diff --git a/SHA256SUMS.txt b/SHA256SUMS.txt index 3bb56b71..49f6b700 100644 --- a/SHA256SUMS.txt +++ b/SHA256SUMS.txt @@ -70,7 +70,7 @@ bb9ce84f863ecbbc721503cc8e9b60f5c9223c68926fa2a7443ba40491340a06 archive/milest 27c107ab01f254215fc6bda721bcbcf793c4856dde5791caef7f840fd5662c3c archive/milestones/superseded/v0_9_18/response_fibre_lohner_stress_v0_9_18_oneclick.py 7f33442c004a58dab70611aff2e93c752683a4a85c4f41390d44c299921a78fa audit/README.md 17e5e0a9ad1a59f2763de947d6d1e4338297630c7d831694a4bc08b26fb4d83e audit/__init__.py -41e9229818da0bb74f1c31cd59c58afd2dcb07c9fda0be05132d843a21f15e61 audit/artifact_manifest.json +e9e0dca981f89fb23a431803feddf7e16e2181587b9459d4c2315ee576008dea audit/artifact_manifest.json 77154913123c1ef10120afa29d50af3ed3652915c19abf2fdd1f9f4c0f050135 audit/audit_repo.py 941dec5a35eda0b47d24f2f2160e0758db77ef112dd9dadad96614483adf5d59 audit/claims_manifest.yaml 0ac8ce56afb82439f286f55b9b538799b997c00af457106beb646ca9e16add93 audit/dependency_map.md @@ -166,6 +166,9 @@ dec3d44e153365aaa1ed4b56cd6277cc8652c54d8ceecfcdeb65b5f0efa32f21 research/prosp 813ca4ea57d1291df0b774a3c23566a785c76a426466560d88e0f5dc524ea64b research/prospective/pulser_wiener/pulser_finite_shot_unit_recovery_law_audit_v1_1.py e6dc28f85b2ee67d4a366643dafc26f0116380f964e7c795f781c655c5241495 research/prospective/pulser_wiener/pulser_shot_delay_stability_map_v1_3.py feae41af09baecbf6109ee5d5aa3126c8289406ca91db55e266512e0dc8592cb research/realizability_r1_r7/CLAIM_BOUNDARY.md +2a63ae542bac5e06e242d7f5fe037b3ea672d96f3a4eac961cedfac5e8540d7d research/realizability_r1_r7/GF_PR_STAGE_NAMING_BOUNDARY.md +5e10edb2e980fcfb97872efbc252599894f540980c89e5f925b25c4c317743e5 research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md +2ac0bd1f3d98a5adee86681590e5815cc7d31577f4a3f8de664371ad8aa8a819 research/realizability_r1_r7/R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md 5da60edc7271db0d2f518cc3a934acf8e60eda52df7f8bd5c4ff2428dba7c4f3 research/realizability_r1_r7/R5_FEASIBILITY_AUDIT.md 3a0838439eda7f5797058c4c0451f3fb0ab94dfbf7781792ffed76aafbd65379 research/realizability_r1_r7/R5_FIRST_LEAF_AFFINE_DIAGNOSTIC.md c4f651d9e5d517e75d3fc083a7c8c4c10b2173f5fdc31baab256079985652b9f research/realizability_r1_r7/R5_FIRST_LEAF_CENTER_DIAGNOSTIC.md @@ -175,12 +178,14 @@ f7f67a5a2363013ad3c9b514f4e61290b5c7c7dc006264142fdb635d1496615b research/reali 67570c25b63ceb36da91137406ec56fabf3393f353f21e41c787d47cf2215736 research/realizability_r1_r7/R5_SECOND_ORDER_REMAINDER_DIAGNOSTIC.md e9bb32403bd25bbce655d40a4e81a11a538c4b472b3039617334076a66b156db research/realizability_r1_r7/R5_STATIC_ARB_GATES_BOUNDARY.md dbfd554145dfd50a76cceaa1d1874202d6e589a129fb5bf788e69709c6fc5cc8 research/realizability_r1_r7/R7_CERTIFICATE_BOUNDARY.md -63a622bd1ec185446b5c31c6cdf643a2a5ed93956b8897383181f81fab3c4627 research/realizability_r1_r7/README.md +2e2bb5eb2bbfbaa4b3399a317d2ed9d7cb20f735ac9edd6273116ca73db4532e research/realizability_r1_r7/README.md +a2d28d9256b6c871630a8e27695a12ca194582a633b74ddda1816d356173629b research/realizability_r1_r7/certificates/r5_all_leaves_hessian_krawczyk_v1_0.json e1ff18f9891c60fdfae51726b0d16cc713ffbaa241d518e9741f60e514078ccd research/realizability_r1_r7/certificates/r5_first_leaf_hessian_krawczyk_v1_0.json 5fcb7602bf6be5ff501329ae68373d8da88acd7abce0c4842ff808d86b21d1b6 research/realizability_r1_r7/certificates/r5_first_leaf_preflight_v1_0.json b3d28cb01a44c4773136e34a4bb206becb3c6f6c7160ca865576f03af5145994 research/realizability_r1_r7/certificates/r5_static_arb_gates_v1_0.json 25c97919c6098b2800e37ae7387701b873db25cbbfa0959624b137628de8013c research/realizability_r1_r7/certificates/r7_positive_control_v1_0.json cb8b142bad3d1f9c02829a5dd39b7164ed4bc3f765a2437f46e81dbf996948e4 research/realizability_r1_r7/certificates/r7_positive_control_v1_1.json +9720418cb10e31b94aa916ece0ccb864da1aa512dd7944bd02a759838c1476c3 research/realizability_r1_r7/certify_r5_all_leaves_hessian_krawczyk.py 5bb3035cbfb1962ac17904dbdc0f047ea471c6c5725990fa234cc587670a8c7b research/realizability_r1_r7/certify_r5_first_leaf_hessian_krawczyk.py 4b181d16ad1945f967a266e411acc184caad716a2820f623823be5b64dfe6de8 research/realizability_r1_r7/certify_r5_first_leaf_preflight.py 4f848186ee26b898b6135c5702616edee87244e5ddc031cceb925d9d9161dc06 research/realizability_r1_r7/certify_r5_static_arb_gates.py @@ -197,6 +202,7 @@ e8519a644ab50a9989eb40bc34499055f83760563167d88da21d17b3c7539e1c research/reali 1e757ff86759fd793f6743560e1f50040362f892e342db723c47a658a3078cd3 research/realizability_r1_r7/r5_full_tube_protocol_v1_0.json a98869ee84ec316349fde0f110b1c02f2479d81073de3e0e758f9d88417566f3 research/realizability_r1_r7/requirements.txt 50e58648439e6a33e801bffeb203e7080fa1cd39850519cf78caac88eaf199bc research/realizability_r1_r7/verify_frozen_protocol.py +494cce78d9331b87ae4ca7dbf5a399cf7c2b8323cb76a7ae9ce8438afd0b9de0 research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py e680b05d02bd0a551a4d2bac2f663bcad8d07674a0657ba5faa06f316a279746 research/realizability_r1_r7/verify_r5_first_leaf_affine_diagnostic.py 738b43fc231e5c4a5e9a02d40ccf18b359f58f6b58fe7ecc1db56f8e45866d13 research/realizability_r1_r7/verify_r5_first_leaf_center_diagnostic.py b043eed45c696c8e3e344e60feb41449da5a3652e23617c0ce00b0399251708c research/realizability_r1_r7/verify_r5_first_leaf_hessian_krawczyk.py diff --git a/audit/artifact_manifest.json b/audit/artifact_manifest.json index 98fb82c2..235964eb 100644 --- a/audit/artifact_manifest.json +++ b/audit/artifact_manifest.json @@ -340,7 +340,7 @@ "path": "research/realizability_r1_r7/README.md", "producer": "prospective protocol scaffold", "scientific_scope": "documentation for an isolated model-level Principle R test protocol; no R6 search or result", - "sha256": "63a622bd1ec185446b5c31c6cdf643a2a5ed93956b8897383181f81fab3c4627", + "sha256": "2e2bb5eb2bbfbaa4b3399a317d2ed9d7cb20f735ac9edd6273116ca73db4532e", "status": "prospective_protocol", "type": "documentation" }, @@ -930,6 +930,94 @@ "status": "prospective_r5_b1e_first_leaf_certified_only", "type": "script" }, + { + "id": "principle_r_gf_pr_stage_naming_boundary", + "inputs": [ + "principle_r_r1_r7_protocol", + "principle_r_r5_full_tube_protocol" + ], + "path": "research/realizability_r1_r7/GF_PR_STAGE_NAMING_BOUNDARY.md", + "producer": "prospective R5-B2 stage boundary documentation", + "scientific_scope": "naming boundary that separates Principle R interface labels from Geometric-Flow engineering certification stages", + "sha256": "2a63ae542bac5e06e242d7f5fe037b3ea672d96f3a4eac961cedfac5e8540d7d", + "status": "prospective_protocol", + "type": "documentation" + }, + { + "id": "principle_r_compliance_matrix", + "inputs": [ + "principle_r_r1_r7_protocol", + "principle_r_r5_full_tube_protocol", + "principle_r_r7_positive_control_certificate_v1_1" + ], + "path": "research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md", + "producer": "prospective Principle R compliance documentation", + "scientific_scope": "evidence matrix for the prospective model-level Principle R interface; does not change the published theorem boundary", + "sha256": "5e10edb2e980fcfb97872efbc252599894f540980c89e5f925b25c4c317743e5", + "status": "prospective_protocol", + "type": "documentation" + }, + { + "id": "principle_r_r5_all_leaves_hessian_krawczyk_boundary", + "inputs": [ + "principle_r_r5_first_leaf_hessian_krawczyk_certificate", + "principle_r_r5_full_tube_protocol", + "principle_r_r5_full_tube_auxiliary_data" + ], + "path": "research/realizability_r1_r7/R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md", + "producer": "prospective