{
  "generated_utc": "2026-09-05T23:29:14.429957+00:00",
  "status": "PASS",
  "target": "ComplementedSubspace.realMainTheorem",
  "generator": "LEAN_PROJECT\\verification\\independent-audit-2026-09-05\\generate_verification_report.py",
  "generator_sha256": "a2827b0dd3fc77da66f1274a5f3cd7ec6e45810c89ed7ce530341cb21f09fb52",
  "issues": [],
  "conditions": [
    {
      "condition": "Compiler steps must not have duplicate records",
      "passed": true,
      "detail": [
        "clean",
        "build",
        "direct main source check",
        "theorem identity",
        "exact definitions",
        "axioms",
        "whole imported project axiom audit",
        "kernel dependency traversal"
      ]
    },
    {
      "condition": "Passed pipeline must record all eight required steps in order",
      "passed": true,
      "detail": [
        "clean",
        "build",
        "direct main source check",
        "theorem identity",
        "exact definitions",
        "axioms",
        "whole imported project axiom audit",
        "kernel dependency traversal"
      ]
    },
    {
      "condition": "Compiler step 'clean' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'clean' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "clean",
        "complemented_subspace_trial"
      ]
    },
    {
      "condition": "Compiler step 'clean' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'clean' 'complemented_subspace_trial'"
    },
    {
      "condition": "Compiler step 'clean' must reference clean.log",
      "passed": true,
      "detail": "clean.log"
    },
    {
      "condition": "Compiler step 'clean' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "clean.log command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "clean.log must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "clean.log start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "clean.log must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'build' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'build' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "build",
        "+ComplementedSubspace:olean"
      ]
    },
    {
      "condition": "Compiler step 'build' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'build' '+ComplementedSubspace:olean'"
    },
    {
      "condition": "Compiler step 'build' must reference build.log",
      "passed": true,
      "detail": "build.log"
    },
    {
      "condition": "Compiler step 'build' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "build.log command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "build.log must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "build.log start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "build.log must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'direct main source check' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'direct main source check' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "env",
        "lean",
        "-j1",
        "-M8192",
        "ComplementedSubspace/RealMainTheorem.lean"
      ]
    },
    {
      "condition": "Compiler step 'direct main source check' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'env' 'lean' '-j1' '-M8192' 'ComplementedSubspace/RealMainTheorem.lean'"
    },
    {
      "condition": "Compiler step 'direct main source check' must reference main_source_check.log",
      "passed": true,
      "detail": "main_source_check.log"
    },
    {
      "condition": "Compiler step 'direct main source check' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "main_source_check.log command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "main_source_check.log must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "main_source_check.log start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "main_source_check.log must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'theorem identity' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'theorem identity' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "env",
        "lean",
        "-j1",
        "-M8192",
        "verification/independent-audit-2026-09-05/MainIdentity.lean"
      ]
    },
    {
      "condition": "Compiler step 'theorem identity' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'env' 'lean' '-j1' '-M8192' 'verification/independent-audit-2026-09-05/MainIdentity.lean'"
    },
    {
      "condition": "Compiler step 'theorem identity' must reference theorem_check.txt",
      "passed": true,
      "detail": "theorem_check.txt"
    },
    {
      "condition": "Compiler step 'theorem identity' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "theorem_check.txt command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "theorem_check.txt must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "theorem_check.txt start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "theorem_check.txt must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'exact definitions' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'exact definitions' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "env",
        "lean",
        "-j1",
        "-M8192",
        "verification/independent-audit-2026-09-05/PrintDefinitions.lean"
      ]
    },
    {
      "condition": "Compiler step 'exact definitions' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'env' 'lean' '-j1' '-M8192' 'verification/independent-audit-2026-09-05/PrintDefinitions.lean'"
    },
    {
      "condition": "Compiler step 'exact definitions' must reference definitions.txt",
      "passed": true,
      "detail": "definitions.txt"
    },
    {
      "condition": "Compiler step 'exact definitions' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "definitions.txt command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "definitions.txt must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "definitions.txt start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "definitions.txt must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'axioms' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'axioms' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "env",
        "lean",
        "-j1",
        "-M8192",
        "verification/independent-audit-2026-09-05/PrintAxioms.lean"
      ]
    },
    {
      "condition": "Compiler step 'axioms' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'env' 'lean' '-j1' '-M8192' 'verification/independent-audit-2026-09-05/PrintAxioms.lean'"
