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"receivers": 100, + "saved_additions": 3288 + } + ] + }, + "selected_targets": [ + 121, + 122, + 123, + 124, + 125, + 126, + 127, + 128, + 129, + 130, + 131, + 135, + 136, + 138, + 139, + 140, + 141, + 142, + 143, + 144, + 146, + 147, + 148, + 149, + 150, + 151, + 152, + 155, + 158, + 159, + 160, + 161, + 162, + 163, + 164, + 165, + 166, + 167, + 168, + 169, + 170, + 171, + 173, + 174, + 175, + 176, + 177, + 178, + 180, + 181, + 184, + 186, + 187, + 189, + 190, + 191, + 192, + 193, + 194, + 195, + 197, + 198, + 199, + 200, + 201, + 202, + 203, + 205, + 206, + 207, + 208, + 209, + 210, + 211, + 212, + 214, + 215, + 216, + 217, + 218, + 219, + 221, + 222, + 223, + 224, + 225, + 226, + 227, + 228, + 229, + 230, + 231, + 232, + 233, + 234, + 235, + 236, + 237, + 238, + 239 + ], + "source_manifest_sha256": "f0546e2e974eec5c0e94544038b2d625b002121e913c734c70a75078826e6bcc", + "status": "PASS_R420_TARGET_STAR", + "symbolic_columns": 660 +} diff --git a/research/r420-target-star/CLAIM.json b/research/r420-target-star/CLAIM.json new file mode 100644 index 0000000000..a9f58a38ee --- /dev/null +++ b/research/r420-target-star/CLAIM.json @@ -0,0 +1,36 @@ +{ + "track": "bit supplier", + "assignment_seed": 0, + "randomness": "Python secrets.randbelow(100), OS entropy, drawn once before task selection", + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "claimed_at_utc": "2026-10-13T04:32:22.523809+00:00", + "expected_finish_utc": "2026-10-13T05:07:56Z", + "coordination": "No pinned issues returned by GitHub pinnedIssues; local claim as instructed. No separate reservation issue opened.", + "object": "PR543 R420 frame-zero D compensation, target 0 (register 120) as one fixed donor", + "method": "A single involutory target-star basis: pre-add donor to each chosen target, replace receiver helper rows by symmetric differences, post-add donor. Enumerate all 119 receiver choices independently; include each strictly positive net saving after both restoration XORs. Seed 0 selects donor target 0.", + "expected_deliverable": "Exact finite circuit with arbitrary dirty-target restoration, source pins, complete native cost/frame/prefix replay, scoped proof and rejection controls; no new kappa.", + "candidates_considered": [ + "Phase-B 12-register block resynthesis: overlaps #670/#674/#688.", + "Phase-A decoder-total joint synthesis: would need a broader changed retained-total interface.", + "Target-star D compensation: selected; changes target rows, while #686/#694 factor helper columns." + ], + "prior_work": [ + "#476/#478 already use reversible target-interval factoring on older R715 B words; the elementary identity is credited, not claimed new.", + "#661 closes fixed-order R420 phase-B frame changes, not D circuit changes.", + "#686/#694 change D by restoring a helper basis; no code or recipe imported." + ], + "initial_overlap_max_pr": 704, + "result": { + "status": "completed finite bit-circuit contribution; no new kappa", + "updated_at_utc": "2026-10-13T05:02:13.305041+00:00", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/742", + "code_commit": "40f0d419a9012c0243e87a686ea22327619c766c", + "evidence_driven_extension": "After #713/#716 arrived with stronger disjoint target pairs, the one bounded extension permitted shared donors while retaining disjoint donor/receiver sets. Limit 16 donors fixed before running the extension; no other pivot.", + "completed_domain": "All 14,280 oriented pair costs and 1,680 candidate donor sets in 15 greedy additions, starting with seed-selected donor target 0; stopped at 16 donors. Best assignment for fixed donors is exact; donor-set optimality is not claimed.", + "result": "16 donors, 100 receivers, 3288 ADDs saved including all preparation/restoration. D 19922->16634; complete native word 26916->23628. Rank mass 5112 and complete frame/copy paths unchanged. Native payload 102 bits under 104-bit cap.", + "verification": "Nine construction controls, all 660 native columns and both directional exports; Python and unchanged C++ 5/9/11-stage replay on both words; actual-stream bridge omissions, native controls, isolated optimized/minimal-checkout reproduction, source/certificate corruption controls and selected-record check passed.", + "time_allocation": "Initial orientation/selection ended at local claim before 04:33 UTC (< first 20% of 40-minute budget). Final circuit fixed by 04:55 UTC; remainder reserved for verification, overlap checks and handoff.", + "concurrent_credit": "#476/#478 identity; #686/#694 helper basis; #713/#716 target pairs. #731 baseline rank audit and #733 stronger two-sided helper/target composition were inspected at final submission; no imported code or recipe, no overall record claim.", + "remaining": "Review/integrate semantic D interface; hosted-parent/whole-owner and global prefix/invoice replays; changed-word assembly. All inherited all-size/physical/hosting/precision/analytic assumptions remain." + } +} diff --git a/research/r420-target-star/NATIVE.json b/research/r420-target-star/NATIVE.json new file mode 100644 index 0000000000..637265674b --- /dev/null +++ b/research/r420-target-star/NATIVE.json @@ -0,0 +1,1152 @@ +{ + "environment": { + "boost_version_header_sha256": "063ed28eceb611d52f58e57aca61edb1e086ed902fbded81ac61936009c52cf0", + "compiler": "Apple clang version 21.0.0 (clang-2100.3.34.2)\nTarget: arm64-apple-darwin27.0.0\nThread model: posix\nInstalledDir: /Library/Developer/CommandLineTools/usr/bin", + "platform": "macOS-27.0.1-arm64-arm-64bit", + "python": "3.9.6 (default, Aug 25 2026, 21:26:21) \n[Clang 21.0.0 (clang-2100.3.34.2)]" + }, + "receipts": { + "baseline": { + "columns": [ + { + "bridge_additions": 720, + "copied_center_original_source_immutable": true, + "five_stage_additions": 134580, + "formal_columns_checked": 900, + "fresh_center_copies": 45, + "global_live_registers": 900, + "independent_dirty_registers": 420, + "local_odd_scalar_additions": 26916, + "local_raw_H": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "local_registers": 660, + "local_scalar_additions": 26916, + "negative_controls": [ + { + "omit_bridge": 0, + "rejected": true + }, + { + "omit_bridge": 1, + "rejected": true + }, + { + "omit_bridge": 2, + "rejected": true + }, + { + "omit_bridge": 3, + "rejected": true + }, + { + "omit_bridge": 4, + "rejected": true + }, + { + "omit_bridge": 5, + "rejected": true + } + ], + "new_Q_categories": [ + 28, + 29 + ], + "payload_prefix_bits": 100, + "payload_prefix_upper": "998206739997057013039187410944", + "reverse_fresh_center_copies": 18, + "scope": "All independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check.", + "signed_lift_prefix": [ + { + "bits": 18, + "cancellation_free_signed_row_l1_upper": "144651", + "reverse": false + }, + { + "bits": 22, + "cancellation_free_signed_row_l1_upper": "2270064", + "reverse": true + } + ], + "signed_reverse_semantics": "Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction.", + "stages": [ + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 0 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 1 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 2 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 3 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 4 + } + ], + "status": "PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL" + }, + { + "bridge_additions": 2160, + "copied_center_original_source_immutable": true, + "formal_columns_checked": 1380, + "fresh_center_copies": 81, + "global_live_registers": 1380, + "independent_dirty_registers": 420, + "local_odd_scalar_additions": 26916, + "local_raw_H": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "local_registers": 660, + "local_scalar_additions": 26916, + "negative_controls": [ + { + "omit_bridge": 0, + "rejected": true + }, + { + "omit_bridge": 1, + "rejected": true + }, + { + "omit_bridge": 2, + "rejected": true + }, + { + "omit_bridge": 3, + "rejected": true + }, + { + "omit_bridge": 4, + "rejected": true + }, + { + "omit_bridge": 5, + "rejected": true + }, + { + "omit_bridge": 6, + "rejected": true + }, + { + "omit_bridge": 7, + "rejected": true + }, + { + "omit_bridge": 8, + "rejected": true + }, + { + "omit_bridge": 9, + "rejected": true + }, + { + "omit_bridge": 10, + "rejected": true + }, + { + "omit_bridge": 11, + "rejected": true + }, + { + "omit_bridge": 12, + "rejected": true + }, + { + "omit_bridge": 13, + "rejected": true + }, + { + "omit_bridge": 14, + "rejected": true + }, + { + "omit_bridge": 15, + "rejected": true + }, + { + "omit_bridge": 16, + "rejected": true + }, + { + "omit_bridge": 17, + "rejected": true + } + ], + "new_Q_categories": [ + 28, + 29 + ], + "payload_prefix_bits": 100, + "payload_prefix_upper": "998206739997057013039187410944", + "reverse_fresh_center_copies": 36, + "scope": "All independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. 