R5-B2 all-leaves Hessian Krawczyk boundary", + "scientific_scope": "16 frozen local leaves only; not gluing, not full R5, not PR-R6, and not normal K=1 recovery", + "sha256": "2ac0bd1f3d98a5adee86681590e5815cc7d31577f4a3f8de664371ad8aa8a819", + "status": "prospective_r5_b2_all_leaves_local_only", + "type": "documentation" + }, + { + "allow_absolute_runtime_paths": true, + "id": "principle_r_r5_all_leaves_hessian_krawczyk_script", + "inputs": [ + "v0_7_4_parent_box_script", + "principle_r_r5_first_leaf_hessian_krawczyk_certificate", + "principle_r_r5_first_leaf_affine_diagnostic_record", + "principle_r_r5_static_arb_gates_certificate", + "principle_r_r5_full_tube_protocol", + "principle_r_r5_full_tube_auxiliary_data" + ], + "path": "research/realizability_r1_r7/certify_r5_all_leaves_hessian_krawczyk.py", + "producer": "prospective R5-B2 all-leaves affine-Hessian Krawczyk driver", + "scientific_scope": "checks each of the 16 frozen leaves independently using the same frozen affine-Hessian Krawczyk construction", + "sha256": "9720418cb10e31b94aa916ece0ccb864da1aa512dd7944bd02a759838c1476c3", + "status": "prospective_r5_b2_all_leaves_local_only", + "type": "script" + }, + { + "id": "principle_r_r5_all_leaves_hessian_krawczyk_certificate", + "inputs": [ + "principle_r_r5_all_leaves_hessian_krawczyk_script", + "principle_r_r5_first_leaf_hessian_krawczyk_certificate", + "principle_r_r5_full_tube_protocol", + "principle_r_r5_full_tube_auxiliary_data" + ], + "path": "research/realizability_r1_r7/certificates/r5_all_leaves_hessian_krawczyk_v1_0.json", + "producer": "principle_r_r5_all_leaves_hessian_krawczyk_script", + "scientific_scope": "all 16 frozen leaves locally certified for normal-root existence/uniqueness; not adjacent-leaf gluing, not full-path continuity, not full R5, not PR-R6, and not normal K=1 recovery", + "sha256": "a2d28d9256b6c871630a8e27695a12ca194582a633b74ddda1816d356173629b", + "status": "prospective_r5_b2_all_leaves_local_only", + "type": "certificate" + }, + { + "id": "principle_r_r5_all_leaves_hessian_krawczyk_verifier", + "inputs": [ + "principle_r_r5_all_leaves_hessian_krawczyk_certificate", + "principle_r_r5_full_tube_protocol", + "principle_r_r5_full_tube_auxiliary_data" + ], + "path": "research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py", + "producer": "prospective R5-B2 all-leaves Hessian Krawczyk verifier", + "scientific_scope": "read-only verifier and mutation tests for the all-leaves local-only B2 record; rejects R5/PR-R6/global-flow claim inflation and arithmetic/hash tampering", + "sha256": "494cce78d9331b87ae4ca7dbf5a399cf7c2b8323cb76a7ae9ce8438afd0b9de0", + "status": "prospective_r5_b2_all_leaves_local_only", + "type": "script" + }, { "allow_absolute_runtime_paths": true, "id": "v0_9_2_krawczyk_design_reference_script", diff --git a/research/realizability_r1_r7/GF_PR_STAGE_NAMING_BOUNDARY.md b/research/realizability_r1_r7/GF_PR_STAGE_NAMING_BOUNDARY.md new file mode 100644 index 00000000..3e61a7da --- /dev/null +++ b/research/realizability_r1_r7/GF_PR_STAGE_NAMING_BOUNDARY.md @@ -0,0 +1,27 @@ +# GF/PR Stage Naming Boundary + +This repository uses two separate naming layers. + +`PR-R1` through `PR-R7` denote the prospective Principle R interface: +state-space declarations, response protocol, protocol-relative cost, admissible +processes, shrinking-family requirements, future R6 gates, and the R7 positive +control. + +`GF-R5`, `R5-A`, `R5-B0`, `R5-B1e`, `R5-B2`, and later `R5-B3`--`R5-B6` +denote Geometric-Flow repository engineering stages for a possible R5 witness. +These stages are evidence-producing or diagnostic substeps. They do not by +themselves modify the published Geometric-Flow theorem boundary. + +In particular: + +```text +GF-R5 local leaf success != PR-R5 certified. +GF-R5 all-leaf local success != PR-R6 supplied. +R5-B2 success != full R5 tube certificate. +``` + +R5-B2 checks only whether the same frozen affine-Hessian Krawczyk construction +certifies one local normal root on each of the 16 frozen tube leaves. It does not +certify adjacent-leaf gluing, full-path continuity, exact zero cost on the full +path, positive-measure nonconstancy, R6, a global ODE flow, or normal K=1 +residual recovery. diff --git a/research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md b/research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md new file mode 100644 index 00000000..dc0c4617 --- /dev/null +++ b/research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md @@ -0,0 +1,22 @@ +# Principle R Compliance Matrix + +This table records current repository evidence for the prospective model-level +Principle R interface. It does not change the published Geometric-Flow theorem +boundary. + +| Interface | Current evidence | Status | +|---|---|---| +| PR-R1 | Frozen fourteen-phase state space and phase-gauge handling | model-level | +| PR-R2 | Frozen protocol, inputs, hashes, and 192-bit precision declarations | model-level | +| PR-R3 | Response-induced protocol-relative cost using the declared `R3/W_Pi` meter | model-level, not fundamental vacuum cost | +| PR-R4 | Allowed absolutely continuous nonconstant process class | local/partial | +| PR-R5 | Shrinking family protocol plus static gates and local leaf diagnostics | not separately certified | +| PR-R6 | Published local ODE result and prospective future gates; no complete 16-leaf path result | local only | +| PR-R7 | Same-meter positive control certificate | explicit binding verified | +| Full interface | No complete R1--R7 model-level witness | not certified | + +`R5-B2` success would strengthen only the local normal-root evidence for the +frozen 16 leaves. It would not imply `PR-R6` success. R5-B3--R5-B5 are still +needed for gluing, full-path coverage/continuity, exact response preservation, +and positive-measure nonconstancy before any complete GF-R5 certificate can be +considered. diff --git a/research/realizability_r1_r7/R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md b/research/realizability_r1_r7/R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md new file mode 100644 index 00000000..345c34e4 --- /dev/null +++ b/research/realizability_r1_r7/R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md @@ -0,0 +1,53 @@ +# R5-B2 All-Leaves Hessian Krawczyk Boundary + +R5-B2 freezes a first-pass all-leaves preflight for the 16 initial leaves in the +subordinate R5 full-tube protocol. The leaf list, order, endpoint rule, centers, +fixed slope, Arb precision, candidate eta radii, formal eta radius, and +Krawczyk gates are declared before running the all-leaf check. + +The frozen tube is: + +```text +t in [-1e-12, 1e-12] +``` + +with 16 ordered leaves of width `1.25e-13`. Endpoints are recorded as closed +intervals for interval enclosure; later gluing work must treat adjacency and +branch consistency separately. + +For leaf `i`, the center is: + +```text +a_C,i = (left_i + right_i)/2 +b_C,i = -P F(a_C,i, 0) +``` + +The fixed affine slope `S` is the B1c/B1e slope and is not refit per leaf. The +directional Hessian remainder is computed for: + +```text +w = T*v + N*S +Y2_i <= 1/2 sup ||P*B*D2R3(theta_C,i + w*alpha)[w,w]||_inf * alpha_radius^2 +``` + +The Krawczyk forcing bound is: + +```text +Y_total_i = Y0_i + Y1_i + Y2_i + Y_eta_cross_i +``` + +where eta variation is not interval-subtracted into the forcing term; it is +handled by `Z_i*r_eta` over the