    },
    {
      "condition": "Compiler step 'axioms' must reference axioms.txt",
      "passed": true,
      "detail": "axioms.txt"
    },
    {
      "condition": "Compiler step 'axioms' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "axioms.txt command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "axioms.txt must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "axioms.txt start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "axioms.txt must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'whole imported project axiom audit' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'whole imported project axiom audit' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "env",
        "lean",
        "-j1",
        "-M8192",
        "WholeProjectAudit.lean"
      ]
    },
    {
      "condition": "Compiler step 'whole imported project axiom audit' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'env' 'lean' '-j1' '-M8192' 'WholeProjectAudit.lean'"
    },
    {
      "condition": "Compiler step 'whole imported project axiom audit' must reference whole_project_axioms.txt",
      "passed": true,
      "detail": "whole_project_axioms.txt"
    },
    {
      "condition": "Compiler step 'whole imported project axiom audit' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "whole_project_axioms.txt command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "whole_project_axioms.txt must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "whole_project_axioms.txt start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "whole_project_axioms.txt must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Compiler step 'kernel dependency traversal' must exit 0",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Compiler step 'kernel dependency traversal' arguments must match the required check",
      "passed": true,
      "detail": [
        "--no-cache",
        "env",
        "lean",
        "-j1",
        "-M8192",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean"
      ]
    },
    {
      "condition": "Compiler step 'kernel dependency traversal' must execute the exact audited portable Lake command",
      "passed": true,
      "detail": "& 'WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lake.exe' '--no-cache' 'env' 'lean' '-j1' '-M8192' 'verification/independent-audit-2026-09-05/TraceDependencies.lean'"
    },
    {
      "condition": "Compiler step 'kernel dependency traversal' must reference dependency_trace_run.txt",
      "passed": true,
      "detail": "dependency_trace_run.txt"
    },
    {
      "condition": "Compiler step 'kernel dependency traversal' must have start/end timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "dependency_trace_run.txt command must agree with run_status.json",
      "passed": true,
      "detail": null
    },
    {
      "condition": "dependency_trace_run.txt must run in the audited project",
      "passed": true,
      "detail": null
    },
    {
      "condition": "dependency_trace_run.txt start/end UTC instants must match its command record (trailing fractional zeroes may differ)",
      "passed": true,
      "detail": null
    },
    {
      "condition": "dependency_trace_run.txt must contain one completed exit-0 footer",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Fresh clean must leave zero root-project .olean files",
      "passed": true,
      "detail": [
        "0"
      ]
    },
    {
      "condition": "Stored theorem kind/type/no-parameters assertion must appear in the successful identity log",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Successful #check output must name the exact target and statement",
      "passed": true,
      "detail": null
    },
    {
      "condition": "All thirteen requested definitions plus the supporting Block abbreviation must appear in actual compiler output",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Whole imported-project axiom audit must report its completed declaration inspection",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Original source snapshot must have unique paths",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Original-source scan scope must include all 230 pre-existing Lean files",
      "passed": true,
      "detail": 230
    },
    {
      "condition": "Before/after SHA256, byte lengths, and original path inventory must agree exactly",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Current original sources/configuration must still match the final snapshot",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Source-immutability completion marker must match the snapshot count",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Executable-source token count 'sorry' must be zero",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Executable-source token count 'admit' must be zero",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Executable-source token count 'sorryAx' must be zero",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Executable-source token count 'axiom' must be zero",
      "passed": true,
      "detail": 0
    },
    {
      "condition": "Source scanner must have zero lexical/import errors",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Source scanner must have zero placeholder/trust-bypass candidates",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Independent rg and Python local-source inventories must agree",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Independent inventories must have no unmatched files",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Scanner must not silently skip directory symlinks",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Source scanner must observe stable source hashes",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Source-lexer self-test must pass",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Scanner file count must equal its complete inventory",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Scanner must cover every original Lean source at its snapshotted hash",
      "passed": true,
      "detail": {
        "missing": [],
        "different": []
      }
    },
    {
      "condition": "All scanned files, including audit helpers, must still match the scanner inventory",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Configured root's complete local syntactic import closure must contain 177 modules",
      "passed": true,
      "detail": 177
    },
    {