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New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check.", + "signed_lift_prefix": [ + { + "bits": 18, + "cancellation_free_signed_row_l1_upper": "144651", + "reverse": false + }, + { + "bits": 22, + "cancellation_free_signed_row_l1_upper": "2270064", + "reverse": true + } + ], + "signed_reverse_semantics": "Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction.", + "stage_additions": 296076, + "stages": [ + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 0 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 1 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 2 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 3 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 4 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 5 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 6 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 7 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 8 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": true, + "stage": 9 + }, + { + "fresh_copies": 9, + "scalar_additions": 26916, + "signed_inverse": false, + "stage": 10 + } + ], + "status": "PASS_NEW_COHORT249_ALL_BRIDGED_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL" + } + ], + "legality": { + "all_final_frames_pass": true, + "common_frame_ADDs": 26916, + "containment_pairs_checked": 2460, + "copies": 9, + "donor_intersections": 0, + "erasures": 9, + "max_inherited_integer_abs": 2, + "nested_MOVEs": 2940, + "new_frame_ids_collision": false, + "nondegeneracy_checked_by_separate_exact_bank_audit": true, + "old_max_frame_id": 671, + "paid_histogram": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "rank_mass": 5112, + "records": 29874, + "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.", + "selected_helpers": 0, + "selected_pairs": 0, + "source_owner_intersections": 0, + "status": "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE" + } + }, + "candidate": { + "columns": [ + { + "bridge_additions": 720, + "copied_center_original_source_immutable": true, + "five_stage_additions": 118140, + "formal_columns_checked": 900, + "fresh_center_copies": 45, + "global_live_registers": 900, + "independent_dirty_registers": 420, + "local_odd_scalar_additions": 23628, + "local_raw_H": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "local_registers": 660, + "local_scalar_additions": 23628, + "negative_controls": [ + { + "omit_bridge": 0, + "rejected": true + }, + { + "omit_bridge": 1, + "rejected": true + }, + { + "omit_bridge": 2, + "rejected": true + }, + { + "omit_bridge": 3, + "rejected": true + }, + { + "omit_bridge": 4, + "rejected": true + }, + { + "omit_bridge": 5, + "rejected": true + } + ], + "new_Q_categories": [ + 28, + 29 + ], + "payload_prefix_bits": 102, + "payload_prefix_upper": "2795129547373030713462210657024", + "reverse_fresh_center_copies": 18, + "scope": "All independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check.", + "signed_lift_prefix": [ + { + "bits": 18, + "cancellation_free_signed_row_l1_upper": "144651", + "reverse": false + }, + { + "bits": 22, + "cancellation_free_signed_row_l1_upper": "3798646", + "reverse": true + } + ], + "signed_reverse_semantics": "Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction.", + "stages": [ + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 0 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 1 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 2 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 3 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 4 + } + ], + "status": "PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL" + }, + { + "bridge_additions": 2160, + "copied_center_original_source_immutable": true, + "formal_columns_checked": 1380, + "fresh_center_copies": 81, + "global_live_registers": 1380, + "independent_dirty_registers": 420, + "local_odd_scalar_additions": 23628, + "local_raw_H": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "local_registers": 660, + "local_scalar_additions": 23628, + "negative_controls": [ + { + "omit_bridge": 0, + "rejected": true + }, + { + "omit_bridge": 1, + "rejected": true + }, + { + "omit_bridge": 2, + "rejected": true + }, + { + "omit_bridge": 3, + "rejected": true + }, + { + "omit_bridge": 4, + "rejected": true + }, + { + "omit_bridge": 5, + "rejected": true + }, + { + "omit_bridge": 6, + "rejected": true + }, + { + "omit_bridge": 7, + "rejected": true + }, + { + "omit_bridge": 8, + "rejected": true + }, + { + "omit_bridge": 9, + "rejected": true + }, + { + "omit_bridge": 10, + "rejected": true + }, + { + "omit_bridge": 11, + "rejected": true + }, + { + "omit_bridge": 12, + "rejected": true + }, + { + "omit_bridge": 13, + "rejected": true + }, + { + "omit_bridge": 14, + "rejected": true + }, + { + "omit_bridge": 15, + "rejected": true + }, + { + "omit_bridge": 16, + "rejected": true + }, + { + "omit_bridge": 17, + "rejected": true + } + ], + "new_Q_categories": [ + 28, + 29 + ], + "payload_prefix_bits": 102, + "payload_prefix_upper": "2795129547373030713462210657024", + "reverse_fresh_center_copies": 36, + "scope": "All independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check.", + "signed_lift_prefix": [ + { + "bits": 18, + "cancellation_free_signed_row_l1_upper": "144651", + "reverse": false + }, + { + "bits": 22, + "cancellation_free_signed_row_l1_upper": "3798646", + "reverse": true + } + ], + "signed_reverse_semantics": "Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction.", + "stage_additions": 212652, + "stages": [ + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 0 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 1 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 2 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 3 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 4 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 5 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 6 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 7 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 8 + } + ], + "status": "PASS_NEW_COHORT249_ALL_BRIDGED_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL" + }, + { + "bridge_additions": 2880, + "copied_center_original_source_immutable": true, + "formal_columns_checked": 1620, + "fresh_center_copies": 99, + "global_live_registers": 1620, + "independent_dirty_registers": 420, + "local_odd_scalar_additions": 23628, + "local_raw_H": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "local_registers": 660, + "local_scalar_additions": 23628, + "negative_controls": [ + { + "omit_bridge": 0, + "rejected": true + }, + { + "omit_bridge": 1, + "rejected": true + }, + { + "omit_bridge": 2, + "rejected": true + }, + { + "omit_bridge": 3, + "rejected": true + }, + { + "omit_bridge": 4, + "rejected": true + }, + { + "omit_bridge": 5, + "rejected": true + }, + { + "omit_bridge": 6, + "rejected": true + }, + { + "omit_bridge": 7, + "rejected": true + }, + { + "omit_bridge": 8, + "rejected": true + }, + { + "omit_bridge": 9, + "rejected": true + }, + { + "omit_bridge": 10, + "rejected": true + }, + { + "omit_bridge": 11, + "rejected": true + }, + { + "omit_bridge": 12, + "rejected": true + }, + { + "omit_bridge": 13, + "rejected": true + }, + { + "omit_bridge": 14, + "rejected": true + }, + { + "omit_bridge": 15, + "rejected": true + }, + { + "omit_bridge": 16, + "rejected": true + }, + { + "omit_bridge": 17, + "rejected": true + }, + { + "omit_bridge": 18, + "rejected": true + }, + { + "omit_bridge": 19, + "rejected": true + }, + { + "omit_bridge": 20, + "rejected": true + }, + { + "omit_bridge": 21, + "rejected": true + }, + { + "omit_bridge": 22, + "rejected": true + }, + { + "omit_bridge": 23, + "rejected": true + } + ], + "new_Q_categories": [ + 28, + 29 + ], + "payload_prefix_bits": 102, + "payload_prefix_upper": "2795129547373030713462210657024", + "reverse_fresh_center_copies": 45, + "scope": "All independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check.", + "signed_lift_prefix": [ + { + "bits": 18, + "cancellation_free_signed_row_l1_upper": "144651", + "reverse": false + }, + { + "bits": 22, + "cancellation_free_signed_row_l1_upper": "3798646", + "reverse": true + } + ], + "signed_reverse_semantics": "Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction.", + "stage_additions": 259908, + "stages": [ + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 0 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 1 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 2 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 3 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 4 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 5 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 6 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 7 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 8 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": true, + "stage": 9 + }, + { + "fresh_copies": 9, + "scalar_additions": 23628, + "signed_inverse": false, + "stage": 10 + } + ], + "status": "PASS_NEW_COHORT249_ALL_BRIDGED_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL" + } + ], + "legality": { + "all_final_frames_pass": true, + "common_frame_ADDs": 23628, + "containment_pairs_checked": 2460, + "copies": 9, + "donor_intersections": 0, + "erasures": 9, + "max_inherited_integer_abs": 2, + "nested_MOVEs": 2940, + "new_frame_ids_collision": false, + "nondegeneracy_checked_by_separate_exact_bank_audit": true, + "old_max_frame_id": 671, + "paid_histogram": [ + [ + 1, + 1320 + ], + [ + 2, + 1440 + ], + [ + 4, + 60 + ], + [ + 5, + 120 + ], + [ + 8, + 9 + ] + ], + "rank_mass": 5112, + "records": 26586, + "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.", + "selected_helpers": 0, + "selected_pairs": 0, + "source_owner_intersections": 0, + "status": "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE" + }, + "missing_preparation_rejected_at_stages": [ + 5, + 9, + 11 + ] + } + }, + "status": "PASS_R420_TARGET_STAR_NATIVE" +} diff --git a/research/r420-target-star/NOTICE.md b/research/r420-target-star/NOTICE.md new file mode 100644 index 0000000000..e65469b662 --- /dev/null +++ b/research/r420-target-star/NOTICE.md @@ -0,0 +1,49 @@ +# Attribution and license + +New files: @ellipsi2, with substantial OpenAI Codex assistance. Apache-2.0, +under the repository root LICENSE. No human-only authorship or independent human +review is claimed. + +Direct predecessor construction and reused files: + +- eumemic, #543 (`2065fe4f72a914d907f1046603f5a36f17018535`): the R420 word, + exact E8/frame/interleaved scalar checker and construction argument, prepared + with substantial Anthropic Claude assistance. Used from main unchanged. +- eumemic, #493: mutable-source D4 carrier skeleton and the imported exporter + tree. Its original notice is pinned, not replaced. +- Dylan Crow / utcorvusvolat-dotcom, #370: bitE8 format, record exporter, copied + totals and finite-checker lineage, with Anthropic