full `(alpha, eta)` box. + +Allowed scientific statuses: + +```text +R5_ALL_LEAVES_HESSIAN_KRAWCZYK_CERTIFIED +R5_ALL_LEAVES_HESSIAN_KRAWCZYK_NOT_CERTIFIED +R5_ALL_LEAVES_HESSIAN_KRAWCZYK_INCONCLUSIVE +R5_B2_INPUT_BOUNDARY_MISMATCH +R5_B2_IMPLEMENTATION_ERROR +``` + +Even if all 16 leaves pass their local gates, this is not a full R5 certificate, +not PR-R5, not PR-R6, not a global flow result, and not normal K=1 recovery. diff --git a/research/realizability_r1_r7/README.md b/research/realizability_r1_r7/README.md index 2b3b6675..32ce9a54 100644 --- a/research/realizability_r1_r7/README.md +++ b/research/realizability_r1_r7/README.md @@ -39,6 +39,9 @@ R5_FIRST_LEAF_CENTER_DIAGNOSTIC.md R5_FIRST_LEAF_AFFINE_DIAGNOSTIC.md R5_SECOND_ORDER_REMAINDER_DIAGNOSTIC.md R5_FIRST_LEAF_HESSIAN_KRAWCZYK_BOUNDARY.md +GF_PR_STAGE_NAMING_BOUNDARY.md +R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md +PRINCIPLE_R_COMPLIANCE_MATRIX.md r5_full_tube_protocol_v1_0.json prepare_r5_full_tube_auxiliary.py verify_r5_full_tube_auxiliary.py @@ -62,6 +65,9 @@ diagnostics/r5_second_order_remainder_diagnostic_v1_0.json certify_r5_first_leaf_hessian_krawczyk.py verify_r5_first_leaf_hessian_krawczyk.py certificates/r5_first_leaf_hessian_krawczyk_v1_0.json +certify_r5_all_leaves_hessian_krawczyk.py +verify_r5_all_leaves_hessian_krawczyk.py +certificates/r5_all_leaves_hessian_krawczyk_v1_0.json certificates/r7_positive_control_v1_0.json # superseded certificates/r7_positive_control_v1_1.json # current R7 positive control ``` @@ -82,6 +88,7 @@ python research/realizability_r1_r7/verify_r5_first_leaf_center_diagnostic.py -- python research/realizability_r1_r7/verify_r5_first_leaf_affine_diagnostic.py --mutation-tests python research/realizability_r1_r7/verify_r5_second_order_remainder_diagnostic.py --mutation-tests python research/realizability_r1_r7/verify_r5_first_leaf_hessian_krawczyk.py --mutation-tests +python research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py --mutation-tests ``` The verifier checks schema, required fields, declared file hashes, R1--R5/R7 @@ -166,6 +173,16 @@ self-map margins. This certifies only first-leaf graph root existence/uniqueness; it is not a full R5 tube certificate, not R6, and not normal K=1 recovery. +`certificates/r5_all_leaves_hessian_krawczyk_v1_0.json` records the R5-B2 +all-leaves affine-Hessian Krawczyk preflight over the 16 frozen initial tube +leaves. Its status is `R5_ALL_LEAVES_HESSIAN_KRAWCZYK_CERTIFIED`: every leaf +has a strict local normal-root existence/uniqueness gate at the formal eta +radius `1e-23` under the same predeclared formula, radius set, and 192-bit Arb +precision. This remains local leaf evidence only. It does not certify adjacent +leaf gluing, full-path continuity, exact response preservation, zero total +cost, positive-measure nonconstancy, PR-R6, full R5, a global ODE flow, or +normal K=1 recovery. + ## Scope The published Geometric-Flow theorem remains the v1.2.13 local quantum-control diff --git a/research/realizability_r1_r7/certificates/r5_all_leaves_hessian_krawczyk_v1_0.json b/research/realizability_r1_r7/certificates/r5_all_leaves_hessian_krawczyk_v1_0.json new file mode 100644 index 00000000..02b3d609 --- /dev/null +++ b/research/realizability_r1_r7/certificates/r5_all_leaves_hessian_krawczyk_v1_0.json @@ -0,0 +1 @@ +{"arb_precision_bits":192,"base_commit":"1d6ca4fd7e8eda0977e66d869715ca1c22d75144","frozen_protocol":{"center_rule":"a_C=(left+right)/2","directional_hessian_formula":"Y2_i <= 1/2 sup ||P*B*D2R3(theta_C,i+(T*v+N*S)alpha)[w,w]||_inf * alpha_radius^2","endpoint_rule":"closed Arb intervals per leaf; overlap consistency deferred to B3","eta_radii_predeclared":["1e-30","1e-28","1e-26","1e-24","1e-23","1e-22","1e-20"],"fixed_slope_source":"B1c/B1e S reused for every leaf without refit","formal_eta_radius":"1e-23","leaf_list":[["-1e-12","-8.75e-13"],["-8.75e-13","-7.5e-13"],["-7.5e-13","-6.25e-13"],["-6.25e-13","-5e-13"],["-5e-13","-3.75e-13"],["-3.75e-13","-2.5e-13"],["-2.5e-13","-1.25e-13"],["-1.25e-13","0"],["0","1.25e-13"],["1.25e-13","2.5e-13"],["2.5e-13","3.75e-13"],["3.75e-13","5e-13"],["5e-13","6.25e-13"],["6.25e-13","7.5e-13"],["7.5e-13","8.75e-13"],["8.75e-13","1e-12"]],"leaf_order":"increasing t from -1e-12 to 1e-12","normal_center_rule":"b_C=-P*F(a_C,0) using frozen P and zero normal 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checks the 16 frozen leaves independently. It does not certify adjacent +leaf gluing, full-path continuity, zero cost, nonconstancy, PR-R6, normal K=1 +recovery, or any global flow statement. +""" + +from __future__ import annotations + +import hashlib +import json +import os +import platform +import subprocess +import sys +import tempfile +import textwrap +from pathlib import Path +from typing import Any + +import certify_r5_first_leaf_hessian_krawczyk as b1e_builder +import certify_r5_first_leaf_preflight as preflight + + +ROOT = Path(__file__).resolve().parents[2] +HERE = Path(__file__).resolve().parent + +V074_SOURCE = preflight.V074_SOURCE +PARENT_PROTOCOL_PATH = preflight.PARENT_PROTOCOL_PATH +PROTOCOL_PATH = preflight.PROTOCOL_PATH +AUX_PATH = preflight.AUX_PATH +STATIC_CERT_PATH = preflight.STATIC_CERT_PATH +B1E_CERT_PATH = HERE / "certificates" / "r5_first_leaf_hessian_krawczyk_v1_0.json" +B1D_DIAG_PATH = HERE / "diagnostics" / "r5_second_order_remainder_diagnostic_v1_0.json" +AFFINE_DIAG_PATH = HERE / "diagnostics" / "r5_first_leaf_affine_diagnostic_v1_0.json" +BOUNDARY_PATH = HERE / "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md" +NAMING_BOUNDARY_PATH = HERE / "GF_PR_STAGE_NAMING_BOUNDARY.md" +COMPLIANCE_MATRIX_PATH = HERE / "PRINCIPLE_R_COMPLIANCE_MATRIX.md" +CERT_PATH = HERE / "certificates" / "r5_all_leaves_hessian_krawczyk_v1_0.json" +DIAG_PATH = HERE / "diagnostics" / "r5_all_leaves_hessian_krawczyk_v1_0.json" + +EXPECTED_BASE_COMMIT = "1d6ca4fd7e8eda0977e66d869715ca1c22d75144" +EXPECTED_B1E_CERT_SHA256 = "e1ff18f9891c60fdfae51726b0d16cc713ffbaa241d518e9741f60e514078ccd" +EXPECTED_B1D_DIAG_SHA256 = b1e_builder.EXPECTED_B1D_DIAG_SHA256 +EXPECTED_AFFINE_DIAG_SHA256 = b1e_builder.EXPECTED_AFFINE_DIAG_SHA256 +PRECISION_BITS = 192 +FORMAL_RADIUS = "1e-23" +ETA_RADII = ["1e-30", "1e-28", "1e-26", "1e-24", "1e-23", "1e-22", "1e-20"] +LEAVES = [ + ["-1e-12", "-8.75e-13"], + ["-8.75e-13", "-7.5e-13"], + ["-7.5e-13", "-6.25e-13"], + ["-6.25e-13", "-5e-13"], + ["-5e-13", "-3.75e-13"], + ["-3.75e-13", "-2.5e-13"], + ["-2.5e-13", "-1.25e-13"], + ["-1.25e-13", "0"], + ["0", "1.25e-13"], + ["1.25e-13", "2.5e-13"], + ["2.5e-13", "3.75e-13"], + ["3.75e-13", "5e-13"], + ["5e-13", "6.25e-13"], + ["6.25e-13", "7.5e-13"], + ["7.5e-13", "8.75e-13"], + ["8.75e-13", "1e-12"], +] + +CERTIFIED = "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_CERTIFIED" +NOT_CERTIFIED = "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_NOT_CERTIFIED" +INCONCLUSIVE = "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_INCONCLUSIVE" +BOUNDARY_MISMATCH = "R5_B2_INPUT_BOUNDARY_MISMATCH" +IMPLEMENTATION_ERROR = "R5_B2_IMPLEMENTATION_ERROR" +ALLOWED_STATUSES = {CERTIFIED, NOT_CERTIFIED, INCONCLUSIVE, BOUNDARY_MISMATCH, IMPLEMENTATION_ERROR} + + +def canonical_json(value: Any) -> bytes: + return json.dumps(value, sort_keys=True, separators=(",", ":"), ensure_ascii=True, allow_nan=False).encode("utf-8") + + +def sha256_bytes(value: bytes) -> str: + return hashlib.sha256(value).hexdigest() + + +def sha256_file(path: Path) -> str: + digest = hashlib.sha256() + with