AutoSamplingTheory.SALD.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorDag

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 cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorDag :
    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

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle110.lower_packet.dominated_generator_to_law_transport
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: pointwise sample-path derivatives plus a local dominated derivative-under-integral package imply the named-law weak-test derivative for hatRhoS=Law(hatX_s), with source signs after the existing drift/diffusion action rewrites. This discharges the older integral-level hsampleGenerator premise instead of adding another weak-FP wrapper.
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.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
3. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated
4. AutoSamplingTheory.lawMapIntegralHasDerivAtOfDominated
5. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
6. Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le
7. appendix.tex:1379-1387
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after the dominated transport: for every admissible weak test, prove the EM interpolation pointwise HasDerivAt and integrable bound/dominated convergence package, identify the resulting derivative integral with driftAction+diffusionAction, and keep the separate barB/no-boundary and diffusion source-action identifications.
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.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
2. ASTIS.SALD.cycle104.remaining_generator_to_law_after_named_transport
3. ASTIS.SALD.cycle100.remaining_no_boundary_after_inner_gradient
4. ASTIS.SALD.cycle110.remaining_condExp_source_representative_after_eq_meas
5. appendix.tex:1379-1387
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle110.reviewer_dominated_generator_to_law_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the compiled theorem removes the integral-level hsampleGenerator premise through Mathlib parametric-integral plus existing lawMapIntegral helpers, and no broad wrapper churn, theorem-status promotion, non-EM fallback, SLT import, Lake dependency change, fake closure, or sald_version_2 use appears.
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.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
3. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated
4. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 110 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 cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle110.lower_packet.dominated_generator_to_law_transport"
      interface := "Compiled lower theorem: pointwise sample-path derivatives plus a local dominated derivative-under-integral package imply the named-law weak-test derivative for hatRhoS=Law(hatX_s), with source signs after the existing drift/diffusion action rewrites. This discharges the older integral-level hsampleGenerator premise instead of adding another weak-FP wrapper."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfDominated",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le",
        "appendix.tex:1379-1387"
      ]
      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.cycle110.remaining_parametric_generator_boundary_after_dominated_transport"
      interface := "Remaining exact theorem after the dominated transport: for every admissible weak test, prove the EM interpolation pointwise HasDerivAt and integrable bound/dominated convergence package, identify the resulting derivative integral with driftAction+diffusionAction, and keep the separate barB/no-boundary and diffusion source-action identifications."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "ASTIS.SALD.cycle104.remaining_generator_to_law_after_named_transport",
        "ASTIS.SALD.cycle100.remaining_no_boundary_after_inner_gradient",
        "ASTIS.SALD.cycle110.remaining_condExp_source_representative_after_eq_meas",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle110.reviewer_dominated_generator_to_law_check"
      interface := "Reviewer check: accept only if the compiled theorem removes the integral-level hsampleGenerator premise through Mathlib parametric-integral plus existing lawMapIntegral helpers, and no broad wrapper churn, theorem-status promotion, non-EM fallback, SLT import, Lake dependency change, fake closure, or sald_version_2 use appears."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 110 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 111: KL target-time derivative at finite-KL `llr` -/

/-- Cycle-111 middle obligation for the KL target-time subboundary.

The active source slice is still `appendix.tex:1358-1366`.  This packet does
not restate the whole pure raw-KL package; it isolates the target-density time
derivative term inside `eq:general_KL_derivative_0_discrete`.
-/

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