Claude assistance. The + exporter is invoked unchanged. +- DaysSky, #381: five/nine/eleven-stage B_K bridge schedule, with Claude + assistance. The new standard-library bridge interpreter follows this + schedule and the prefix formula recorded in the pinned `columns_k.cpp`. +- Zhihao Chen / jacklightChen, #425/#386: mutable-basis scalar-interface and + nine-stage realization lineage, with OpenAI Codex assistance. +- DreamingOfClouds, #503/#510: dead-register retained totals and + nine-stage pricing; #315 supplies the moment-engine lineage. +- Dugongue, #476/#478: predecessor reversible target-interval factoring on + R715 phase-B words. The identity is credited; no code is copied here. + +Mikhail R. Gadelha's concurrent #686 and Greer Guthrie's #694 are credited for R420 D helper-basis +factoring. This construction uses a target basis while keeping helpers unchanged +throughout D. No priority over those contributions or composition with their +results is claimed; their code is not imported. + +The unchanged broader supplier and realization lineage includes Jacob Sussman's +E8 unit, Chafik Boukhalfa's physical/compiler checks (#443/#445/#472), DaysSky's +whole-residual hosting (#442), DreamingOfClouds' circuits and moment engines, +icekylinx's stopped-product and source-carryover work, Rohan Arun's accounting +work, and the cumulative contributors named in the original source notices. +The selected #626 context additionally credits Chafik Boukhalfa, Jeremy Kothe, +Jeremy Diviney and the #622/#623/#617 predecessors, rather than attributing the +selected construction to this experiment. + +The repository's original Apache-2.0 license, NOTICE, source-specific notices, +and all files under `upstream/` remain unchanged. + +Concurrent target-row constructions #713 (Scott Woolsey Biggart / swbiggart, +head 1a19af5c5ddb6de9797a6d085e5df0b90ed6d58b) and #716 (Sagar Thakrar / +thakrarsagar, head c804e7d79ac524723aa8c2d0d6a59d5e662763b3) are explicitly +credited. They use disjoint target pairs. Their arrival prompted the one bounded +extension here to shared-donor stars with disjoint donor/receiver sets. No code +or recipe was imported and no priority for target-basis compensation is claimed. diff --git a/research/r420-target-star/OVERLAP.json b/research/r420-target-star/OVERLAP.json new file mode 100644 index 0000000000..5663040c2f --- /dev/null +++ b/research/r420-target-star/OVERLAP.json @@ -0,0 +1,199 @@ +{ + "checked_at_utc": "2026-10-13T04:32:22.523809+00:00", + "open_pr_count": 524, + "max_pr": 704, + "pinned_issue_count": 0, + "related_prs": [ + { + "number": 694, + "title": "Research: save 6,934 R420 XORs with a restored helper basis", + "headRefOid": "9732ac127dd4bef98a846aaa904c20b5a84e72c1", + "updatedAt": "2026-10-13T04:25:50Z" + }, + { + "number": 691, + "title": "Research: shorten R420 phase-A quad 13 from 19 to 12 XORs (no new kappa)", + "headRefOid": "ee6b9175fe006c11871802866c487b5ecc1a93a4", + "updatedAt": "2026-10-13T04:16:35Z" + }, + { + "number": 688, + "title": "Research: compose R420 circuits with 16,704 fewer hosted instructions (no new kappa)", + "headRefOid": "bb05c40c3e6319aa8c131b06a105e3648ac6c95b", + "updatedAt": "2026-10-13T04:08:46Z" + }, + { + "number": 686, + "title": "Research: save 108 R420 XORs with restored frame-zero sharing (no new kappa)", + "headRefOid": "23dcb610c2b156b76b9d599ea296c3cbde224b2d", + "updatedAt": "2026-10-13T04:06:36Z" + }, + { + "number": 678, + "title": "Independent verification of the #543 bit moment using binomial enclosures", + "headRefOid": "bdc9317efd6d928a0f050159670d1316ba5f4c5b", + "updatedAt": "2026-10-13T03:47:52Z" + }, + { + "number": 674, + "title": "Research: reduce R420 block 5 from 46 to 34 XOR gates (no new kappa)", + "headRefOid": "1b01fd8b135fb2c458554fbbbab4338336bf366d", + "updatedAt": "2026-10-13T03:41:09Z" + }, + { + "number": 670, + "title": "Research: simplify one R420 block from 50 to 33 XOR gates (no new kappa)", + "headRefOid": "2e31fcad7f9ecc8b97039ecb2333e581fd725fa1", + "updatedAt": "2026-10-13T03:30:19Z" + }, + { + "number": 661, + "title": "Scoped negative result: R420 phase-B frames are moment-optimal at fixed gate order", + "headRefOid": "9ca7aa3ab0a3260a2f36ac86b9911a31fd88bd89", + "updatedAt": "2026-10-13T03:07:36Z" + }, + { + "number": 620, + "title": "Research notes (no \u03ba claim): E8 decoder floors are tight; #615 levers exhausted; +1.1e-7 \u03ba owner-map headroom on #617", + "headRefOid": "e9cf03bbdf7094b5a83f6dbd1d74bfd77a05fb87", + "updatedAt": "2026-10-13T02:36:29Z" + }, + { + "number": 612, + "title": "[Lean] Verify current R420 boundaries and B-XOR interfaces", + "headRefOid": "ce37f3ce35ba8891771e01492b3a21978763bebb", + "updatedAt": "2026-10-12T18:31:54Z" + }, + { + "number": 478, + "title": "Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)", + "headRefOid": "bea1d52fd330c699903f81612ee58be81697d1eb", + "updatedAt": "2026-10-11T18:31:32Z" + }, + { + "number": 476, + "title": "Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)", + "headRefOid": "e850569c33ad1d5771e2f8b1c6dfe7a445396167", + "updatedAt": "2026-10-11T18:14:32Z" + } + ], + "pre_submission_refresh": { + "checked_at_utc": "2026-10-13T04:54:15.566409+00:00", + "max_pr": 720, + "open_pr_count": 539, + "pinned_issue_count": 0, + "related_prs": [ + { + "number": 718, + "title": "Scoped negative result: R420 split target reads cannot lower the paid moment", + "headRefOid": "688258f863410419d10e34b0b3014b91cdce632c", + "updatedAt": "2026-10-13T04:45:35Z" + }, + { + "number": 716, + "title": "Research: R420 target-pair compensation, concurrent reproduction of #713", + "headRefOid": "c804e7d79ac524723aa8c2d0d6a59d5e662763b3", + "updatedAt": "2026-10-13T04:42:59Z" + }, + { + "number": 713, + "title": "Research: save 3,150 R420 XORs with a restored target basis", + "headRefOid": "1a19af5c5ddb6de9797a6d085e5df0b90ed6d58b", + "updatedAt": "2026-10-13T04:42:18Z" + }, + { + "number": 711, + "title": "Scoped negative result: R420 adjacent A swaps force both frames", + "headRefOid": "ebd567a22d26fadc1c8292b5c57056fb52331266", + "updatedAt": "2026-10-13T04:39:17Z" + }, + { + "number": 710, + "title": "Research: shorten R420 cleanup by two XORs with certified conjugation (no new kappa)", + "headRefOid": "d97c8d20a8b885271a24c5a4e8446ac7f5697d5c", + "updatedAt": "2026-10-13T04:39:03Z" + }, + { + "number": 708, + "title": "Research: save 114 R420 XORs by sharing restored decoder operands (no new kappa)", + "headRefOid": "2ec522a466ec448f148d4355dc43b51c0ef1e0b5", + "updatedAt": "2026-10-13T04:35:11Z" + } + ], + "conclusion": "#713/#716 independently reached 3150 savings with disjoint pairs. One bounded extension to shared donors gives 3288 savings, with no imported code and no priority claim for target-basis compensation. #708/#710/#711/#718 concern other stages or constraints." + }, + "final_recent_arrivals": { + "checked_at_utc": "2026-10-13T04:58:01.569704+00:00", + "max_pr": 728, + "recent_prs_examined": 50, + "new_prs": [ + { + "number": 728, + "title": "Research construction: save 20 R439 mini-node XORs (no new kappa)", + "headRefOid": "d454ae19fdd474b4dfa7bd2c28bbe5b0996365fb", + "updatedAt": "2026-10-13T04:55:42Z" + }, + { + "number": 727, + "title": "Tooling: exact owner footprint masks reduce checker wall time by 13\u201319%", + "headRefOid": "71ba94c981477b3527ef21dd0f8140e795a7664d", + "updatedAt": "2026-10-13T04:55:01Z" + }, + { + "number": 726, + "title": "Exact E8 A2 Triple-Gather Census and Verification", + "headRefOid": "a3041f751114df12453afcb7ac7d0066973797fa", + "updatedAt": "2026-10-13T04:54:30Z" + }, + { + "number": 725, + "title": "Scoped negative result: sharp global-star punctures and 67 attaining patterns", + "headRefOid": "6eadc4eb4ebc355b13fa36a3138d97a583ea7f37", + "updatedAt": "2026-10-13T04:52:28Z" + }, + { + "number": 724, + "title": "Research audit: resolve R/R0 revert expectations with exact PR626 accounting", + "headRefOid": "624ccfe44b1c5816f0279481d91cca6a5a2290ab", + "updatedAt": "2026-10-13T04:51:19Z" + }, + { + "number": 723, + "title": "Research: save 3,276 JP8 scalar primitives per orientation with signed digits", + "headRefOid": "d3bc41b87fc7d23f50d064a0f06f1a89e3ab02a7", + "updatedAt": "2026-10-13T04:52:24Z" + }, + { + "number": 722, + "title": "Research: share JP8 cleanup coefficient work, saving 19,688 primitives (no new kappa)", + "headRefOid": "a0766ab0fab379e1997fadc3ca157578d57986c1", + "updatedAt": "2026-10-13T04:50:10Z" + }, + { + "number": 721, + "title": "Tooling: reduce reconciliation replay peak RSS by 56% with exact streaming", + "headRefOid": "0038fa9051bcbf52ccea8e29272840b13126e539", + "updatedAt": "2026-10-13T04:47:47Z" + } + ], + "base_still_current": true, + "same_scope_found": false + }, + "immediate_pre_submission_refresh": { + "checked_at_utc": "2026-10-13T05:02:13.305041+00:00", + "through_pr": 735, + "related_prs": [ + { + "number": 731, + "headRefOid": "cf5ff54a358b400a7e69abe941d1d0ad0944b25e", + "scope": "independent baseline rank/kernel audit; not imported" + }, + { + "number": 733, + "headRefOid": "dfe84e09298abc5c5e0074afda59a821e10abfb4", + "scope": "two-sided helper/target-basis composition reporting 8368 saving; changes helper values during D, unlike this immutable-helper target-star construction; not imported" + } + ], + "conclusion": "No competing shared-donor target-star circuit found. No overall saving record or priority claim." + } +} diff --git a/research/r420-target-star/PROOF.md b/research/r420-target-star/PROOF.md new file mode 100644 index 0000000000..1486600d13 --- /dev/null +++ b/research/r420-target-star/PROOF.md @@ -0,0 +1,120 @@ +# Exact target-star identity and paid scope + +All endpoint algebra is over F2. Fix the pinned R420 word, write `s` for its +420 arbitrary helper values and `y` for its 120 arbitrary target values. The +original D has one helper-only row `K_i` per target and implements +`y <- y + K s`. It never changes `s` or the 120 sources `x`. + +## Construction + +Choose disjoint donor and receiver target sets Q and S. For every receiver i, +choose one donor `d(i)` in Q; different receivers may share a donor. Let P have +one nonzero entry `P[i,d(i)]=1` for each receiver, and zero rows elsewhere. +Every donor row is zero and every nonzero column indexes a donor, so `P^2=0`. +Thus `T=I+P` satisfies `T^2=I`. + +Execute at frame zero, before A: + +1. For each receiver i, add its donor target into `y_i` (apply T). +2. For receivers, add `(K_i + K_d(i))s` into `y_i`. For every other target, + including all donors, add the original `K_i s`. This adds `T K s`. +3. Apply the literal reverse of step 1 (T again). + +The aggregate output is `T (T y + T K s) = y + K s` for every initial target +vector, not just clean targets. Helpers are only read; sources are untouched. +No receiver is a donor, even when a donor is reused. The preparation operations +commute. For one receiver and its donor d the cancellation is explicitly + +`(y_i + y_d) + (K_i + K_d)s + (y_d + K_d s) = y_i + K_i s`. + +The identity is predecessor target-interval factoring from #476/#478. +Concurrent #713/#716 apply disjoint target pairs to D. Here several receivers +may share a donor, retaining an immutable helper basis and a square-zero target +change of basis. No novelty of the elementary identity or priority for +frame-zero target-basis compensation is claimed. + +## Complete cost and bounded search + +For a row K let `|K|` count its nonzero helper coefficients. A receiver i using +donor d costs `|K_i xor K_d| + 2` additions, including preparation and +restoration. Its net saving is + +`g_i,d = |K_i| - |K_i xor K_d| - 2 = 2|K_i intersect K_d| - |K_d| - 2`. + +The verifier checks both formulas independently for all 14,280 oriented target +pairs. Every other D row has its old cost, so total savings are exactly +`sum(i in S) g_i,d(i)`. For fixed Q, each target outside Q independently chooses +the donor with maximal gain, or stays unchanged if that gain is nonpositive. +This maximizes savings over all receiver subsets and assignments for that Q. +Smaller donor IDs break ties. It does not optimize the choice of Q. + +The bounded nomination starts with Q={0} in target coordinates, adds the donor +giving the greatest strict increase in this complete objective, and stops at +16 donors or when no addition improves it. All 1,680 candidate donor sets in +15 addition steps were evaluated. It reached the prescribed 16-donor limit. +The certificate records every candidate score and selected set. No removal, +swap, layered basis or general XOR synthesis was searched; no global or +single-addition local optimum follows from hitting the limit. The initial +single-donor experiment remains the first trace entry: 892 additions saved. + +The final 16 nominated donors serve 100 receivers, with total gain 3,288. +The middle step costs 16,434 helper additions; preparation and restoration cost +100 each. D therefore costs 16,634 instead of 19,922. Every source-access term +is individually emitted; no multi-input XOR is priced as one addition. The +complete native word costs 23,628 instead of 26,916, including unchanged A, +B, C and scatter additions. This is 138 fewer additions than #713/#716's +reported 3,150-saving disjoint-pair construction, without importing, replaying +or composing it. + +There are no new registers, copied centers, helper preparations/restorations, +frames, frame changes or recursive children. All targets and helpers start at +frame zero. D finishes before A; the actual MOVE/COPY/ERASE sequence is identical. +The 2,940 MOVEs, nine COPYs, nine ERASEs, per-register ordered frame paths, +histogram `{1:1320,2:1440,4:60,5:120,8:9}` and rank mass 5,112 remain unchanged. +Both words are actually exported; their complete streams and ADD counts are +checked. No accounting equality is inferred only from syntactic gate counts. + +## Interface extension + +The pinned #543 lemma uses `z=(x,s)` and allows interleaved z-writes in B. Its +raw A/scatter/B map has the certified form + +`z' = U z, y' = y + x + K s`, + +and C is the literal inverse of the z-destination gates. H2 requires D to read +helpers only. A sufficient replacement is that all D gates act at frame zero +on target/helper registers and the aggregate D operator equals +`(x,s,y) -> (x,s,y+K s)`. + +The identity above proves this replacement, while keeping helpers unchanged +even between gates. Since A/scatter/B/C are unchanged, composition gives the +same restored native endpoint `y <- y+x`. All 660 independent input columns +include every source, initial target and dirty helper. + +The old H2 and literal `K_equals_D` extractor remain false on this syntax. +The verifier requires precisely these diagnostics to fail and all others to +pass. It compares complete D operators, independently replays the whole word +and the exported stream, and checks the replacement frame/operand condition. +Actual changed-word geometry is checked; no normalized helper-only substitute +is passed off as the candidate's native execution. + +## Integer lift and remaining obligations + +The two F2-equivalent recipes are not claimed to have the same unsigned integer +matrix. The cancellation-free forward row-sum bound stays 144,651. The inverse +bound rises from 2,270,064 to 3,798,646. The exact native formula gives + +`64 * forward^3 * inverse^2 = 2795129547373030713462210657024 < 2^104`. + +Its bit length is 102. Every actual exported ADD, COPY and ERASE is counted in +both directions, including intermediate target mixing. Fewer gates alone do +not imply a lower integer prefix bound. The unchanged C++ checkers independently +confirm both directional bounds, the invoice and 5/9/11-stage finite endpoints. + +The unchanged rank profile cannot improve the recursive moment by itself, and +the selected assembly is complex-limited. No new kappa is claimed. Acceptance +of the new D contract, hosted-parent/whole-owner reconstruction, global prefix +bounds, complete finite invoices and changed-word assembly remain separate work. +All-size/common-label/mutable-basis realization, pooled hosting, residual, +precision/tape/recovery and analytic assumptions are inherited. Finite replay +is not a formal proof of the complete integer-multiplication theorem. diff --git a/research/r420-target-star/README.md b/research/r420-target-star/README.md new file mode 100644 index 0000000000..7c60d85844 --- /dev/null +++ b/research/r420-target-star/README.md @@ -0,0 +1,177 @@ +# R420 compensation through restored target stars + +**Finite bit-circuit improvement; no new κ.** On eumemic's accepted #543 R420 +word, a forest of target stars shares 16 nominated donors among 100 receivers +during the frame-zero dirt-compensation stage D. This saves **3,288 binary XOR additions**, +including every preparation and restoration operation. Helpers remain unchanged +throughout D, including its intermediate states. + +| Quantity | Pinned #543 | This word | +|---|---:|---:| +| D binary additions | 19,922 | 16,634 | +| Complete native binary additions | 26,916 | 23,628 | +| Native records | 29,874 | 26,586 | +| Helpers / copied totals | 420 / 9 | 420 / 9 | +| Paid local rank mass | 5,112 | 5,112 | +| Forward positive-prefix bound | 144,651 | 144,651 | +| Inverse positive-prefix bound | 2,270,064 | 3,798,646 | +| Native payload bound, bits | 100 | 102 | + +The inverse prefix **increases**, despite the smaller instruction count. Both +words satisfy the inherited strict native bound `payload < 2^104`; no old prefix +receipt is reused. Every register's ordered frame path and the complete +MOVE/COPY/ERASE subsequence are identical. The profile remains +`{1:1320, 2:1440, 4:60, 5:120, 8:9}`. Only D changes. + +## Reproduce + +From the repository root, with Python 3.9 or newer and its standard library: + +```sh +python3 -B research/r420-target-star/verify.py +``` + +Expected final line: + +```text +PASS_R420_TARGET_STAR receivers=100 D=19922->16634 native_ADDs=26916->23628 saved=3288 columns=660 rank_mass=5112 +``` + +The same command works under `python3 -I -O -B`. To materialize the exact word, +add `--write-word /absolute/new/path.json.gz`; existing outputs are not overwritten. +Equality is checked on canonical decompressed JSON, not gzip container bytes. +`CERTIFICATE.json` includes the complete 1,680-candidate donor-set trace, final +receiver costs, the selected 100 target/donor pairs, +the canonical word hash, complete native invoices and exact prefix integers. +`--check PATH` allows an independently supplied certificate to be checked. + +An additional native replay uses the unchanged repository C++17 checkers and +requires Boost headers (tested with 1.85.0): + +```sh +python3 -B research/r420-target-star/native_verify.py \ + --boost-include /path/to/boost_1_85_0 \ + --output /absolute/new/replay-directory \ + --check research/r420-target-star/NATIVE.json +``` + +Expected: `PASS_R420_TARGET_STAR_NATIVE both_words=5/9/11 columns=900/1380/1620 missing_preparation=rejected`. +It compiles fresh binaries, checks both words, compares every native invoice and +directional prefix with the Python certificate, and rejects the actual missing +preparation instruction at all three stage counts. `NATIVE.json` records the +normalized mathematical receipts separately from compiler/platform metadata. + +The checker reuses **unchanged, pinned** #543 `xcheck.py` for the E8 lattice, +all 672 closed frames, legal native paths, arbitrary-dirty 660-column replay and +interface diagnostics. It reuses Dylan Crow's record exporter, then executes +those actual records using a separately written set-valued interpreter, checks +the forward and inverse maps and COPY lifecycle, and counts all instructions. +This reuse is not called a wholly independent reimplementation of the E8 audit. + +A Python implementation of DaysSky's #381 bridged schedule replays both actual +words