      "condition": "Fresh build.log must report Built for every root-closure local module",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Successful fresh build must have an .olean for every configured-root local module",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Exactly three local allowUnsafeReducibility settings must be recorded",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Captured pinned Lean reducibility implementation must match its current source hash",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved initial run must record failure at the theorem identity helper",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Initial failed run must preserve successful clean/build/direct-source checks and exit-1 identity attempt",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Resumed pipeline must preserve the first three successful commands/results exactly and their timestamp instants unchanged",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved failed helper must have executed the exact recorded identity-check command",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved failed helper log must match its original command and timestamps",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved failed helper log must explicitly retain exit 1",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved helper failure must have exactly the unsupported pp.width diagnostic",
      "passed": true,
      "detail": [
        "verification/independent-audit-2026-09-05/MainIdentity.lean:5:0: error: Unknown option `pp.width`"
      ]
    },
    {
      "condition": "Preserved failed helper output must show both checks, standard axioms, and stored-type assertion without treating its exit-1 run as success",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Successful corrected pipeline must link its preserved initial failure using resumedFrom",
      "passed": true,
      "detail": null
    },
    {
      "condition": "MainIdentity.lean must differ byte-for-byte from its preserved original only by removing line 5: set_option pp.width 110",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved MainIdentity.lean must match the initial scanner's original SHA256",
      "passed": true,
      "detail": null
    },
    {
      "condition": "PrintDefinitions.lean must differ byte-for-byte from its preserved original only by removing line 5: set_option pp.width 110",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved PrintDefinitions.lean must match the initial scanner's original SHA256",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Dependency auditor must differ from preserved helper bytes only by the ten explicit IO-to-MetaM lift replacements",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Corrected dependency auditor must use all ten explicit lifts without an evaluation/trust bypass",
      "passed": true,
      "detail": []
    },
    {
      "condition": "Preserved dependency helper must match the pre-IO-fix scanner's SHA256",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved second run must record dependency-helper failure after the display-option correction",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved dependency failure must have seven successful core steps followed by exit-1 walker",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Walker retry must retain the seven successful commands/results exactly and their UTC timestamp instants unchanged",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Failed walker must have used the exact audited dependency-traversal command",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved failed walker log must match its command and project directory",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved failed walker log must match the recorded UTC instants",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved failed dependency helper must retain exit code 1",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved helper must contain the ten failing IO lifts and one unchanged run_cmd inspection entry",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Preserved walker failure must contain exactly ten IO-monad mismatches and the recovery-placeholder evaluation abort",
      "passed": true,
      "detail": [
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:59:2: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:60:17: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:61:17: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:62:19: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:83:6: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:117:6: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:136:10: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:140:12: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:176:2: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:177:2: error: Type mismatch",
        "verification/independent-audit-2026-09-05/TraceDependencies.lean:191:0: error: Aborting evaluation since the expression depends on the 'sorry' axiom, which can lead to runtime instability and crashes."
      ]
    },
    {
      "condition": "All ten preserved walker type errors must specifically compare CommandElabM against MetaM",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Successful walker retry must link its preserved second failure using dependencyResumedFrom",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Environment evidence must include exact Lean and Lake version commands",
      "passed": true,
      "detail": null
    },
    {
      "condition": "Lean/Lake version command must succeed and agree with the pinned toolchain",
      "passed": true,
      "detail": {
        "command": "\"WORKSPACE\\tmp\\lean_library_definition_audit_2026-09-05\\lean-4.34.0-rc2-windows\\bin\\lean.exe\" --version",
        "stdout": "Lean (version 4.34.0-rc2, x86_64-w64-windows-gnu, commit 6a10ac8c22beadecabdbb0919c2b50214762f91d, Release)",
        "stderr": "",
        "exit_code": 0,
        "cwd": "LEAN_PROJECT"
      }
    },
    {
      "condition": "Lean/Lake version command must succeed and agree with the pinned toolchain",
      "passed": true,
      "detail": {
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      "detail": null
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    "ComplementedSubspace.FrameCoefficient",
    "ComplementedSubspace.FrameCoefficientHilbert",
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