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

AutoSamplingTheory.SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. 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 cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportDag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

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.

Ordered data items

  1. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle104.global_phase_judgment
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle 104 judgment: cycle 103 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for single-backend cited-theory backfill; the risk-reducing packet is the named-law generator-to-law weak-FP transport for appendix.tex:1379-1387, still under sald.general_moving_target_discrete.em_interpolation_fp.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportUpperObligation
    2. SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation
    3. sald.general_moving_target_discrete.em_interpolation_fp
    4. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 104 lower packet
    2. cycle 104 reviewer
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

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

    Stable plan-node identifier.

    ASTIS.SALD.cycle104.lower_packet.named_law_generator_to_law_transport
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower handoff: if hatRhoS s = Measure.map (hatX s) P and the sample-space split-generator integral has derivative driftAction phi + diffusionAction phi, then the named-law weak-test integral against hatRhoS has derivative -(driftDiv phi) + (sigma_eta^2/2) smul laplacian phi once the drift and diffusion source-action equalities are supplied. This removes a primitive named-law hlawDerivative premise rather than wrapping it.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportLowerObligation
    2. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample
    3. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
    4. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff
    5. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    3. thm:forward-KL-discrete
    4. thm:general-moving-target-SALD-discrete
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle104.remaining_generator_to_law_after_named_transport
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary: prove the sample-path/Bochner parametric-integral derivative of the split generator sum for the frozen EM interpolation; prove driftAction through the named conditional drift barB and the no-boundary divergence theorem for hatRhoS * barB; prove the diffusion/Laplacian source action; keep admissible-test, density/time regularity, and conditional-law compatibility explicit.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. ASTIS.SALD.cycle92.remaining_generator_to_law_boundary
    2. ASTIS.SALD.cycle100.remaining_no_boundary_after_inner_gradient
    3. ASTIS.SALD.cycle103.condC_condDistrib_condExpKernel_sample_version
    4. Mathlib.Analysis.Calculus.ParametricIntegral
    5. Mathlib.MeasureTheory.Integral.Bochner.Basic
    6. Mathlib.MeasureTheory.Integral.DivergenceTheorem
    7. appendix.tex:1379-1387
    8. appendix.tex:1368-1377
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

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

    Stable plan-node identifier.

    ASTIS.SALD.cycle104.reviewer_named_transport_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer checklist: accept only if the generic named-law transport helper and SALD named-law derivative theorem compile, the packet is classified as discharges-supplied-hypothesis, appendix.tex:1379-1387 remains fixed, and no source-sign/no-boundary/KL/LSI/DV/Gronwall wrapper churn, theorem-status promotion, SLT import, Lake dependency change, fake closure, or sald_version_2 use is introduced.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff
    2. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample
    3. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 104 reviewer
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
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 cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle104.global_phase_judgment"
      interface := "Cycle 104 judgment: cycle 103 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for single-backend cited-theory backfill; the risk-reducing packet is the named-law generator-to-law weak-FP transport for appendix.tex:1379-1387, still under sald.general_moving_target_discrete.em_interpolation_fp."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportUpperObligation",
        "SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 104 lower packet", "cycle 104 reviewer"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle104.lower_packet.named_law_generator_to_law_transport"
      interface := "Compiled lower handoff: if hatRhoS s = Measure.map (hatX s) P and the sample-space split-generator integral has derivative driftAction phi + diffusionAction phi, then the named-law weak-test integral against hatRhoS has derivative -(driftDiv phi) + (sigma_eta^2/2) smul laplacian phi once the drift and diffusion source-action equalities are supplied. This removes a primitive named-law hlawDerivative premise rather than wrapping it."
      source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportLowerObligation",
        "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle104.remaining_generator_to_law_after_named_transport"
      interface := "Remaining exact theorem boundary: prove the sample-path/Bochner parametric-integral derivative of the split generator sum for the frozen EM interpolation; prove driftAction through the named conditional drift barB and the no-boundary divergence theorem for hatRhoS * barB; prove the diffusion/Laplacian source action; keep admissible-test, density/time regularity, and conditional-law compatibility explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle92.remaining_generator_to_law_boundary",
        "ASTIS.SALD.cycle100.remaining_no_boundary_after_inner_gradient",
        "ASTIS.SALD.cycle103.condC_condDistrib_condExpKernel_sample_version",
        "Mathlib.Analysis.Calculus.ParametricIntegral",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic",
        "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
        "appendix.tex:1379-1387",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle104.reviewer_named_transport_check"
      interface := "Reviewer checklist: accept only if the generic named-law transport helper and SALD named-law derivative theorem compile, the packet is classified as discharges-supplied-hypothesis, appendix.tex:1379-1387 remains fixed, and no source-sign/no-boundary/KL/LSI/DV/Gronwall wrapper churn, theorem-status promotion, SLT import, Lake dependency change, fake closure, or sald_version_2 use is introduced."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff",
        "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 104 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 105: pure no-mass KL/log-ratio differentiability boundary -/

/-- Cycle-105 middle obligation for the pure no-mass KL/log-ratio boundary.

This cycle returns to `appendix.tex:1358-1366` and narrows the cycle-99
no-mass package.  Once the mass term has been removed, the remaining KL
differentiability theorem should not carry sample-space law data.
-/

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