at 5/9/11 stages on 900/1,380/1,620 independent physical columns. Each of +the 6/18/24 omitted-bridge controls replays the full changed record stream. +Nine additional controls cover missing preparation, restoration, donor +compensation, a receiver correction, a helper read, a previously modified receiver used as donor, an illegal frame, an +F2-neutral but paid pair and an omitted exported instruction. In particular, +omitting one preparation passes on **zero-initialized targets** and fails on +arbitrary targets. Zero-target tests alone would miss this error. + +## Interface and scope + +See [PROOF.md](PROOF.md) for the exact identity and complete cost. The inherited +syntactic H2 rule requires D to read helpers only and therefore **rejects** this +word. The inherited literal `K_equals_D` extractor also returns false: it does +not follow target values through D. These failures are expected and explicitly +required by the new verifier; the old checker is not patched or bypassed. +The replacement condition proves and checks that D still implements exactly +`(x,s,y) -> (x,s,y+K*s)` and keeps every operation at frame zero. All other +inherited hypotheses and conclusions pass on the actual changed word. + +This is a complete finite native circuit, with a scoped interface extension. +It is not a new accepted supplier or a multiplication theorem. Hosted-parent +reconstruction, literal whole-owner emission, finite global invoices, global +prefix bounds and a changed-word outer assembly remain integration obligations. +The standard-library command does not invoke the C++ binaries. The optional +native command above is a separate replay. Full repository `make verify`, +remote CI and Lean are not claimed by either command. + +The original all-size compiler, common-label/mutable-basis realization, pooled +hosting, normalized residual, precision/tape/exact recovery and analytic +assumptions remain. Local F2 equality is not equality of the two unsigned +integer transfer matrices. The positive bounds account for the actual integer +lift, but do not establish the full precision theorem. There is no measured +runtime claim or global circuit optimum. + +## Assignment, current state and overlap + +Base commit: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. +Reviewed bit source #543: `2065fe4f72a914d907f1046603f5a36f17018535`. +Selected complex source #626: `660de893d27bb7abd1d5b01b1640207528a5c851`. +`SOURCES.json` binds every consumed source and the selected review/assembly by +SHA-256 and Git blob. The accepted baseline is +`κ = 51110230636731/31250000000000000 = 0.001635527380375392`, with +bit `c = 0.001653826988146798944268` and complex +`b = 0.001638206712308086862575`; the selected assembly is complex-limited. +These values identify the baseline, not a changed-word certification. + +The assignment seed was **0**, drawn once with OS randomness through +`secrets.randbelow(100)`. It selects the bit track and fixes the first donor to +target 0 (register 120). After the initial single-star experiment, an overlap +refresh found #713/#716's stronger disjoint-pair constructions. The one bounded +extension permits **shared donors** while retaining disjoint donor/receiver sets. +It scores all 14,280 ordered target pairs, then greedily adds the donor producing +the best complete saving, recomputing each receiver's best donor. Smaller register +IDs break ties. The limit of **16 donors** was fixed before the extension ran. +All **1,680** candidate donor sets in the 15 addition steps were evaluated; the +run stopped at the limit, not at an asserted optimum. The first trace entry +preserves the original target-0 result (892 additions saved). + +For any fixed donor set the best receiver assignment is proved by independent +per-row maximization. The greedy choice of the donor set has **no optimality +claim**. No alternative initial donor, removal/swap, layered target basis, helper +basis or composition with pending circuits was searched. This extends the +**disjoint-pair** class to a star forest, rather than repeating a matching with +a different seed. + +`CLAIM.json` records the three candidates and the local claim. GitHub returned +no pinned coordination issue, so no reservation issue was opened. `OVERLAP.json` +records the checked related PR heads and later refresh. + +- **#476/#478 (Dugongue)** already use reversible target-interval factoring on + historical R715 phase-B words. The elementary identity is predecessor work; + this contribution instantiates a target-only star in the accepted R420 D + stage and checks the arbitrary-target interface and full native cost. +- **#686 / #694** factor the R420 D matrix using a temporarily changed helper + basis; #694 saves more native additions. Here no helper is ever written in D. + This is distinct evidence for a different restriction, not a stronger record + or a claim of priority for reversible factoring. No concurrent code is imported + and no combined gain is claimed. +- **#713 (Scott Woolsey Biggart) / #716 (Sagar Thakrar)** independently construct + 57 disjoint target pairs and report saving 3,150 additions. This star forest permits + donor reuse, saves **138 more additions** than their reported count on the same + baseline, and checks the + entire 48 omitted-bridge family against the actual changed record stream in + Python in addition to the unchanged native checkers. Their target-basis result + is credited and has not been independently replayed here; no code or recipe is imported, and no priority for that mechanism + is claimed. The stronger helper-basis #694 remains distinct and is not beaten. +- **#731 (Joshua Snider)** independently audits baseline compensation rank and + kernel structure. **#733 (Scott Woolsey Biggart)** reports a larger 8,368 saving + by combining helper and target bases. It changes helper values during D; this + construction retains immutable helpers and shares target donors. Neither is + imported or independently replayed here; no overall saving record is claimed. +- **#708** shares full-frame decoder operands; **#710** changes cleanup; + **#711/#718** give scoped frame obstructions. None changes this D star-forest + construction or is composed here. +- **#670/#674/#688/#691** shorten or compose phase-A/B circuits. **#661** bounds + fixed-order phase-B frame changes and explicitly excludes changes of circuit + or D. **#612** concerns a formalization of the prior scalar interface. + +## Attribution and license + +Prepared for **@ellipsi2 with substantial OpenAI Codex assistance** in the +construction, mathematical argument, implementation, checks and packaging. +No independent human review is claimed. New work is Apache-2.0 under the root +license. [NOTICE.md](NOTICE.md) retains the direct and cumulative predecessors; +their original notices and files remain unchanged. Neither `upstream/` nor the +selected-frontier pointer is modified. diff --git a/research/r420-target-star/SOURCES.json b/research/r420-target-star/SOURCES.json new file mode 100644 index 0000000000..713dc67b42 --- /dev/null +++ b/research/r420-target-star/SOURCES.json @@ -0,0 +1,67 @@ +{ + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "files": { + "certificates/selected-result.json": { + "git_blob": "92a10096dee76479af88a897714b3818d8263141", + "sha256": "b3bf402f31a69bde0629936a9b569bed48281568d7b16d5fba120b5311ea1f53" + }, + "docs/research/community-k492-review.md": { + "git_blob": "11efcd07ae2b9d93d355c6adaf773dca70dbce91", + "sha256": "3b731d30e80010b15408a289b0b32192700885474c8b36d48ee3320a7a8c5c47" + }, + "research/community-k492-audit/pr626/replay/ASSEMBLY.json": { + "git_blob": "2e97b75bd8e74e8aa1b5fb83adcdc461aa07c398", + "sha256": "6127732e2fcdd470dab349c1c51d03cd9f0787ad0309b1b4a7c811a908028f4e" + }, + "research/e8-bit-carrier-skeleton/NOTICE.md": { + "git_blob": "5a0ecdcd2c7fad0488740a1da0f633b73b56a809", + "sha256": "5f4b7fcbf99f572be28b6da612ce775363908cdfc7810f7aca167be01c86e49a" + }, + "research/e8-bit-carrier-skeleton/code/bit/checkers/columns_k.cpp": { + "git_blob": "42bb232fbec4de703e70cc13dc2f39a3b43a3a01", + "sha256": "1c344d18fcd494eeca93e259f10cafae7705780e6592f6dcb35b34752dab9bc2" + }, + "research/e8-bit-carrier-skeleton/code/bit/checkers/json.hpp": { + "git_blob": "82d69f7c5d044c9887c96b90c97f5639083ecd14", + "sha256": "aaf127c04cb31c406e5b04a63f1ae89369fccde6d8fa7cdda1ed4f32dfc5de63" + }, + "research/e8-bit-carrier-skeleton/code/bit/checkers/legality_h.cpp": { + "git_blob": "cb1233c7e96b1aa8bbf4d2e4165d75ab0dca64b9", + "sha256": "6c1ef2b24e57781d6951c172a1024fc4300e6fd392c9d6672079a7806ab663b3" + }, + "research/e8-bit-carrier-skeleton/code/bit/export_records.py": { + "git_blob": "3632d370486a02f5456f7643ced03f8c925b2350", + "sha256": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3" + }, + "research/e8-bit-carrier-skeleton/code/bit/regression/stage_cohort.py": { + "git_blob": "f6d7afe3e623208c4207b6a683a1e3e49249e31c", + "sha256": "6c288f6f234b528c1a7c0a4adfb724e91e0fe6b18c8dffad96af3f973de1829a" + }, + "research/e8-bit-carrier-skeleton/portable-include/bits/stdc++.h": { + "git_blob": "fc5664e929d9a81d9b4926bee049a93330be86ec", + "sha256": "420094be2af295eed03a983dd66debbbe9cfb78d8252859f4498a615a0074b99" + }, + "research/e8-bit-r420/NOTICE.md": { + "git_blob": "cb68783d7d76c3fc13faa571429e9b067a0db3f7", + "sha256": "12ba6e0845f222e9940b00f6c60d261db104246a8d3143da267682973479f811" + }, + "research/e8-bit-r420/README.md": { + "git_blob": "6751eba6f617292fc919e58d5a9f9f06ab037391", + "sha256": "9807be57c6adf26b30e4f54e2f8160075bbc05091f1a6d157e43d2a4620c1c9f" + }, + "research/e8-bit-r420/code/xcheck.py": { + "git_blob": "fbff8607e4c61e18481f696b99dd38a32444e90d", + "sha256": "5737d18a7826fd51e131035f2d7bebba2e2868af91dd7672a5f11208b036d424" + }, + "research/e8-bit-r420/data/bitE8mut-r420.json.gz": { + "git_blob": "0c63ca62759dc63d302be6552aeeee1ede70350f", + "sha256": "9721a3819efd68307f66f00d84a952eb28eb7c3ad2ce79653ce295c98a764784" + } + }, + "notes": "The