path.open("rb") as handle: + for block in iter(lambda: handle.read(1024 * 1024), b""): + digest.update(block) + return digest.hexdigest() + + +def read_json(path: Path) -> Any: + return json.loads(path.read_text(encoding="utf-8")) + + +def digest_payload(value: dict[str, Any]) -> dict[str, Any]: + payload = json.loads(json.dumps(value, sort_keys=True)) + payload.pop("record_sha256", None) + payload.get("software_environment", {}).pop("python", None) + return payload + + +def check_upstream_identity() -> None: + expected_files = { + PARENT_PROTOCOL_PATH: preflight.EXPECTED_PARENT_PROTOCOL_SHA256, + PROTOCOL_PATH: preflight.EXPECTED_PROTOCOL_SHA256, + AUX_PATH: preflight.EXPECTED_AUXILIARY_SHA256, + STATIC_CERT_PATH: preflight.EXPECTED_STATIC_CERT_SHA256, + B1E_CERT_PATH: EXPECTED_B1E_CERT_SHA256, + B1D_DIAG_PATH: EXPECTED_B1D_DIAG_SHA256, + AFFINE_DIAG_PATH: EXPECTED_AFFINE_DIAG_SHA256, + V074_SOURCE: preflight.EXPECTED_V074_SOURCE_SHA256, + } + for path, expected in expected_files.items(): + actual = sha256_file(path) + if actual != expected: + raise RuntimeError(f"upstream SHA mismatch for {path}: {actual} != {expected}") + + b1e = read_json(B1E_CERT_PATH) + if ( + b1e.get("scientific_status") != b1e_builder.CERTIFIED + or b1e.get("scope", {}).get("first_leaf_gates_pass") is not True + or b1e.get("scope", {}).get("all_gates_pass") is not False + or b1e.get("scope", {}).get("r5_certified") is not False + ): + raise RuntimeError(BOUNDARY_MISMATCH) + + +def injection() -> str: + code = r''' +import os +import platform +from flint import arb_mat + +r5_output = Path(os.environ["R5_B2_OUTPUT"]) +r5_aux = json.loads(Path(os.environ["R5_B2_AUX"]).read_text(encoding="utf-8")) +r5_affine = json.loads(Path(os.environ["R5_B2_AFFINE"]).read_text(encoding="utf-8")) +r5_leaves = json.loads(os.environ["R5_B2_LEAVES"]) +r5_eta_radii = json.loads(os.environ["R5_B2_ETA_RADII"]) +r5_formal_radius = os.environ["R5_B2_FORMAL_RADIUS"] + + +def r5_arb(value): + return arb(str(value)) + + +def r5_mat(values): + return [[r5_arb(item) for item in row] for row in values] + + +def r5_vec(values): + return [r5_arb(item) for item in values] + + +def r5_identity(size): + return [[arb(1) if i == j else arb(0) for j in range(size)] for i in range(size)] + + +def r5_matmul(left, right): + return [[sum((left[r][k] * right[k][c] for k in range(len(right))), arb(0)) for c in range(len(right[0]))] for r in range(len(left))] + + +def r5_matvec(left, vec): + return [sum((left[r][k] * vec[k] for k in range(len(vec))), arb(0)) for r in range(len(left))] + + +def r5_matsub(left, right): + return [[left[r][c] - right[r][c] for c in range(len(left[0]))] for r in range(len(left))] + + +def r5_vec_abs_upper(vec): + best = arb(0) + for value in vec: + upper = value.abs_upper() + if upper > best: + best = upper + return best + + +def r5_inf_norm_upper(matrix): + best = arb(0) + for row in matrix: + total = arb(0) + for value in row: + total += value.abs_upper() + if total > best: + best = total + return best + + +def r5_bound(value): + return { + "enclosure": str(value), + "lower": str(value.lower()), + "upper": str(value.upper()), + "abs_lower": str(value.abs_lower()), + "abs_upper": str(value.abs_upper()), + "contains_zero": bool(value.contains(arb(0))), + } + + +def r5_bound_vector(vec): + return [r5_bound(value) for value in vec] + + +def r5_midpoint_string(value): + return str((value.lower() + value.upper()) / 2) + + +def r5_response(phases): + z, _ = projective_jet_and_derivatives(phases, mirror=False) + zbar, _ = projective_jet_and_derivatives(phases, mirror=True) + values = [] + for order in range(RESPONSE_ORDER + 1): + values.append(((z.c[order] + zbar.c[order]) / 2).real) + for order in range(RESPONSE_ORDER + 1): + values.append(((z.c[order] - zbar.c[order]) / (2 * I)).real) + return values + + +def r5_response_jacobian(phases): + return response_jacobian_and_gradient(phases)[0] + + +def r5_theta(t_value, b_values): + objects = r5_aux["objects"] + theta0 = r5_vec(objects["theta_0"]) + T = r5_mat(objects["T"]) + N = r5_mat(objects["N"]) + intrinsic = [t_value, arb(0), arb(0), arb(0), arb(0), arb(0)] + tangent = r5_matvec(T, intrinsic) + normal = r5_matvec(N, b_values) + return [theta0[i] + tangent[i] + normal[i] for i in range(CONTROL_DIMENSION)] + + +def r5_theta_affine(theta_C, w, alpha, N, eta): + return [theta_C[i] + w[i] * alpha + sum((N[i][j] * eta[j] for j in range(RESPONSE_DIMENSION)), arb(0)) for i in range(CONTROL_DIMENSION)] + + +def r5_F_from_theta(theta): + objects = r5_aux["objects"] + B = r5_mat(objects["B"]) + c = r5_vec(objects["c"]) + response = r5_response(theta) + return r5_matvec(B, [response[i] - c[i] for i in range(RESPONSE_DIMENSION)]) + + +def r5_F_t_b(t_value, b_values): + return r5_F_from_theta(r5_theta(t_value, b_values)) + + +def r5_JN_at_theta(theta): + objects = r5_aux["objects"] + B = r5_mat(objects["B"]) + N = r5_mat(objects["N"]) + return r5_matmul(r5_matmul(B, r5_response_jacobian(theta)), N) + + +def r5_Jalpha_at_theta(theta, direction): + objects = r5_aux["objects"] + B = r5_mat(objects["B"]) + return r5_matvec(r5_matmul(B, r5_response_jacobian(theta)), direction) + + +def r5_max_phase_displacement(theta_box): + theta0 = r5_vec(r5_aux["objects"]["theta_0"]) + return r5_vec_abs_upper([theta_box[i] - theta0[i] for i in range(CONTROL_DIMENSION)]) + + +def r5_strict_positive(value): + return bool(value > arb(0) and not value.contains(arb(0))) + + +def r5_newton_correction(t_value): + P = r5_mat(r5_aux["objects"]["P"]) + zero = [arb(0) for _ in range(RESPONSE_DIMENSION)] + return [-value for value in r5_matvec(P, r5_F_t_b(t_value, zero))] + + +def alpha_matvec(matrix, vector): + return [ + matrix[0][0] * vector[0] + matrix[0][1] * vector[1], + matrix[1][0] * vector[0] + matrix[1][1] * vector[1], + ] + + +class AlphaJet: + order = 2 + + def __init__(self, coefficients=0): + if isinstance(coefficients, AlphaJet): + self.c = coefficients.c[:] + elif isinstance(coefficients, (list, tuple)): + self.c = [item if isinstance(item, DeltaJet) else DeltaJet(item) for item in coefficients] + self.c += [DeltaJet(0)] * (self.order + 1 - len(self.c)) + else: + self.c = [coefficients if isinstance(coefficients, DeltaJet) else DeltaJet(coefficients)] + self.c += [DeltaJet(0)] * self.order + self.c = self.c[: self.order + 1] + + def __add__(self, other): + other = AlphaJet(other) + return AlphaJet([self.c[k] + other.c[k] for k in range(self.order + 1)]) + + __radd__ = __add__ + + def __neg__(self): + return AlphaJet([-item for item in self.c]) + + def __sub__(self, other): + return self + (-AlphaJet(other)) + + def __rsub__(self, other): + return AlphaJet(other) - self + + def __mul__(self, other): + other = AlphaJet(other) + return AlphaJet([ + sum((self.c[k] * other.c[n - k] for k in range(n + 1)), DeltaJet(0)) + for n in range(self.order + 1) + ]) + + __rmul__ = __mul__ + + def inv(self): + result = [self.c[0].inv()] + for n in range(1, self.order + 1): + result.append(-result[0] * sum((self.c[k] * result[n - k] for k in range(1, n + 1)), DeltaJet(0))) + return AlphaJet(result) + + def __truediv__(self, other): + return self * AlphaJet(other).inv() + + def __rtruediv__(self, other): + return AlphaJet(other) / self + + +def alpha_exp_linear(sign, phase0, velocity): + base = (sign * I * acb(phase0)).exp() + slope = sign * I * acb(velocity) + return AlphaJet([ + DeltaJet(base), + DeltaJet(base * slope), + DeltaJet(base * slope * slope / 2), + ]) + + +def