Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.firstAppendixMiddleAuditObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def firstAppendixMiddleAuditObligation : ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

id : String (explicit)

Stable obligation identifier.

sald.first_appendix.middle_source_to_lean_map
statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Maintain the first appendix middle source-to-Lean map for lem:gronwall, lem:dv_variation, def:PI, and eq:LSI-KL-FI: every source proof step in the focus windows must be classified as an existing Lean contract, a cited result, or a named proof obligation, with a lower-ready target that does not change later SALD theorem statements.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldAppendixSource — audited data reference, not expanded and not a compiled dependency edge
status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

  1. SALD.cycle13FirstAppendixSourceIndexAuditContract
  2. SALD.cycle13FirstAppendixMiddleAuditContract
  3. SALD.cycle17FirstAppendixVocabularyPacket
  4. SALD.cycle17FirstAppendixMiddleAuditContract
  5. SALD.cycle21FirstAppendixVocabularyPacket
  6. SALD.cycle21FirstAppendixMiddleAuditContract
  7. SALD.cycle25FirstAppendixVocabularyPacket
  8. SALD.cycle25FirstAppendixMiddleAuditContract
  9. SALD.cycle25FirstAppendixPiVelocityNormMiddleObligation
  10. SALD.cycle25PiVelocityNormLowerObligation
  11. SALD.cycle29FirstAppendixVocabularyPacket
  12. SALD.cycle29FirstAppendixMiddleAuditContract
  13. SALD.cycle29LsiKlFiDensityTestMiddleObligation
  14. SALD.cycle29LsiKlFiDensityTestLowerObligation
  15. SALD.cycle36GronwallUpperPacket
  16. SALD.cycle36GronwallUpperObligation
  17. SALD.cycle36GronwallMiddleObligation
  18. SALD.cycle41GronwallMiddleObligation
  19. SALD.cycle37DvVariationUpperPacket
  20. SALD.cycle37DvVariationUpperObligation
  21. SALD.cycle37DvVariationMiddleAuditContract
  22. SALD.cycle37DvVariationMiddleObligation
  23. SALD.cycle38LsiKlFiUpperPacket
  24. SALD.cycle38LsiKlFiUpperObligation
  25. AutoSamplingTheory.dvVariationalOneSidedOfTiltedRight
  26. AutoSamplingTheory.dvVariationalTiltedRightOneSidedConsequence
  27. SALD.lsiKlFiCoefficientAuditScalar
  28. SALD.piVelocityNormMeanZeroH1UpperScalar
  29. SALD.piVelocityNormBoundedFunctionalScalar
  30. sald.first_appendix.source_index_audit
  31. SALD.saldGronwallEndpointCalculusContract
  32. SALD.saldGronwallExponentRewriteContract
  33. SALD.gronwallIntegratingFactorProductDerivative
  34. SALD.gronwallIntegratingFactorDerivativeInequalityScalar
  35. SALD.gronwallIntegratingFactorDerivativeLe
  36. SALD.gronwallIntegratingFactorDerivativeLeOfIntegral
  37. SALD.gronwallEndpointIntegralRewrite
  38. SALD.gronwallIntegratingFactorBoundOfDerivatives
  39. SALD.gronwallIntegratingFactorBoundOfIntegral
  40. SALD.gronwallCoefficientSideConditionsOfContinuous
  41. SALD.gronwallIntegratingFactorBoundOfContinuousData
  42. SALD.gronwallIntegratingFactorBoundOfDifferentiable
  43. SALD.gronwallIntegratingFactorBoundOfC1
  44. SALD.saldPiVelocityNormDependencyContract
  45. SALD.saldDvFiniteLogMgfContract
  46. SALD.saldLsiKlFiDensityTestContract
  47. research-wiki/source-index/SALD_original.jsonl
note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