xcheck and exporter are reused unchanged. columns_k.cpp supplies the schedule/prefix reference and is invoked unchanged by optional native_verify.py, along with the pinned staging/legality/header files. Selected files bind baseline context, not a fresh full assembly replay.", + "reviewed_bit_source_head": "2065fe4f72a914d907f1046603f5a36f17018535", + "reviewed_bit_source_pr": 543, + "selected_complex_source_head": "660de893d27bb7abd1d5b01b1640207528a5c851", + "selected_complex_source_pr": 626, + "selected_kappa": "51110230636731/31250000000000000" +} diff --git a/research/r420-target-star/VALIDATION.json b/research/r420-target-star/VALIDATION.json new file mode 100644 index 0000000000..23a328668d --- /dev/null +++ b/research/r420-target-star/VALIDATION.json @@ -0,0 +1,55 @@ +{ + "status": "PASS_SCOPED_LOCAL_VERIFICATION", + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "recorded_at_utc": "2026-10-13T04:58:01.569704+00:00", + "platform": "macOS-27.0.1-arm64-arm-64bit", + "python": "3.9.6 (default, Aug 25 2026, 21:26:21) \n[Clang 21.0.0 (clang-2100.3.34.2)]", + "commands": [ + { + "command": "python3 -B research/r420-target-star/verify.py", + "result": "PASS; exact certificate, 660 arbitrary-input columns, nine construction controls, both exported streams, positive prefixes, 5/9/11-stage Python replays and 48 actual-stream bridge omissions" + }, + { + "command": "python3 -I -O -B research/r420-target-star/verify.py", + "result": "PASS; also run from a minimal relocated tree containing only the package and the 14 pinned inputs" + }, + { + "command": "python3 -I -O -B research/r420-target-star/native_verify.py --boost-include /private/tmp/imb-boost-headers/boost_1_85_0 --output /private/tmp/r420-target-forest-native-check --check research/r420-target-star/NATIVE.json", + "result": "PASS; fresh unchanged C++17 legality and 5/9/11-stage checks for both words, all 96 built-in bridge controls, and candidate missing-preparation rejection at all three stage counts; full normalized receipts agree" + }, + { + "command": "make selected-record-check", + "result": "PASS" + }, + { + "command": "git diff --check; git diff --exit-code BASE -- upstream certificates docs scripts", + "result": "PASS; all additions confined to research/r420-target-star/" + } + ], + "supplemental_controls": [ + "Corrupted saved_additions in a supplied certificate rejected with certificate mismatch.", + "Changed pinned xcheck bytes rejected before import, then restored in the temporary minimal tree.", + "Relocated candidate canonical JSON equals the original generated candidate. Recompression with a different gzip level and timestamp preserves its certificate content hash." + ], + "toolchain": { + "boost_version_header_sha256": "063ed28eceb611d52f58e57aca61edb1e086ed902fbded81ac61936009c52cf0", + "compiler": "Apple clang version 21.0.0 (clang-2100.3.34.2)\nTarget: arm64-apple-darwin27.0.0\nThread model: posix\nInstalledDir: /Library/Developer/CommandLineTools/usr/bin", + "platform": "macOS-27.0.1-arm64-arm-64bit", + "python": "3.9.6 (default, Aug 25 2026, 21:26:21) \n[Clang 21.0.0 (clang-2100.3.34.2)]" + }, + "boost_source": { + "url": "https://archives.boost.io/release/1.85.0/source/boost_1_85_0.tar.bz2", + "sha256": "7009fe1faa1697476bdc7027703a2badb84e849b7b0baad5086b087b971f8617", + "authenticated": true, + "installation": "headers extracted in temporary storage only" + }, + "not_run": [ + "repository-wide make verify", + "selected supplier cold reconstruction", + "hosted-parent/whole-owner emission and complete global invoices", + "changed-word outer assembly", + "Lean", + "remote Linux CI" + ], + "limitations": "New semantic D interface needs review and integration. Global coefficient and tape bounds are not inferred from native bounds. All inherited all-size/physical/hosting/precision/analytic assumptions remain. No new kappa or global search optimum." +} diff --git a/research/r420-target-star/native_verify.py b/research/r420-target-star/native_verify.py new file mode 100644 index 0000000000..6e433d21ff --- /dev/null +++ b/research/r420-target-star/native_verify.py @@ -0,0 +1,124 @@ +#!/usr/bin/env python3 +"""Optional unchanged C++ replay. @ellipsi2 with OpenAI Codex; Apache-2.0.""" +import argparse +import gzip +import importlib.util +import json +import os +from pathlib import Path +import platform +import subprocess +import sys + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location("target_star", HERE / "verify.py") +v = importlib.util.module_from_spec(spec) +spec.loader.exec_module(v) +CK = v.ROOT / "research/e8-bit-carrier-skeleton/code/bit/checkers" +STAGE = v.ROOT / "research/e8-bit-carrier-skeleton/code/bit/regression/stage_cohort.py" +PORTABLE = v.ROOT / "research/e8-bit-carrier-skeleton/portable-include" + + +def execute(args, log, reject=False): + result = subprocess.run([str(x) for x in args], capture_output=True, text=True) + log.write_text(result.stdout + result.stderr) + v.need((result.returncode != 0) if reject else (result.returncode == 0), + "unexpected command result; see " + str(log)) + if reject: + v.need("local defining-decoder full formal column" in result.stderr, + "control failed for an unrelated reason; see " + str(log)) + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--boost-include", type=Path, required=True) + parser.add_argument("--output", type=Path, required=True, help="new output directory") + parser.add_argument("--check", type=Path, help="compare proof-relevant receipts, ignoring environment") + args = parser.parse_args() + sources = v.check_pins() + v.need((args.boost_include / "boost/multiprecision/cpp_int.hpp").is_file(), "Boost headers missing") + args.output.mkdir() # never overwrite an earlier replay + out = args.output.resolve() + compiler = os.environ.get("CXX", "c++") + flags = [compiler, "-O2", "-std=c++17", "-include", "algorithm", "-DHDIM=8", "-DNCOPY=9", + "-DVPORTS=120", "-DRHELP=420", "-I" + str(CK), "-I" + str(PORTABLE), + "-I" + str(args.boost_include.resolve())] + binaries = {} + for name, source, extra in [("legality", "legality_h.cpp", [])] + [ + ("columns%d" % k, "columns_k.cpp", ["-DKPAIRS=%d" % k]) for k in (2, 4, 5)]: + binary = out / name + execute(flags + extra + [CK / source, "-o", binary], out / (name + "-compile.log")) + binaries[name] = binary + original = json.loads(gzip.decompress((v.ROOT / v.WORD).read_bytes())) + candidate, _, _, _ = v.synthesize(original) + certificate = json.loads((HERE / "CERTIFICATE.json").read_text()) + v.need(v.digest(sources) == certificate["source_manifest_sha256"], "source manifest binding") + v.need(v.digest(candidate) == certificate["candidate_content_sha256"], "candidate hash") + receipts = {} + for label, word, pricekey in [("baseline", original, "original"), ("candidate", candidate, "candidate")]: + work = out / label + work.mkdir() + records = work / "records" + records.mkdir() + v.export(word, records) + cin, cout = work / "cin", work / "cout" + execute([sys.executable, "-I", "-B", STAGE, records, records, cin, cout], work / "stage.log") + execute([binaries["legality"], cin, cout, work / "legality.json"], work / "legality.log") + legality = json.loads((work / "legality.json").read_text()) + expected = certificate[pricekey] + v.need(legality["status"] == "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE", + "native legality status") + for key, price in [("records", "records"), ("common_frame_ADDs", "scalar_additions"), + ("nested_MOVEs", "moves"), ("copies", "copies"), ("rank_mass", "rank_mass")]: + v.need(legality[key] == expected[price], "native legality price: " + key) + columns = [] + stream = cout / "COHORT249-RECORDS.bin" + for k in (2, 4, 5): + receipt = work / ("columns%d.json" % k) + execute([binaries["columns%d" % k], stream, receipt], work / ("columns%d.log" % k)) + result = json.loads(receipt.read_text()) + v.need(result["formal_columns_checked"] == 2*k*120+420, "native column count") + v.need(result["local_scalar_additions"] == expected["scalar_additions"], "native ADD count") + v.need(result["payload_prefix_bits"] == expected["payload_bits"] + and int(result["payload_prefix_upper"]) == expected["payload_upper"], "native prefix") + bounds = [int(x["cancellation_free_signed_row_l1_upper"]) for x in result["signed_lift_prefix"]] + v.need(bounds == [expected["forward_positive_bound"], expected["inverse_positive_bound"]], + "native directional bounds") + v.need(dict(result["local_raw_H"]) == {int(a): b for a, b in expected["local_histogram"].items()}, + "native histogram") + v.need(len(result["negative_controls"]) == 6*(k-1) + and all(x["rejected"] for x in result["negative_controls"]), "native bridge controls") + result.pop("seconds") + result.pop("local_scalar_stream") + columns.append(result) + receipts[label] = dict(legality=legality, columns=columns) + if label == "candidate": + raw = stream.read_bytes() + records6 = [raw[i:i+24] for i in range(0, len(raw), 24)] + first = next(i for i, r in enumerate(v.struct.iter_unpack("<6i", raw)) if r[0] == 1) + damaged = work / "missing-preparation.bin" + damaged.write_bytes(b"".join(records6[:first] + records6[first+1:])) + for k in (2, 4, 5): + execute([binaries["columns%d" % k], damaged, work / ("must-not-pass%d.json" % k)], + work / ("missing-preparation%d.log" % k), reject=True) + receipts[label]["missing_preparation_rejected_at_stages"] = [5, 9, 11] + report = dict(status="PASS_R420_TARGET_STAR_NATIVE", receipts=receipts, + environment=dict(python=sys.version, platform=platform.platform(), + compiler=subprocess.check_output([compiler, "--version"], text=True).strip(), + boost_version_header_sha256=v.hashlib.sha256( + (args.boost_include / "boost/version.hpp").read_bytes()).hexdigest())) + if args.check: + expected = json.loads(args.check.read_text()) + v.need(report["status"] == expected["status"] and report["receipts"] == expected["receipts"], + "native certificate mismatch") + v.write_json(out / "NATIVE.json", report) + print("PASS_R420_TARGET_STAR_NATIVE both_words=5/9/11 columns=900/1380/1620 missing_preparation=rejected") + + +if __name__ == "__main__": + try: + main() + except (ValueError, OSError, subprocess.CalledProcessError) as error: + print("REJECT_R420_TARGET_STAR_NATIVE:", error, file=sys.stderr) + sys.exit(1) diff --git a/research/r420-target-star/verify.py b/research/r420-target-star/verify.py new file mode 100644 index 0000000000..d256587787 --- /dev/null +++ b/research/r420-target-star/verify.py @@ -0,0 +1,461 @@ +#!