alpha_projective_jet(phases0, direction, alpha_box, mirror=False): + delta = DeltaJet([0, 1]) + radius = (1 + delta * delta).sqrt() + half_duration = ap(TAU) / 2 + cosine = AlphaJet((radius * half_duration).cos()) + sine = AlphaJet((radius * half_duration).sin() / radius) + state = [AlphaJet(DeltaJet(1)), AlphaJet(DeltaJet(0))] + + for phase_index in range(CONTROL_DIMENSION): + phase0 = acb(phases0[phase_index] + direction[phase_index] * alpha_box) + velocity = acb(direction[phase_index]) + em = alpha_exp_linear(-1, phase0, velocity) + ep = alpha_exp_linear(1, phase0, velocity) + if not mirror: + matrix = [ + [cosine - AlphaJet(I) * sine * AlphaJet(delta), -AlphaJet(I) * sine * em], + [-AlphaJet(I) * sine * ep, cosine + AlphaJet(I) * sine * AlphaJet(delta)], + ] + else: + matrix = [ + [cosine + AlphaJet(I) * sine * AlphaJet(delta), AlphaJet(I) * sine * ep], + [AlphaJet(I) * sine * em, cosine - AlphaJet(I) * sine * AlphaJet(delta)], + ] + state = alpha_matvec(matrix, state) + + if not mirror: + numerator_weights = [item.conjugate() for item in orthogonal] + denominator_weights = [item.conjugate() for item in target] + else: + numerator_weights = orthogonal + denominator_weights = target + + numerator = AlphaJet(DeltaJet(numerator_weights[0])) * state[0] + AlphaJet(DeltaJet(numerator_weights[1])) * state[1] + denominator = AlphaJet(DeltaJet(denominator_weights[0])) * state[0] + AlphaJet(DeltaJet(denominator_weights[1])) * state[1] + return numerator / denominator + + +def r5_response_directional_hessian(phases0, direction, alpha_box): + z = alpha_projective_jet(phases0, direction, alpha_box, mirror=False) + zbar = alpha_projective_jet(phases0, direction, alpha_box, mirror=True) + values = [] + for order in range(RESPONSE_ORDER + 1): + alpha_second_coeff = ((z.c[2].c[order] + zbar.c[2].c[order]) / 2).real + values.append(2 * alpha_second_coeff) + for order in range(RESPONSE_ORDER + 1): + alpha_second_coeff = ((z.c[2].c[order] - zbar.c[2].c[order]) / (2 * I)).real + values.append(2 * alpha_second_coeff) + return values + + +def r5_leaf_status(gates): + if gates["unique_root"]: + return "CERTIFIED" + if not gates["chart"]: + return "CHART_FAILED" + if not gates["no_wrap"]: + return "NO_WRAP_FAILED" + if not gates["J_eta_invertible"]: + return "JACOBIAN_FAILED" + if not gates["contraction"]: + return "CONTRACTION_FAILED" + if not gates["self_map"]: + return "SELF_MAP_FAILED" + return "INCONCLUSIVE" + + +def r5_formal_radius_record(radius_records): + for item in radius_records: + if item["r_eta"] == r5_formal_radius: + return item + raise RuntimeError("formal radius missing") + + +def r5_main(): + objects = r5_aux["objects"] + P = r5_mat(objects["P"]) + B = r5_mat(objects["B"]) + T = r5_mat(objects["T"]) + N = r5_mat(objects["N"]) + Tv = [T[row][0] for row in range(CONTROL_DIMENSION)] + S = r5_vec(r5_affine["candidate_slope"]["S"]) + NS = r5_matvec(N, S) + w = [Tv[i] + NS[i] for i in range(CONTROL_DIMENSION)] + B_inv = arb_mat(B).inv() + B_defect = r5_matsub(r5_identity(RESPONSE_DIMENSION), r5_matmul([[B_inv[r, c] for c in range(RESPONSE_DIMENSION)] for r in range(RESPONSE_DIMENSION)], B)) + B_defect_norm = r5_inf_norm_upper(B_defect) + + leaf_records = [] + certified_count = 0 + worst_margin = None + worst_leaf = None + max_Y2 = arb(0) + max_Y2_leaf = None + max_Z = arb(0) + max_Z_leaf = None + + for leaf_index, leaf_interval in enumerate(r5_leaves): + left = r5_arb(leaf_interval[0]) + right = r5_arb(leaf_interval[1]) + a_C = (left + right) / 2 + alpha_radius = (right - left).abs_upper() / 2 + alpha = arb(0, str(alpha_radius.upper())) + b_C = r5_newton_correction(a_C) + theta_C = r5_theta(a_C, b_C) + theta_alpha = r5_theta_affine(theta_C, w, alpha, N, [arb(0) for _ in range(RESPONSE_DIMENSION)]) + F0 = r5_F_from_theta(theta_C) + J_alpha = r5_Jalpha_at_theta(theta_C, w) + first_alpha = [alpha * value for value in J_alpha] + Y0 = r5_vec_abs_upper(r5_matvec(P, F0)) + Y1 = r5_vec_abs_upper(r5_matvec(P, first_alpha)) + response_hessian = r5_response_directional_hessian(theta_C, w, alpha) + B_response_hessian = r5_matvec(B, response_hessian) + P_B_response_hessian = r5_matvec(P, B_response_hessian) + H_alpha = r5_vec_abs_upper(P_B_response_hessian) + alpha_radius_arb = r5_arb(str(alpha_radius.upper())) + alpha_radius_squared = alpha_radius_arb * alpha_radius_arb + Y2 = H_alpha * alpha_radius_squared / 2 + if Y2.abs_upper() > max_Y2: + max_Y2 = Y2.abs_upper() + max_Y2_leaf = leaf_index + + component_records = [] + for component in range(RESPONSE_DIMENSION): + component_records.append({ + "component": component, + "raw_D2R3_ww": r5_bound(response_hessian[component]), + "after_B": r5_bound(B_response_hessian[component]), + "after_P": r5_bound(P_B_response_hessian[component]), + "lagrange_contribution_bound": r5_bound(P_B_response_hessian[component].abs_upper() * alpha_radius_squared / 2), + }) + + radius_records = [] + for radius_text in r5_eta_radii: + r_eta = r5_arb(radius_text) + eta = [arb(0, str(r_eta.upper())) for _ in range(RESPONSE_DIMENSION)] + theta_total = r5_theta_affine(theta_C, w, alpha, N, eta) + Y_eta_cross = arb(0) + Y_total = Y0 + Y1 + Y2 + Y_eta_cross + JN_box = r5_JN_at_theta(theta_total) + JN_det = arb_mat(JN_box).det() + Z_mat = r5_matsub(r5_identity(RESPONSE_DIMENSION), r5_matmul(P, JN_box)) + Z = r5_inf_norm_upper(Z_mat) + if radius_text == r5_formal_radius and Z.abs_upper() > max_Z: + max_Z = Z.abs_upper() + max_Z_leaf = leaf_index + Zr = Z * r_eta + image_radius = Y_total + Zr + margin = r_eta - image_radius + if radius_text == r5_formal_radius and (worst_margin is None or margin.lower() < worst_margin.lower()): + worst_margin = margin + worst_leaf = leaf_index + max_displacement = r5_max_phase_displacement(theta_total) + chart_margin = arb(1) - max_displacement + nowrap_margin = arb.pi() - max_displacement + chart_gate = r5_strict_positive(chart_margin) + nowrap_gate = r5_strict_positive(nowrap_margin) + b_gate = bool(B_defect_norm < arb(1) and not B_defect_norm.contains(arb(1))) + det_gate = bool(not JN_det.contains(arb(0)) and JN_det.abs_lower() > arb(0)) + contraction_gate = bool(Z < arb(1) and not Z.contains(arb(1))) + self_map_gate = r5_strict_positive(margin) + unique_root_gate = bool(self_map_gate and contraction_gate and chart_gate and nowrap_gate and b_gate and det_gate) + radius_records.append({ + "r_eta": radius_text, + "chart_margin_lower": str(chart_margin.lower()), + "no_wrap_margin_lower": str(nowrap_margin.lower()), + "B_inverse_defect_upper": str(B_defect_norm.abs_upper().upper()), + "det_J_eta_enclosure": str(JN_det), + "det_J_eta_abs_lower": str(JN_det.abs_lower().lower()), + "Y0_center_residual": r5_bound(Y0), + "Y1_first_order_cancellation_defect": r5_bound(Y1), + "Y2_directional_hessian_lagrange": r5_bound(Y2), + "Y_eta_cross": r5_bound(Y_eta_cross), + "Y_eta_cross_policy": "zero because eta variation is handled by Z*r_eta in the Krawczyk linear term, not by interval-subtracted forcing", + "Y_total": r5_bound(Y_total), + "Z": r5_bound(Z), + "Z_times_r_eta": r5_bound(Zr), + "krawczyk_image_radius_upper": str(image_radius.abs_upper().upper()), + "strict_self_map_margin": r5_bound(margin), + "contraction_upper": str(Z.abs_upper().upper()), + "gates": { + "chart": chart_gate, + "no_wrap": nowrap_gate, + "B_inverse": b_gate, + "J_eta_invertible": det_gate, + "self_map": self_map_gate, + "contraction": contraction_gate, + "unique_root": unique_root_gate, + }, + }) + + formal_record = r5_formal_radius_record(radius_records) + leaf_status = r5_leaf_status(formal_record["gates"]) + if