This is a middle-role workflow obligation. Cycles 17 and 21 rebaseline the map for the same first-layer packet; cycle 25 adds a lower-ready PI velocity-norm source map; cycle 29 adds a lower-ready LSI/KL/FI density-test source map and a scalar coefficient lower lemma; cycle 31 adds proof-producing Gronwall line 58-65 helpers; cycle 36 adds proof-producing Gronwall assembly theorems under explicit Mathlib and continuous-data side conditions; cycle 41 rewrites the Gronwall derivative as deriv K and adds a C1-style proof-producing wrapper while leaving the endpoint-safe source bridge open; cycle 37 returns to the DV target and adds proof-producing one-sided tilted-measure backend and lower one-sided consequence while preserving the source-cited status of the Boucheron supremum equality; cycle 38 returns to eq:LSI-KL-FI and selects the Fisher chain-rule/admissibility bridge after the cycle 33 sqrt-density scalar helpers.
Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def firstAppendixMiddleAuditObligation : ProofObligation where
  id := "sald.first_appendix.middle_source_to_lean_map"
  statement := "Maintain the first appendix middle source-to-Lean map for lem:gronwall, lem:dv_variation, def:PI, and eq:LSI-KL-FI: every source proof step in the focus windows must be classified as an existing Lean contract, a cited result, or a named proof obligation, with a lower-ready target that does not change later SALD theorem statements."
  source := saldAppendixSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle13FirstAppendixSourceIndexAuditContract",
    "SALD.cycle13FirstAppendixMiddleAuditContract",
    "SALD.cycle17FirstAppendixVocabularyPacket",
    "SALD.cycle17FirstAppendixMiddleAuditContract",
    "SALD.cycle21FirstAppendixVocabularyPacket",
    "SALD.cycle21FirstAppendixMiddleAuditContract",
    "SALD.cycle25FirstAppendixVocabularyPacket",
    "SALD.cycle25FirstAppendixMiddleAuditContract",
    "SALD.cycle25FirstAppendixPiVelocityNormMiddleObligation",
    "SALD.cycle25PiVelocityNormLowerObligation",
    "SALD.cycle29FirstAppendixVocabularyPacket",
    "SALD.cycle29FirstAppendixMiddleAuditContract",
    "SALD.cycle29LsiKlFiDensityTestMiddleObligation",
    "SALD.cycle29LsiKlFiDensityTestLowerObligation",
    "SALD.cycle36GronwallUpperPacket",
    "SALD.cycle36GronwallUpperObligation",
    "SALD.cycle36GronwallMiddleObligation",
    "SALD.cycle41GronwallMiddleObligation",
    "SALD.cycle37DvVariationUpperPacket",
    "SALD.cycle37DvVariationUpperObligation",
    "SALD.cycle37DvVariationMiddleAuditContract",
    "SALD.cycle37DvVariationMiddleObligation",
    "SALD.cycle38LsiKlFiUpperPacket",
    "SALD.cycle38LsiKlFiUpperObligation",
    "AutoSamplingTheory.dvVariationalOneSidedOfTiltedRight",
    "AutoSamplingTheory.dvVariationalTiltedRightOneSidedConsequence",
    "SALD.lsiKlFiCoefficientAuditScalar",
    "SALD.piVelocityNormMeanZeroH1UpperScalar",
    "SALD.piVelocityNormBoundedFunctionalScalar",
    "sald.first_appendix.source_index_audit",
    "SALD.saldGronwallEndpointCalculusContract",
    "SALD.saldGronwallExponentRewriteContract",
    "SALD.gronwallIntegratingFactorProductDerivative",
    "SALD.gronwallIntegratingFactorDerivativeInequalityScalar",
    "SALD.gronwallIntegratingFactorDerivativeLe",
    "SALD.gronwallIntegratingFactorDerivativeLeOfIntegral",
    "SALD.gronwallEndpointIntegralRewrite",
    "SALD.gronwallIntegratingFactorBoundOfDerivatives",
    "SALD.gronwallIntegratingFactorBoundOfIntegral",
    "SALD.gronwallCoefficientSideConditionsOfContinuous",
    "SALD.gronwallIntegratingFactorBoundOfContinuousData",
    "SALD.gronwallIntegratingFactorBoundOfDifferentiable",
    "SALD.gronwallIntegratingFactorBoundOfC1",
    "SALD.saldPiVelocityNormDependencyContract",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "research-wiki/source-index/SALD_original.jsonl"
  ]
  note := "This is a middle-role workflow obligation. Cycles 17 and 21 rebaseline the map for the same first-layer packet; cycle 25 adds a lower-ready PI velocity-norm source map; cycle 29 adds a lower-ready LSI/KL/FI density-test source map and a scalar coefficient lower lemma; cycle 31 adds proof-producing Gronwall line 58-65 helpers; cycle 36 adds proof-producing Gronwall assembly theorems under explicit Mathlib and continuous-data side conditions; cycle 41 rewrites the Gronwall derivative as deriv K and adds a C1-style proof-producing wrapper while leaving the endpoint-safe source bridge open; cycle 37 returns to the DV target and adds proof-producing one-sided tilted-measure backend and lower one-sided consequence while preserving the source-cited status of the Boucheron supremum equality; cycle 38 returns to eq:LSI-KL-FI and selects the Fisher chain-rule/admissibility bridge after the cycle 33 sqrt-density scalar helpers."

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