/usr/bin/env python3 +"""Exact R420 target-star experiment. @ellipsi2 with OpenAI Codex; Apache-2.0. + +Only the Python standard library is required. No producer or optimizer is used. +The inherited xcheck and record exporter are source-pinned and reused explicitly. +""" +import argparse +from collections import Counter +import copy +import gzip +import hashlib +import importlib.util +import json +from pathlib import Path +import struct +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORD = "research/e8-bit-r420/data/bitE8mut-r420.json.gz" +XCHECK = "research/e8-bit-r420/code/xcheck.py" +EXPORT = "research/e8-bit-carrier-skeleton/code/bit/export_records.py" +DONOR = 120 # assignment seed 0 fixes the first donor target to 0 +DONOR_LIMIT = 16 # fixed before the bounded extension was run + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":")).encode() + + +def digest(value): + return hashlib.sha256(canonical(value)).hexdigest() + + +def write_json(path, value): + Path(path).write_text(json.dumps(value, indent=2, sort_keys=True) + "\n") + + +def check_pins(): + source = json.loads((HERE / "SOURCES.json").read_text()) + for path, pin in source["files"].items(): + data = (ROOT / path).read_bytes() + need(hashlib.sha256(data).hexdigest() == pin["sha256"], "source pin: " + path) + blob = hashlib.sha1(b"blob %d\0" % len(data) + data).hexdigest() + need(blob == pin["git_blob"], "source blob: " + path) + return source + + +def synthesize(word): + """Bounded donor-set nomination; exact best assignment for each donor set. + + Donors and receivers are disjoint, but one donor may serve many receivers. + Starting with target 0, add the best strict-improvement donor up to 16 total. + Smaller register IDs break all ties. No global donor-set optimum is claimed. + """ + rows = {d: set(s) for f, d, s in word["D"]} + zero = word["frames"].index([]) + need(len(rows) == 120 and set(rows) == set(range(120, 240)), "baseline D shape") + need(all(f == zero and len(s) == len(set(s)) and all(240 <= a < 660 for a in s) + for f, d, s in word["D"]), "baseline D is not helper-only") + gains = {(i, d): len(rows[i])-len(rows[i] ^ rows[d])-2 + for i in rows for d in rows if i != d} + + def assignment(donors): + census = [] + for target in sorted(rows.keys() - donors): + donor = max(donors, key=lambda d: (gains[target, d], -d)) + census.append(dict(target=target, donor=donor, old_terms=len(rows[target]), + new_terms=len(rows[target] ^ rows[donor]), net_saved=gains[target, donor])) + return sum(max(0, r["net_saved"]) for r in census), census + + donors, trace = {DONOR}, [] + while True: + saving, census = assignment(donors) + step = dict(donors=sorted(donors), saved_additions=saving, + receivers=sum(r["net_saved"] > 0 for r in census)) + trace.append(step) + if len(donors) == DONOR_LIMIT: + break + candidates = [[d, assignment(donors | {d})[0]] for d in sorted(rows.keys()-donors)] + step["candidate_scores"] = candidates + donor, next_score = max(candidates, key=lambda p: (p[1], -p[0])) + if next_score <= saving: + break + donors.add(donor) + selected = [r["target"] for r in census if r["net_saved"] > 0] + by = {r["target"]: r["donor"] for r in census if r["net_saved"] > 0} + need(not (donors & set(selected)), "donor/receiver overlap") + result = copy.deepcopy(word) + setup = [[zero, target, [by[target]]] for target in selected] + middle = [[zero, d, sorted(rows[d] ^ rows[by[d]] if d in selected else rows[d])] + for _, d, _ in word["D"]] + need(all(s for _, _, s in middle), "empty compensation row") + result["D"] = setup + middle + list(reversed(setup)) + search = dict(donors=sorted(donors), donor_limit=DONOR_LIMIT, trace=trace, + oriented_pair_scores=len(gains), candidate_donor_sets=sum( + len(s.get("candidate_scores", [])) for s in trace), + stopping_rule="16 donors or no strictly profitable donor addition", + gains_sha256=digest([[i, d, gains[i, d]] for i, d in sorted(gains)])) + return result, census, selected, search + + +def xor_replay(word, sections=("D", "A", "scatter", "B", "C"), zero_targets=False): + """Own integer-bitset interpreter; every live input is an independent column.""" + n, v = 2 * word["v"] + word["R"], word["v"] + values = [0 if zero_targets and v <= i < 2*v else 1 << i for i in range(n)] + for section in sections: + if section == "scatter": + copied = [values[r] for r in word["ret"]] + for t, row in enumerate(word["scatter"]): + for k in row: + values[v+t] ^= copied[k] + else: + for _, d, sources in word[section]: + for s in sources: + values[d] ^= values[s] + return values + + +def endpoint(word, zero_targets=False): + want = [1 << i for i in range(660)] + for t in range(120): + want[120+t] = (0 if zero_targets else 1 << (120+t)) ^ (1 << t) + return xor_replay(word, zero_targets=zero_targets) == want + + +def export(word, directory): + path = directory / "word.json.gz" + path.write_bytes(gzip.compress(canonical(word), mtime=0)) + subprocess.run([sys.executable, "-I", "-B", str(ROOT / EXPORT), str(path), str(directory)], + check=True, capture_output=True, text=True) + data = (directory / "249-records.bin").read_bytes() + need(len(data) % 24 == 0, "record alignment") + return list(struct.iter_unpack("<6i", data)) + + +def audit_records(records, word, W): + """Separate set-valued execution of the actual exported stream, both ways. + + Checks every geometry move, live COPY lifetime, arbitrary dirty input, + scalar cost and exact positive row-sum bound. No word-level gate interpreter + is called here. Reverse COPY/ERASE use the original immutable center. + """ + n, v = 660, 120 + cur = list(word["start"]) + [W.ZERO] + paths = [[] for _ in range(n)] + H = Counter() + counts = Counter() + values = [{r} for r in range(n)] + [set()] + center = None + for op, a, b, c, f, phase in records: + need(0 <= a <= n and (op == 0 or 0 <= b <= n), "record register") + if op == 0: + need(a < n and 0 <= b < len(W.fdim) and 0 <= c < len(W.fdim), "MOVE indices") + need(cur[a] == b and W.nested(b, c), "illegal MOVE") + need(f == W.fdim[c] - W.fdim[b] and f > 0, "mispriced MOVE") + paths[a].append([b, c, f]) + H[f] += 1 + cur[a] = c + elif op == 1: + need(a != b and a < n and c == 1, "ADD operands") + need(cur[a] == cur[b] == f, "ADD common frame") + need(b != n or center is not None, "read inactive copy") + need(a != center, "write copied center") + values[a] ^= values[b] + elif op == 2: + need(center is None and b == n and cur[a] == c and f == W.ZERO, + "COPY lifecycle") + need(phase == W.fdim[c], "COPY price") + center = a + values[n] = set(values[a]) + cur[n] = f + H[phase] += 1 + elif op == 3: + need(center == a and b == n and cur[a] == c and cur[n] == f, + "ERASE lifecycle") + need(values[n] == values[a], "copied value mutated") + values[n] = set() + center = None + else: + raise ValueError("unknown opcode") + counts[op] += 1 + want = [{r} for r in range(n)] + [set()] + for t in range(v): + want[v+t].add(t) + need(values == want and center is None, "exported forward endpoint") + need(cur[:n] == word["final"], "exported final frames") + need(counts[2] == counts[3] == 9, "COPY count") + + values = [{r} for r in range(n)] + [set()] + center = None + for op, a, b, c, f, phase in reversed(records): + if op == 1: + need(a != center and (b != n or center is not None), "reverse copy access") + values[a] ^= values[b] + elif op == 3: + need(center is None, "reverse COPY overlap") + center = a + values[n] = set(values[a]) + elif op == 2: + need(center == a and values[n] == values[a], "reverse ERASE") + values[n] = set() + center = None + need(values == want and center is None, "exported inverse endpoint") + + maxima = [] + for reverse in (False, True): + norms, high = [1] * (n+1), 1 + opened = False + for op, a, b, c, f, phase in (reversed(records) if reverse else records): + if op == 1: + norms[a] += abs(c) * norms[b] + high = max(high, norms[a]) + elif op == (3 if reverse else 2): + need(not opened, "norm COPY overlap") + norms[n] = norms[a] + opened = True + elif op == (2 if reverse else 3): + need(opened, "norm ERASE without COPY") + norms[n] = 0 + opened = False + need(not opened, "norm COPY closure") + maxima.append(high) + payload = 64 * maxima[0]**3 * maxima[1]**2 + need(payload < 2**104, "native payload exceeds inherited 104-bit cap") + return dict(records=len(records), scalar_additions=counts[1], copies=counts[2], + moves=counts[0], local_histogram=dict(sorted(H.items())), + rank_mass=sum(k*v for k, v in H.items()), + frame_paths_sha256=digest(paths), forward_positive_bound=maxima[0], + inverse_positive_bound=maxima[1], payload_upper=payload, + payload_bits=payload.bit_length()) + + +def bridge_replay(records, pairs, omit=None): + """Fresh literal replay on 2*pairs target/source banks and shared dirty helpers. + + Stage/bridge schedule is DaysSky's B_K schedule (PR381), explicitly credited. + This is a Python replay, not a claim to have run its C++ implementation. + Each omitted-bridge control replays the entire actual record stream. + """ + v, n = 120, 660 + total = 2*pairs*v + 420 + values = [1 << r for r in range(total)] + [0] + stages = 2*pairs+1 + after = [[] for _ in range(stages)] + X, Y = lambda p: 2*(p-1), lambda p: 2*(p-1)+1 + for p in range(2, pairs+1): + after[2*p-3] += [(X(p-1), X(p)), (Y(p), Y(p-1))] + after[2*p-2] += [(Y(p), Y(p-1)), (X(p-1), X(p))] + for p in range(pairs, 