackage[hidelinks]{hyperref} +\setlength{\emergencystretch}{3em} +\allowdisplaybreaks +\newtheorem{theorem}{Theorem}[section] +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{proposition}[theorem]{Proposition} +\title{A conditional integer-multiplication saving of $194869/2500000000$\\ +\large Stopped product-ring interchange and rational retained centers} +\author{icekylinx\\\small With substantial OpenAI GPT-6 Astra and Codex assistance} +\date{9 October 2026} +\begin{document}\maketitle +\begin{abstract} +A common rational basis and opposite bank orders reduce each projector +residual to one contiguous reversed child over a fixed atom product ring. +Ordered atom adapters are paid explicitly; stopping at a growing atom +width and using the retained ordinary primitive supplies an ordinary +bit interface. An independent 24-dimensional complex producer uses +rational retained-center decoding on one exact common grid. The selected +interfaces and retained semantic/bulk assembly give the conditional bound +$T(n)=O(n(\log n)^{1-\kappa})$, where +$\kappa=194869/2500000000=0.0000779476$. +\end{abstract} + +\section{Scope and retained dependencies} +The model is the retained fixed finite-alphabet multitape Turing machine. +Finite graphs, rational bases, address primes, coefficient tables and tape +counts are fixed independently of input length. Bit payload arithmetic is +binary, while its address geometry is rational and then evaluated on atom +rings. Complex payloads use exact Gaussian rational arithmetic with the +specified common grid; their address labels remain binary. + +The proof predecessor is icekylinx's merged copied-center PR36, +\texttt{11817ccacb564bb7f98789c20dc11d3fece207e3}, whose proof is +\path{notes/copied-centers-note.tex}. Its ordinary interchange saving +$a_{\rm old}=384599/10^{10}$, copied-center schedule in both orientations, +two-stage data and auxiliary endpoint identities, general binary residual +normal form, and fixed-tape complete-row contracts are retained. +The present opposite-bank factorization, stopped product-ring interface, +rational-center specialization and exact composition are by icekylinx, +with substantial OpenAI GPT-6 Astra assistance and Codex integration. +Earlier own contributions include PR10 batching, PR18 partial swaps, +PR24 endpoint gauges and PR32 structured blocks and semantic composition. + +Aurel Prosz (Paureel) supplies the two-stage topology and paid endpoint +copy, with Swapnil Jain's linked development credited by Zhihao Chen's +PR29. The retained leaf proof also credits Rohan Arun's PR31 corner method +and Dominik Scholz's PR33 parameterization. Zhihao Chen's PR21/23 and the +RaD/hipotures PR20 source provide the phase endpoints, semantic guard, +arbitrary-source routing, phase-cell inverse and bulk locality/tape +interfaces. Their pinned proof map remains in +\path{notes/structured-bulk-assembly.tex}; adopted sources and notices are +in \path{references/semantic-bulk/} and \path{references/copied-centers/}. +The underlying Douglas Colkitt framework, OpenAI manuscript, eumemic, +Bortlesboat, dleen, earlier finite contributions and Harvey--van der Hoeven +analytic work retain their credits and recorded AI assistance in +\texttt{NOTICE} and \texttt{SOURCES.json}. + +The conclusion remains conditional on those analytic, ordered-affine, +exact-recovery and machine interfaces and their eventual setup and +prime-existence thresholds. The new algebraic and tape constructions +below establish the changed finite interfaces; exact arithmetic certifies +their selected counts and margins. + +\section{One reversed child for each projector} +\input{notes/stopped-product-factorization.tex} +\section{Stopped atom recursion and ordinary interchange} +\input{notes/stopped-product-interface.tex} +\section{Rational centers and exact semantic precision} +\input{notes/stopped-product-complex.tex} +\section{Product rows and exact assembly} +\input{notes/stopped-product-assembly.tex} +\end{document} diff --git a/research/joint-dual/SOURCE.json b/research/joint-dual/SOURCE.json index 80c0f29dc4..a119bae377 100644 --- a/research/joint-dual/SOURCE.json +++ b/research/joint-dual/SOURCE.json @@ -3,9 +3,9 @@ "base_pr57_commit": "cd350f76c9bc01489ec83568bded532cb69be938", "base_pr58_commit": "bc2f7ed4c20dc18898305ab17165c0c995cbb804", "files": { - "Makefile": "97620e0205736d9c0fce736e8ac6ab67f8ed0e490c381f6cac152cc6a003dca7", - "NOTICE": "1c53970fb4face631a1b331ec66d33111eccd280a129f9b64c2da6df96861c3f", - "README.md": "fd92de31aece76b1f5ff897e6e0dbc38dd3bf67c140579bbcb03a1a11a792668", + "Makefile": "0bd8071c6a4899b9e6975b53690069b4ffc70ac3514c019485b59f02ed994a6b", + "NOTICE": "46b84a2254d554c8adbe67ddaf33640e1b99e31168a1d90305d470e4fdab8e23", + "README.md": "083799d50375b5a16bd5af0eb1b0e4f630a6d05b414fe7010bc266206d9eda11", "certificates/joint-dual-compiler.json": "516c4d85158553dabd0a98216a064b2a7397957a9d5dd0df1d6e5aec53a4e805", "certificates/joint-dual-profiles-23.json": "159fa8fee175fc1d24f63e72d3c2f1dc9f4fcd78b938c5e7d2f735fd0fd37209", "certificates/joint-dual-profiles-25.json": "8d190ce42d097e828c5756918c52f2963df576cf4c6600b0fc7f2b7fdb6ad223", diff --git a/scripts/stopped_product/README.md b/scripts/stopped_product/README.md new file mode 100644 index 0000000000..6c18be051f --- /dev/null +++ b/scripts/stopped_product/README.md @@ -0,0 +1,36 @@ +# Selected rational-center producer + +Run from the repository root: + +```sh +python3 scripts/stopped_product_producer.py --output /tmp/stopped-product-producers.json +``` + +Only the new aligned complex producer at h=24 is rebuilt. It retains all +24 disjoint-point sums and decodes the total by exact division by21. The +pair-star input order is aligned with global pairs. Its generator adapts +`structured_bulk.complex`, preserving exact support, output orthogonality, +binary frame nesting and nondegeneracy checks. Rational decoder and scatter +coefficients are checked with `Fraction`; their only odd denominator is21. +The unchanged deterministic matcher compares every count and histogram +entry against `stopped-product-complex-input.json`. + +The h23 bit record is compared with the preceding validated copied-center +input. No old bit DAG, matching, or corner is regenerated. Both copied-center +histogram transformations reuse the established exact rank-mass checker. + +All DAGs, labels and the compiled matcher are temporary by default; +`--work-dir` retains them. Python assertions must be enabled. Standard-library +Python and a C++17 compiler suffice. No binary archive is an input. + +The odd-grid extension is a written recursive invariant, not a claim proved +by the finite scalar tests. With dyadic root inputs, K=G(D+1) supplies enough +odd-divisor reserve along the active chain. A completed child preserves its +incoming odd valuation; it does not generally make rational child inputs +dyadic. Only the completed outer dyadic operator restores the original +dyadic grid. No child return is rounded. + +Copyright 2026 icekylinx, Apache-2.0. New selected alignment, rational centers +and integration were prepared with OpenAI GPT-6 Astra/Codex assistance. +Underlying paired producers and deterministic carrier matching retain the +previous contributors' attribution in `NOTICE` and `SOURCES.json`. diff --git a/scripts/stopped_product/__init__.py b/scripts/stopped_product/__init__.py new file mode 100644 index 0000000000..f7a6e90661 --- /dev/null +++ b/scripts/stopped_product/__init__.py @@ -0,0 +1 @@ +"""Selected stopped-product inputs and rational producer; icekylinx, 2026.""" diff --git a/scripts/stopped_product/complex.py b/scripts/stopped_product/complex.py new file mode 100644 index 0000000000..ef1af25507 --- /dev/null +++ b/scripts/stopped_product/complex.py @@ -0,0 +1,228 @@ +"""Selected aligned rational-center producer, h=24 with all centers disjoint. + +Copyright 2026 icekylinx, Apache-2.0. AI-assisted adaptation of the research +round-five handoff, using the credited retained PairedTriple circuit; see NOTICE. +Adapted from structured_bulk.complex: align pair-star inputs and permit the +fixed rational divisor21; retain all exact support/frame/scalar checks. + +Builds a concrete scalar addition DAG, its nondegenerate binary frames, and +the unmixed carrier histogram. No historical audit suite is invoked. +""" +import json, struct, array +from itertools import combinations +from pathlib import Path +from partial_swap.binary import write_array +from paired_triple_circuit import PairedTriple + +def build(h, prefix, central_disjoint, base=2): + assert (h, central_disjoint, base) == (24,24,2) + d=central_disjoint + assert 0