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

AutoSamplingTheory.SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionDag

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 cycle103GeneralMovingTargetDiscreteConditionalKernelVersionDag :
    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.cycle103.middle_conditional_kernel_component_version
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle source map: appendix.tex:1368-1377 defines bar b_{k,s} by conditioning the frozen guide and score summands on hat X_s=x. Cycle 103 selects only the condC guide component and lower narrows hguideComp to a condExpKernel.map bridge plus remaining measure-valued kernel/version-selection facts.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionMiddleObligation
    2. SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation
    3. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
    4. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap
    5. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
    6. AutoSamplingTheory.condDistribAeEqCondExpKernelMap
    7. AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap
    8. appendix.tex:1368-1377
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
    2. sald.general_moving_target_discrete.em_interpolation_fp
    3. 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
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle103.lower_condExpKernel_map_version_bridge
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower bridge: a measure-valued a.e. equality condDistrib X_k^eta hatXAtS P (hatXAtS omega) = condExpKernel P (mState.comap hatXAtS).map X_k^eta omega, together with the selected condExpKernel-map version of condC, supplies the condDistrib sample-space equality consumed by cycle 91 and ae_map_iff.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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. AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap
    2. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap
    3. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
    4. appendix.tex:1368-1377
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
    2. ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary
    3. sald.general_moving_target_discrete.em_interpolation_fp
    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.cycle103.condC_condDistrib_condExpKernel_sample_version
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary after the compiled lower bridge: prove the measure-valued P-a.e. kernel equality condDistrib X_k^eta hatXAtS P (hatXAtS omega) = condExpKernel P (mState.comap hatXAtS).map X_k^eta omega, prove the selected condExpKernel-map guide-component version for condC, and prove the equality set is measurable for ae_map_iff. Imports: Mathlib.Probability.Kernel.CondDistrib, Mathlib.Probability.Kernel.Condexp, Mathlib.MeasureTheory.Integral.Bochner.Basic.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource — 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.cycle103.lower_condExpKernel_map_version_bridge
    2. AutoSamplingTheory.condDistribAeEqCondExpKernelMap
    3. AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap
    4. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap
    5. ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map
    6. ProbabilityTheory.condExp_ae_eq_integral_condExpKernel
    7. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib
    8. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
    9. Mathlib.Probability.Kernel.CondDistrib
    10. Mathlib.Probability.Kernel.Condexp
    11. Mathlib.MeasureTheory.Integral.Bochner.Basic
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary
    2. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
    3. sald.general_moving_target_discrete.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.cycle103.rejected_wrapper_churn_guard
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reject wrappers that take the same hguideComp, hfieldAe, hcanonical, weak-FP, KL, LSI, DV, Gronwall, or no-boundary hypotheses as premises. Accept only a proof of the condC condDistrib/condExpKernel sample-version theorem or a strictly smaller named Mathlib theorem needed by it.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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.cycle103.condC_condDistrib_condExpKernel_sample_version
    2. ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 103 lower
    2. cycle 103 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 cycle103GeneralMovingTargetDiscreteConditionalKernelVersionDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle103.middle_conditional_kernel_component_version"
      interface := "Middle source map: appendix.tex:1368-1377 defines bar b_{k,s} by conditioning the frozen guide and score summands on hat X_s=x.  Cycle 103 selects only the condC guide component and lower narrows hguideComp to a condExpKernel.map bridge plus remaining measure-valued kernel/version-selection facts."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionMiddleObligation",
        "SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "AutoSamplingTheory.condDistribAeEqCondExpKernelMap",
        "AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle103.lower_condExpKernel_map_version_bridge"
      interface := "Compiled lower bridge: a measure-valued a.e. equality condDistrib X_k^eta hatXAtS P (hatXAtS omega) = condExpKernel P (mState.comap hatXAtS).map X_k^eta omega, together with the selected condExpKernel-map version of condC, supplies the condDistrib sample-space equality consumed by cycle 91 and ae_map_iff."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle103.condC_condDistrib_condExpKernel_sample_version"
      interface := "Remaining exact theorem boundary after the compiled lower bridge: prove the measure-valued P-a.e. kernel equality condDistrib X_k^eta hatXAtS P (hatXAtS omega) = condExpKernel P (mState.comap hatXAtS).map X_k^eta omega, prove the selected condExpKernel-map guide-component version for condC, and prove the equality set is measurable for ae_map_iff. Imports: Mathlib.Probability.Kernel.CondDistrib, Mathlib.Probability.Kernel.Condexp, Mathlib.MeasureTheory.Integral.Bochner.Basic."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle103.lower_condExpKernel_map_version_bridge",
        "AutoSamplingTheory.condDistribAeEqCondExpKernelMap",
        "AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap",
        "ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map",
        "ProbabilityTheory.condExp_ae_eq_integral_condExpKernel",
        "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "Mathlib.Probability.Kernel.CondDistrib",
        "Mathlib.Probability.Kernel.Condexp",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic"
      ]
      reusedBy := [
        "ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle103.rejected_wrapper_churn_guard"
      interface := "Reject wrappers that take the same hguideComp, hfieldAe, hcanonical, weak-FP, KL, LSI, DV, Gronwall, or no-boundary hypotheses as premises.  Accept only a proof of the condC condDistrib/condExpKernel sample-version theorem or a strictly smaller named Mathlib theorem needed by it."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle103.condC_condDistrib_condExpKernel_sample_version",
        "ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary"
      ]
      reusedBy := ["cycle 103 lower", "cycle 103 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 104: named-law generator-to-law weak-FP transport -/

/-- Cycle-104 upper packet for the named-law generator-to-law weak-FP
transport boundary.

This cycle stays on the active EM conditional-law/Fokker--Planck backend over
`appendix.tex:1358-1387`, narrowed to `appendix.tex:1379-1387`.  It does not
add a broad wrapper around the source-sign route; it removes the named-law
bookkeeping premise between `hatRhoS s = Law(hatX s)` and the cycle-92
`Measure.map` derivative handoff.
-/

Existing module entry · Audited data-reader index · All teaching coverage