1, -1): + after[-1] += [(Y(p-1), Y(p)), (X(p), X(p-1))] + bridge_index = 0 + for stage in range(stages): + p = 1 if stage < 3 else (stage+1)//2 + reverse = stage == 1 or (stage >= 3 and stage % 2 == 1) + xb, yb = (Y(p), X(p)) if reverse else (X(p), Y(p)) + mapping = ([xb*v+i for i in range(v)] + [yb*v+i for i in range(v)] + + [2*pairs*v+i for i in range(420)] + [total]) + opened = False + copies = 0 + for op, a, b, c, f, phase in (reversed(records) if reverse else records): + if op == 1: + values[mapping[a]] ^= values[mapping[b]] + elif op == (3 if reverse else 2): + need(not opened, "bridge COPY overlap") + values[total] = values[mapping[a]] + opened = True + copies += 1 + elif op == (2 if reverse else 3): + need(opened, "bridge ERASE") + values[total] = 0 + opened = False + need(not opened and copies == 9, "stage copy lifecycle") + for d, s in after[stage]: + if bridge_index != omit: + for t in range(v): + values[d*v+t] ^= values[s*v+t] + bridge_index += 1 + for bank in range(0, 2*pairs, 2): + a, b = bank*v, (bank+1)*v + values[a:a+v], values[b:b+v] = values[b:b+v], values[a:a+v] + need(bridge_index == 6*(pairs-1), "bridge count") + return values == [1 << r for r in range(total)] + [0] + + +def controls(base, candidate, selected, W, records): + """Failure-mode controls, checked without comparing a recipe hash.""" + passed = [] + # Crucial dirty-target control: deleting setup is invisible if targets start zero. + mutant = copy.deepcopy(candidate) + del mutant["D"][0] + need(endpoint(mutant, zero_targets=True), "zero-target control was not blind") + need(not endpoint(mutant), "missing preparation accepted on arbitrary targets") + passed.append("missing_setup_passes_zero_targets_but_fails_arbitrary_targets") + mutant = copy.deepcopy(candidate) + del mutant["D"][-1] + need(not endpoint(mutant), "missing restoration accepted") + passed.append("missing_target_restoration") + mutant = copy.deepcopy(candidate) + ix = len(selected) + next(i for i, g in enumerate(base["D"]) if g[1] == selected[0]) + mutant["D"][ix] = copy.deepcopy(next(g for g in base["D"] if g[1] == selected[0])) + need(not endpoint(mutant), "untransformed compensation accepted") + passed.append("untransformed_receiver_compensation") + mutant = copy.deepcopy(candidate) + mutant["D"] = [g for g in mutant["D"] if g[1] != DONOR] + need(not endpoint(mutant), "missing donor compensation accepted") + passed.append("missing_donor_compensation") + mutant = copy.deepcopy(candidate) + mutant["D"][ix][2].pop() + need(not endpoint(mutant), "missing source-access term accepted") + passed.append("missing_helper_read") + # A donor already changed by an earlier setup creates an extra dependency. + # Merely XORing its original K row then omits that dependency's correction. + mutant = copy.deepcopy(candidate) + earlier, later = selected[:2] + mutant["D"][1][2] = [earlier] + mutant["D"][-2][2] = [earlier] + rows = {d: set(s) for _, d, s in base["D"]} + position = len(selected) + next(i for i, g in enumerate(base["D"]) if g[1] == later) + mutant["D"][position][2] = sorted(rows[later] ^ rows[earlier]) + need(not endpoint(mutant), "already-modified receiver admitted as a star donor") + passed.append("donor_is_an_already_modified_receiver") + # Geometry-only failure: scalar semantics still pass at the wrong common frame. + mutant = copy.deepcopy(candidate) + mutant["D"][0][0] = W.FULL + need(endpoint(mutant), "frame-only mutant changed scalar endpoint") + old = W.w + W.w = mutant + try: + try: + W.full() + except Exception as error: + need("climb not nested" in str(error) or "left frame 0" in str(error), + "unexpected frame control failure: " + str(error)) + else: + raise ValueError("illegal frame accepted") + finally: + W.w = old + passed.append("scalar_valid_illegal_frame") + mutant = copy.deepcopy(candidate) + pair = copy.deepcopy(candidate["D"][0]) + mutant["D"] = [pair, copy.deepcopy(pair)] + mutant["D"] + need(endpoint(mutant), "neutral pair should preserve F2 semantics") + with tempfile.TemporaryDirectory(prefix="r420-neutral-control-") as name: + neutral_records = export(mutant, Path(name)) + paid = audit_records(neutral_records, mutant, W) + need(paid["scalar_additions"] == sum(r[0] == 1 for r in records)+2, + "exported neutral pair not paid") + passed.append("scalar_valid_neutral_pair_pays_two_additions") + # Drop one actual exported preparation ADD, independently of word parsing. + damaged = list(records) + del damaged[next(i for i, r in enumerate(damaged) if r[0] == 1)] + need(not bridge_replay(damaged, 4), "missing exported ADD accepted") + passed.append("missing_exported_preparation_add") + return passed + + +def run(): + source = check_pins() + base = json.loads(gzip.decompress((ROOT / WORD).read_bytes())) + candidate, census, selected, search = synthesize(base) + # Independent incidence-count identity for every receiver's cost, including + # losers and ties. No symmetric-difference operation is used in this check. + row_bits = {d: sum(1 << s for s in sources) for _, d, sources in base["D"]} + weight = lambda bits: bin(bits).count("1") + independent_gains = [] + for i in range(120, 240): + for d in range(120, 240): + if i != d: + saving = 2*weight(row_bits[i] & row_bits[d])-weight(row_bits[d])-2 + independent_gains.append([i, d, saving]) + need(digest(independent_gains) == search["gains_sha256"], "independent incidence cost mismatch") + need(all(candidate[k] == base[k] for k in base if k != "D"), "changed field outside D") + need(xor_replay(base, ("D",)) == xor_replay(candidate, ("D",)), "D operator changed") + need(endpoint(base) and endpoint(candidate), "word endpoint") + spec = importlib.util.spec_from_file_location("pinned_r420_xcheck", ROOT / XCHECK) + inherited = importlib.util.module_from_spec(spec) + spec.loader.exec_module(inherited) + W0, labels, full0, H0, C0, _ = inherited.check(base) + need(all(H0.values()) and all(C0.values()), "baseline interface") + W = inherited.Word(candidate) + full = W.full() + H, C, _ = W.interface() + need([k for k, v in H.items() if not v] == ["H2_D_frame0_targets_from_helpers"], + "unexpected inherited hypothesis change") + need([k for k, v in C.items() if not v] == ["K_equals_D"], "unexpected literal K result") + need(all(f == W.ZERO and 120 <= d < 240 and all(120 <= s < 660 for s in srcs) + for f, d, srcs in candidate["D"]), "replacement D frame/operand condition") + with tempfile.TemporaryDirectory(prefix="r420-target-star-") as name: + tmp = Path(name) + (tmp / "baseline").mkdir() + (tmp / "candidate").mkdir() + original_records = export(base, tmp / "baseline") + records = export(candidate, tmp / "candidate") + original = audit_records(original_records, base, W0) + changed = audit_records(records, candidate, W) + need([r for r in records if r[0] != 1] == [r for r in original_records if r[0] != 1], + "MOVE/COPY/ERASE stream changed") + need([r for r in records if r[0] == 1 and r[5] != 1] + == [r for r in original_records if r[0] == 1 and r[5] != 1], "non-D ADD stream changed") + need(original["frame_paths_sha256"] == changed["frame_paths_sha256"], "paths changed") + bridge_results = [] + for pairs in (2, 4, 5): + need(bridge_replay(original_records, pairs), "baseline multistage failure") + need(bridge_replay(records, pairs), "candidate multistage failure") + for omitted in range(6*(pairs-1)): + need(not bridge_replay(records, pairs, omitted), "omitted bridge accepted") + bridge_results.append(dict(stages=2*pairs+1, columns=2*pairs*120+420, + actual_stream_omission_controls=6*(pairs-1))) + rejected = controls(base, candidate, selected, W, records) + savings = sum(r["net_saved"] for r in census if r["net_saved"] > 0) + need(original["scalar_additions"] - changed["scalar_additions"] == savings, "net cost mismatch") + return candidate, dict(status="PASS_R420_TARGET_STAR", assignment_seed=0, initial_donor=DONOR, + base_commit=source["base_commit"], candidate_content_sha256=digest(candidate), + source_manifest_sha256=digest(source), selected_targets=selected, census=census, + search=search, receivers=len(selected), saved_additions=savings, + donor_degrees=dict(sorted(Counter(r["donor"] for r in census if r["net_saved"] > 0).items())), + preparation_additions=len(selected), restoration_additions=len(selected), + baseline_D_additions=sum(len(g[2]) for g in base["D"]), + candidate_D_additions=sum(len(g[2]) for g in candidate["D"]), + original=original, candidate=changed, inherited_labels=labels, + symbolic_columns=full["columns"], inherited_hypotheses=H, inherited_conclusions=C, + replacement_D_operator="exactly the baseline y <- y + K*s; x,s unchanged", + multistage_python_replays=bridge_results, controls=rejected, + scope="Finite bit-circuit construction; no new kappa, no full theorem or global optimum.") + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--check", type=Path, default=HERE / "CERTIFICATE.json") + parser.add_argument("--write-certificate", type=Path) + parser.add_argument("--write-word", type=Path) + args = parser.parse_args() + word, result = run() + if args.write_certificate: + need(not args.write_certificate.exists(), "refusing to overwrite certificate") + write_json(args.write_certificate, result) + else: + need(json.loads(args.check.read_text()) == json.loads(json.dumps(result)), "certificate mismatch") + if args.write_word: + need(not args.write_word.exists(), "refusing to overwrite word") + args.write_word.write_bytes(gzip.compress(canonical(word), mtime=0)) + print("PASS_R420_TARGET_STAR receivers=%d D=%d->%d native_ADDs=%d->%d saved=%d columns=660 rank_mass=%d" + % (result["receivers"], result["baseline_D_additions"], result["candidate_D_additions"], + result["original"]["scalar_additions"], result["candidate"]["scalar_additions"], + result["saved_additions"], result["candidate"]["rank_mass"])) + + +if __name__ == "__main__": + try: + main() + except (ValueError, OSError, subprocess.CalledProcessError) as error: + print("REJECT_R420_TARGET_STAR:", error, file=sys.stderr) + sys.exit(1)