leaf_status == "CERTIFIED": + certified_count += 1 + leaf_records.append({ + "leaf_index": leaf_index, + "leaf_interval": leaf_interval, + "endpoint_rule": "closed interval enclosure; adjacent branch gluing is deferred", + "a_C": str(a_C), + "alpha_radius": r5_bound(alpha_radius_arb), + "b_C": r5_bound_vector(b_C), + "S": r5_bound_vector(S), + "w": r5_bound_vector(w), + "P_F_at_center_inf_norm": r5_bound(Y0), + "directional_hessian_components": component_records, + "H_alpha": r5_bound(H_alpha), + "Y0": r5_bound(Y0), + "Y1": r5_bound(Y1), + "Y2": r5_bound(Y2), + "radius_records": radius_records, + "formal_radius": r5_formal_radius, + "formal_radius_status": leaf_status, + "formal_radius_record": formal_record, + }) + + all_pass = certified_count == len(r5_leaves) + if all_pass: + status = "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_CERTIFIED" + elif certified_count < len(r5_leaves): + status = "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_NOT_CERTIFIED" + else: + status = "R5_ALL_LEAVES_HESSIAN_KRAWCZYK_INCONCLUSIVE" + + record = { + "schema_version": "1.0", + "record_id": "r5_all_leaves_hessian_krawczyk_v1_0", + "record_kind": "prospective_r5_b2_all_leaves_hessian_krawczyk_preflight", + "scientific_status": status, + "arb_precision_bits": PRECISION_BITS, + "base_commit": os.environ["R5_B2_BASE_COMMIT"], + "software_environment": {"python": platform.python_version(), "python_flint": "0.8.0"}, + "inputs": { + "parent_protocol_sha256": os.environ["R5_B2_PARENT_SHA"], + "protocol_sha256": os.environ["R5_B2_PROTOCOL_SHA"], + "auxiliary_sha256": os.environ["R5_B2_AUX_SHA"], + "static_certificate_sha256": os.environ["R5_B2_STATIC_SHA"], + "b1e_certificate_sha256": os.environ["R5_B2_B1E_SHA"], + "affine_diagnostic_sha256": os.environ["R5_B2_AFFINE_SHA"], + "v0_7_4_source_sha256": os.environ["R5_B2_V074_SHA"], + "object_sha256": r5_aux["object_sha256"], + }, + "frozen_protocol": { + "leaf_list": r5_leaves, + "leaf_order": "increasing t from -1e-12 to 1e-12", + "endpoint_rule": "closed Arb intervals per leaf; overlap consistency deferred to B3", + "center_rule": "a_C=(left+right)/2", + "normal_center_rule": "b_C=-P*F(a_C,0) using frozen P and zero normal seed", + "fixed_slope_source": "B1c/B1e S reused for every leaf without refit", + "directional_hessian_formula": "Y2_i <= 1/2 sup ||P*B*D2R3(theta_C,i+(T*v+N*S)alpha)[w,w]||_inf * alpha_radius^2", + "formal_eta_radius": r5_formal_radius, + "eta_radii_predeclared": r5_eta_radii, + "precision_bits": PRECISION_BITS, + "result_adaptive_changes_allowed": False, + }, + "method": { + "equation": "F_i(alpha,eta)=B(R3(theta_C,i+(T*v+N*S)*alpha+N*eta)-c)", + "w_definition": "w=T*v+N*S", + "Y_total_decomposition": "Y0+Y1+Y2+Y_eta_cross", + "Y2_source": "explicit directional-Hessian Lagrange remainder computed per leaf", + "B1c_interval_subtraction_used_as_Y2": False, + "finite_difference_used_as_strict_bound": False, + "binary64_theorem_decision_used": False, + "one_half_factor_included": True, + "alpha_radius_squared_included": True, + "Y_eta_cross_included": True, + "eta_variation_handled_by_Z_times_radius": True, + }, + "leaf_records": leaf_records, + "summary": { + "leaf_count": len(r5_leaves), + "certified_leaf_count": certified_count, + "worst_leaf_by_formal_self_map_margin": worst_leaf, + "minimum_formal_self_map_margin": r5_bound(worst_margin if worst_margin is not None else arb(0)), + "max_Y2_leaf": max_Y2_leaf, + "max_Y2_abs_upper": r5_bound(max_Y2), + "max_Z_leaf_at_formal_radius": max_Z_leaf, + "max_Z_abs_upper_at_formal_radius": r5_bound(max_Z), + "endpoint_or_branch_anomaly_detected": False, + "can_enter_B3_gluing": all_pass, + }, + "scope": { + "all_leaf_local_root_gates_pass": all_pass, + "r5_all_leaves_locally_certified": all_pass, + "adjacent_leaf_gluing_certified": False, + "full_path_continuity_certified": False, + "positive_measure_nonconstancy_certified": False, + "zero_cost_full_path_certified": False, + "principle_r_r6_supplied": False, + "r5_certified": False, + "global_ode_flow_certified": False, + "r6_search_performed": False, + "normal_K1_residual_recovery_performed": False, + "other_leaf_inspected_outside_frozen_16": False, + }, + } + payload = json.loads(json.dumps(record, sort_keys=True)) + payload.pop("record_sha256", None) + payload.get("software_environment", {}).pop("python", None) + record["record_sha256"] = hashlib.sha256(json.dumps(payload, sort_keys=True, separators=(",", ":"), ensure_ascii=True, allow_nan=False).encode("utf-8")).hexdigest() + r5_output.parent.mkdir(parents=True, exist_ok=True) + r5_output.write_text(json.dumps(record, sort_keys=True, separators=(",", ":"), ensure_ascii=True, allow_nan=False) + "\n", encoding="utf-8") + + +r5_main() +raise SystemExit(0) +''' + return textwrap.indent(textwrap.dedent(code).strip("\n") + "\n", " ") + + +def patch_frozen_source(source: bytes) -> str: + text = source.decode("utf-8") + needle = ''' banner( + "STAGE A FROZEN-SOLVE DESCENT / " + "STAGE B FROZEN KKT-WITNESS ALIGNMENT" + ) +''' + if text.count(needle) != 1: + raise RuntimeError("frozen Stage-A insertion point not unique") + return text.replace(needle, injection() + needle) + + +def build_record() -> dict[str, Any]: + check_upstream_identity() + with tempfile.TemporaryDirectory(prefix="r5_b2_all_leaves_") as tmp: + output = Path(tmp) / "r5_all_leaves_hessian_krawczyk_v1_0.json" + patched = Path(tmp) / "_r5_b2_backend.py" + patched.write_text(patch_frozen_source(V074_SOURCE.read_bytes()), encoding="utf-8") + env = dict(os.environ) + env.update({ + "R5_B2_OUTPUT": str(output), + "R5_B2_AUX": str(AUX_PATH), + "R5_B2_AFFINE": str(AFFINE_DIAG_PATH), + "R5_B2_BASE_COMMIT": EXPECTED_BASE_COMMIT, + "R5_B2_PARENT_SHA": preflight.EXPECTED_PARENT_PROTOCOL_SHA256, + "R5_B2_PROTOCOL_SHA": preflight.EXPECTED_PROTOCOL_SHA256, + "R5_B2_AUX_SHA": preflight.EXPECTED_AUXILIARY_SHA256, + "R5_B2_STATIC_SHA": preflight.EXPECTED_STATIC_CERT_SHA256, + "R5_B2_B1E_SHA": EXPECTED_B1E_CERT_SHA256, + "R5_B2_AFFINE_SHA": EXPECTED_AFFINE_DIAG_SHA256, + "R5_B2_V074_SHA": preflight.EXPECTED_V074_SOURCE_SHA256, + "R5_B2_LEAVES": json.dumps(LEAVES), + "R5_B2_ETA_RADII": json.dumps(ETA_RADII), + "R5_B2_FORMAL_RADIUS": FORMAL_RADIUS, + }) + completed = subprocess.run( + [ + sys.executable, + str(patched), + "--inputs-zip", + str(ROOT / "inputs" / "response_fibre_v0_6_2_backend_inputs.zip"), + "--output", + str(Path(tmp) / "unused"), + ], + env=env, + stdout=subprocess.PIPE, + stderr=subprocess.PIPE, + text=True, + ) + if completed.returncode != 0: + raise RuntimeError(f"patched backend failed\nSTDOUT:\n{completed.stdout}\nSTDERR:\n{completed.stderr}") + return read_json(output) + + +def write_record(record: dict[str, Any]) -> Path: + target = CERT_PATH if record.get("scientific_status") == CERTIFIED else DIAG_PATH + stale = DIAG_PATH if target == CERT_PATH else CERT_PATH + if stale.exists(): + stale.unlink() + target.parent.mkdir(parents=True, exist_ok=True) + target.write_text(json.dumps(record, sort_keys=True, separators=(",", ":"), ensure_ascii=True, allow_nan=False) + "\n", encoding="utf-8") + return target + + +def main() -> int: + record = build_record() + target = write_record(record) + print(json.dumps({ + "scientific_status": record["scientific_status"], + "target": str(target.relative_to(ROOT)), + "record_sha256": record["record_sha256"], + "certified_leaf_count": record["summary"]["certified_leaf_count"], + "leaf_count": record["summary"]["leaf_count"], + "worst_leaf_by_formal_self_map_margin": record["summary"]["worst_leaf_by_formal_self_map_margin"], + "can_enter_B3_gluing": record["summary"]["can_enter_B3_gluing"], + }, indent=2, sort_keys=True)) + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py b/research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py new file mode 100644 index 00000000..ffb171eb --- /dev/null +++ b/research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py @@ -0,0 +1,316 @@ +#!/usr/bin/env python3 +"""Verify the R5-B2 all-leaves Hessian Krawczyk preflight record.""" + +from __future__ import annotations + +import argparse +import copy +import json +import re +from decimal import Decimal, InvalidOperation +from pathlib import Path +from typing import Any + +import certify_r5_all_leaves_hessian_krawczyk as builder +import certify_r5_first_leaf_preflight as preflight + + +HERE = Path(__file__).resolve().parent +CERT_PATH = HERE / "certificates" / "r5_all_leaves_hessian_krawczyk_v1_0.json" +DIAG_PATH = HERE / "diagnostics" / "r5_all_leaves_hessian_krawczyk_v1_0.json" +RECORD_PATH = CERT_PATH if CERT_PATH.exists() else DIAG_PATH + +ARB_RE = re.compile( + r"^\[(?P[+-]?(?:\d+(?:\.\d*)?|\.\d+)(?:[eE][+-]?\d+)?) " + r"\+/- (?P(?:\d+(?:\.\d*)?|\.\d+)(?:[eE][+-]?\d+)?)\]$" +) +ZERO_ARB_RE = re.compile(r"^\[\+/- (?P(?:\d+(?:\.\d*)?|\.\d+)(?:[eE][+-]?\d+)?)\]$") + + +def read_json(path: Path) -> Any: + return json.loads(path.read_text(encoding="utf-8")) + + +def decimal_bounds(value: Any) -> tuple[Decimal, Decimal] | None: + if not isinstance(value, str): + return None + try: + parsed = Decimal(value) + except (InvalidOperation, ValueError, OverflowError): + match = ARB_RE.match(value) + if match: + mid = Decimal(match.group("mid")) + rad = Decimal(match.group("rad")) + else: + zero = ZERO_ARB_RE.match(value) + if not zero: + return None + mid = Decimal("0") + rad = Decimal(zero.group("rad")) + lower = mid - rad + upper = mid + rad + else: + lower = upper = parsed + if not lower.is_finite() or not upper.is_finite() or lower > upper: + return None + return lower, upper + + +def lower(value: Any) -> Decimal: + bounds = decimal_bounds(value) + if bounds is None: + raise ValueError(value) + return bounds[0] + + +def upper(value: Any) -> Decimal: + bounds = decimal_bounds(value) + if bounds is None: + raise ValueError(value) + return bounds[1] + + +def bound_record(value: Any) -> bool: + if not isinstance(value, dict): + return False + required = {"enclosure", "lower", "upper", "abs_lower", "abs_upper", "contains_zero"} + return ( + set(value) == required + and all(decimal_bounds(value[key]) is not None for key in ["enclosure", "lower", "upper", "abs_lower", "abs_upper"]) + and isinstance(value["contains_zero"], bool) + ) + + +def comparable(value: dict[str, Any]) -> dict[str, Any]: + return builder.digest_payload(value) + + +def gates_valid(gates: Any) -> bool: + return ( + isinstance(gates, dict) + and set(gates) == {"chart", "no_wrap", "B_inverse", "J_eta_invertible", "self_map", "contraction", "unique_root"} + and all(isinstance(value, bool) for value in gates.values()) + ) + + +def radius_records_valid(records: Any) -> bool: + if not isinstance(records, list) or [item.get("r_eta") for item in records] != builder.ETA_RADII: + return False + for item in records: + if not isinstance(item, dict): + return False + for key in [ + "Y0_center_residual", + "Y1_first_order_cancellation_defect", + "Y2_directional_hessian_lagrange", + "Y_eta_cross", + "Y_total", + "Z", + "Z_times_r_eta", + "strict_self_map_margin", + ]: + if not bound_record(item.get(key)): + return False + if not gates_valid(item.get("gates")): + return False + if item.get("Y_eta_cross_policy") != "zero because eta variation is handled by Z*r_eta in the Krawczyk linear term, not by interval-subtracted forcing": + return False + gates = item["gates"] + margin_positive = lower(item["strict_self_map_margin"]["lower"]) > 0 + expected_unique = bool(margin_positive and all(gates[key] for key in ["chart", "no_wrap", "B_inverse", "J_eta_invertible", "contraction"])) + if gates["unique_root"] != expected_unique: + return False + return True + + +def leaf_records_valid(leaves: Any, status: str) -> bool: + if not isinstance(leaves, list) or len(leaves) != 16: + return False + seen = set() + all_formal_pass = True + for expected_index, leaf in enumerate(leaves): + if not isinstance(leaf, dict): + return False + if leaf.get("leaf_index") != expected_index: + return False + interval = leaf.get("leaf_interval") + if interval != builder.LEAVES[expected_index]: + return False + key = tuple(interval) + if key in seen: + return False + seen.add(key) + if leaf.get("endpoint_rule") != "closed interval enclosure; adjacent branch gluing is deferred": + return False + if leaf.get("formal_radius") != builder.FORMAL_RADIUS: + return False + if leaf.get("formal_radius_status") not in {"CERTIFIED", "SELF_MAP_FAILED", "CONTRACTION_FAILED", "CHART_FAILED", "NO_WRAP_FAILED", "JACOBIAN_FAILED", "IMPLEMENTATION_ERROR", "INCONCLUSIVE"}: + return False + for key_name in ["alpha_radius", "P_F_at_center_inf_norm", "H_alpha", "Y0", "Y1", "Y2"]: + if not bound_record(leaf.get(key_name)): + return False + for key_name, expected_len in [("b_C", 8), ("S", 8), ("w", 14)]: + if not isinstance(leaf.get(key_name), list) or len(leaf[key_name]) != expected_len: + return False + if not all(bound_record(item) for item in leaf[key_name]): + return False + components = leaf.get("directional_hessian_components") + if not isinstance(components, list) or len(components) != 8: + return False + if [item.get("component") for item in components] != list(range(8)): + return False + for component in components: + for key_name in ["raw_D2R3_ww", "after_B", "after_P", "lagrange_contribution_bound"]: + if not bound_record(component.get(key_name)): + return False + if not radius_records_valid(leaf.get("radius_records")): + return False + formal = leaf.get("formal_radius_record") + if not isinstance(formal, dict) or formal.get("r_eta") != builder.FORMAL_RADIUS: + return False + if not gates_valid(formal.get("gates")): + return False + if formal["gates"]["unique_root"] != (leaf.get("formal_radius_status") == "CERTIFIED"): + return False + all_formal_pass = all_formal_pass and formal["gates"]["unique_root"] + return all_formal_pass == (status == builder.CERTIFIED) + + +def verify(record: dict[str, Any], expected: dict[str, Any] | None = None) -> dict[str, bool]: + if expected is None: + expected = builder.build_record() + status = record.get("scientific_status") + inputs = record.get("inputs", {}) + protocol = record.get("frozen_protocol", {}) + method = record.get("method", {}) + summary = record.get("summary", {}) + scope = record.get("scope", {}) + leaves = record.get("leaf_records") + certified_count = sum(1 for leaf in leaves if isinstance(leaf, dict) and leaf.get("formal_radius_status") == "CERTIFIED") if isinstance(leaves, list) else -1 + + checks = { + "record_matches_recomputed_arb_record": comparable(record) == comparable(expected), + "record_sha256": record.get("record_sha256") == builder.sha256_bytes(builder.canonical_json(comparable(record))), + "schema_version": record.get("schema_version") == "1.0", + "record_id": record.get("record_id") == "r5_all_leaves_hessian_krawczyk_v1_0", + "record_kind": record.get("record_kind") == "prospective_r5_b2_all_leaves_hessian_krawczyk_preflight", + "scientific_status_allowed": status in builder.ALLOWED_STATUSES, + "scientific_status_consistent": ( + (status == builder.CERTIFIED and certified_count == 16) + or (status == builder.NOT_CERTIFIED and 0 <= certified_count < 16) + or status in {builder.INCONCLUSIVE, builder.BOUNDARY_MISMATCH, builder.IMPLEMENTATION_ERROR} + ), + "arb_precision": record.get("arb_precision_bits") == 192, + "base_commit": record.get("base_commit") == builder.EXPECTED_BASE_COMMIT, + "input_hashes": ( + inputs.get("parent_protocol_sha256") == preflight.EXPECTED_PARENT_PROTOCOL_SHA256 + and inputs.get("protocol_sha256") == preflight.EXPECTED_PROTOCOL_SHA256 + and inputs.get("auxiliary_sha256") == preflight.EXPECTED_AUXILIARY_SHA256 + and inputs.get("static_certificate_sha256") == preflight.EXPECTED_STATIC_CERT_SHA256 + and inputs.get("b1e_certificate_sha256") == builder.EXPECTED_B1E_CERT_SHA256 + and inputs.get("affine_diagnostic_sha256") == builder.EXPECTED_AFFINE_DIAG_SHA256 + and inputs.get("v0_7_4_source_sha256") == preflight.EXPECTED_V074_SOURCE_SHA256 + and inputs.get("object_sha256") == preflight.EXPECTED_OBJECT_SHA256 + ), + "frozen_protocol": ( + protocol.get("leaf_list") == builder.LEAVES + and protocol.get("leaf_order") == "increasing t from -1e-12 to 1e-12" + and protocol.get("endpoint_rule") == "closed Arb intervals per leaf; overlap consistency deferred to B3" + and protocol.get("center_rule") == "a_C=(left+right)/2" + and protocol.get("normal_center_rule") == "b_C=-P*F(a_C,0) using frozen P and zero normal seed" + and protocol.get("fixed_slope_source") == "B1c/B1e S reused for every leaf without refit" + and protocol.get("formal_eta_radius") == builder.FORMAL_RADIUS + and protocol.get("eta_radii_predeclared") == builder.ETA_RADII + and protocol.get("precision_bits") == 192 + and protocol.get("result_adaptive_changes_allowed") is False + ), + "method": ( + method.get("equation") == "F_i(alpha,eta)=B(R3(theta_C,i+(T*v+N*S)*alpha+N*eta)-c)" + and method.get("w_definition") == "w=T*v+N*S" + and method.get("Y_total_decomposition") == "Y0+Y1+Y2+Y_eta_cross" + and method.get("Y2_source") == "explicit directional-Hessian Lagrange remainder computed per leaf" + and method.get("B1c_interval_subtraction_used_as_Y2") is False + and method.get("finite_difference_used_as_strict_bound") is False + and method.get("binary64_theorem_decision_used") is False + and method.get("one_half_factor_included") is True + and method.get("alpha_radius_squared_included") is True + and method.get("Y_eta_cross_included") is True + and method.get("eta_variation_handled_by_Z_times_radius") is True + ), + "leaf_records": leaf_records_valid(leaves, status), + "summary": ( + summary.get("leaf_count") == 16 + and summary.get("certified_leaf_count") == certified_count + and summary.get("worst_leaf_by_formal_self_map_margin") in range(16) + and bound_record(summary.get("minimum_formal_self_map_margin")) + and summary.get("max_Y2_leaf") in range(16) + and bound_record(summary.get("max_Y2_abs_upper")) + and summary.get("max_Z_leaf_at_formal_radius") in range(16) + and bound_record(summary.get("max_Z_abs_upper_at_formal_radius")) + and isinstance(summary.get("endpoint_or_branch_anomaly_detected"), bool) + and summary.get("can_enter_B3_gluing") == (status == builder.CERTIFIED) + ), + "scope": ( + scope.get("all_leaf_local_root_gates_pass") == (status == builder.CERTIFIED) + and scope.get("r5_all_leaves_locally_certified") == (status == builder.CERTIFIED) + and scope.get("adjacent_leaf_gluing_certified") is False + and scope.get("full_path_continuity_certified") is False + and scope.get("positive_measure_nonconstancy_certified") is False + and scope.get("zero_cost_full_path_certified") is False + and scope.get("principle_r_r6_supplied") is False + and scope.get("r5_certified") is False + and scope.get("global_ode_flow_certified") is False + and scope.get("r6_search_performed") is False + and scope.get("normal_K1_residual_recovery_performed") is False + and scope.get("other_leaf_inspected_outside_frozen_16") is False + ), + } + return checks + + +def mutation_cases(record: dict[str, Any]) -> dict[str, dict[str, Any]]: + cases: dict[str, dict[str, Any]] = {} + mutated = copy.deepcopy(record); mutated["frozen_protocol"]["leaf_list"][0] = ["-1e-12", "-9e-13"]; cases["leaf_endpoint_change_fails"] = mutated + mutated = copy.deepcopy(record); mutated["frozen_protocol"]["leaf_list"][0], mutated["frozen_protocol"]["leaf_list"][1] = mutated["frozen_protocol"]["leaf_list"][1], mutated["frozen_protocol"]["leaf_list"][0]; cases["leaf_order_change_fails"] = mutated + mutated = copy.deepcopy(record); mutated["leaf_records"][1] = copy.deepcopy(mutated["leaf_records"][0]); cases["duplicate_leaf_fails"] = mutated + mutated = copy.deepcopy(record); mutated["leaf_records"] = mutated["leaf_records"][:-1]; cases["missing_leaf_fails"] = mutated + mutated = copy.deepcopy(record); mutated["inputs"]["b1e_certificate_sha256"] = "0" * 64; cases["b1e_sha_change_fails"] = mutated + mutated = copy.deepcopy(record); mutated["leaf_records"][0]["Y2"]["abs_upper"] = "1e-99"; cases["hessian_bound_tamper_fails"] = mutated + mutated = copy.deepcopy(record); mutated["method"]["one_half_factor_included"] = False; cases["missing_half_factor_fails"] = mutated + mutated = copy.deepcopy(record); mutated["frozen_protocol"]["formal_eta_radius"] = "1e-22"; cases["formal_radius_change_fails"] = mutated + mutated = copy.deepcopy(record); mutated["leaf_records"][0]["formal_radius_record"]["strict_self_map_margin"]["lower"] = "-1e-30"; cases["self_map_margin_tamper_fails"] = mutated + mutated = copy.deepcopy(record); mutated["leaf_records"][0]["formal_radius_record"]["contraction_upper"] = "2"; cases["contraction_bound_tamper_fails"] = mutated + mutated = copy.deepcopy(record); mutated["leaf_records"][0]["formal_radius_record"]["gates"]["unique_root"] = False; cases["unique_root_false_fails"] = mutated + mutated = copy.deepcopy(record); mutated["scope"]["r5_certified"] = True; cases["local_success_as_r5_certified_fails"] = mutated + mutated = copy.deepcopy(record); mutated["scope"]["principle_r_r6_supplied"] = True; cases["principle_r_r6_forged_fails"] = mutated + mutated = copy.deepcopy(record); mutated["scope"]["global_ode_flow_certified"] = True; cases["global_flow_forged_fails"] = mutated + mutated = copy.deepcopy(record); mutated["scope"]["r6_search_performed"] = True; cases["R6_marked_run_fails"] = mutated + mutated = copy.deepcopy(record); mutated["scope"]["normal_K1_residual_recovery_performed"] = True; cases["normal_K1_marked_run_fails"] = mutated + mutated = copy.deepcopy(record); mutated["method"]["B1c_interval_subtraction_used_as_Y2"] = True; cases["interval_subtraction_reintroduced_fails"] = mutated + mutated = copy.deepcopy(record); mutated["method"]["Y_eta_cross_included"] = False; cases["missing_Y_eta_cross_fails"] = mutated + return cases + + +def run_mutation_tests(record: dict[str, Any], expected: dict[str, Any]) -> dict[str, bool]: + return {name: not all(verify(case, expected).values()) for name, case in mutation_cases(record).items()} + + +def main() -> int: + parser = argparse.ArgumentParser() + parser.add_argument("--mutation-tests", action="store_true") + args = parser.parse_args() + record = read_json(RECORD_PATH) + expected = builder.build_record() + checks = verify(record, expected) + if args.mutation_tests: + checks.update(run_mutation_tests(record, expected)) + print(json.dumps(checks, indent=2, sort_keys=True)) + if not all(checks.values()): + print("FAIL") + return 1 + print("PASS") + return 0 + + +if __name__ == "__main__": + raise SystemExit(main())