AutoSamplingTheory.SALD.cycle113GeneralMovingTargetDiscreteNamedBarBStateFieldRegularityDag

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 cycle113GeneralMovingTargetDiscreteNamedBarBStateFieldRegularityDag :
    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.cycle113.lower_packet.named_barB_state_field_regularity
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteNamedBarBComapRegularityOfStateField derives the cycle-112 hbarBMeas and hbarBInt candidate-regularity inputs from StronglyMeasurable barB, Integrable barB hatRhoS, hatRhoS=Law(hatXAtS), and Measurable hatXAtS.
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.generalMovingTargetDiscreteNamedBarBComapRegularityOfStateField
2. MeasureTheory.Integrable.comp_measurable
3. Measurable.of_comap_le
4. appendix.tex:1368-1377
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-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.cycle113.lower_packet.named_barB_state_field_set_integral_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled downstream handoff: SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef feeds the derived regularity facts into the cycle-112 state-event set-integral bridge, replacing hbarBMeas and hbarBInt with source-facing state-field hypotheses.
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.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateSetIntegralDef
3. SALD.generalMovingTargetDiscreteNamedBarBComapRegularityOfStateField
4. 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
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.cycle113.remaining_named_barB_state_event_set_integral
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact non-wrapper blocker after cycle 113: prove the source Bochner set-integral characterization for the selected representative over events {omega | hatXAtS omega in t}; if the selected state representative is not already known integrable under hatRhoS, prove that state-field integrability from the same source construction.
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.cycle112.remaining_named_barB_set_integral_characterization
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef
3. 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
3. thm:forward-KL-discrete
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 cycle113GeneralMovingTargetDiscreteNamedBarBStateFieldRegularityDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle113.lower_packet.named_barB_state_field_regularity"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteNamedBarBComapRegularityOfStateField derives the cycle-112 hbarBMeas and hbarBInt candidate-regularity inputs from StronglyMeasurable barB, Integrable barB hatRhoS, hatRhoS=Law(hatXAtS), and Measurable hatXAtS."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteNamedBarBComapRegularityOfStateField",
        "MeasureTheory.Integrable.comp_measurable",
        "Measurable.of_comap_le",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle113.lower_packet.named_barB_state_field_set_integral_bridge"
      interface := "Compiled downstream handoff: SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef feeds the derived regularity facts into the cycle-112 state-event set-integral bridge, replacing hbarBMeas and hbarBInt with source-facing state-field hypotheses."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateSetIntegralDef",
        "SALD.generalMovingTargetDiscreteNamedBarBComapRegularityOfStateField",
        "appendix.tex:1368-1377"
      ]
      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.cycle113.remaining_named_barB_state_event_set_integral"
      interface := "Remaining exact non-wrapper blocker after cycle 113: prove the source Bochner set-integral characterization for the selected representative over events {omega | hatXAtS omega in t}; if the selected state representative is not already known integrable under hatRhoS, prove that state-field integrability from the same source construction."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle112.remaining_named_barB_set_integral_characterization",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpStateFieldSetIntegralDef",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 114: canonical `barB` state-event set integral -/

/-- Cycle-114 lower obligation for the canonical state-event set-integral
part of the remaining named `barB` boundary.

This packet stays on the dynamic leaf
`ASTIS.SALD.cycle113.remaining_named_barB_state_event_set_integral` for
`appendix.tex:1368-1377`.  It does not assume the paper's separately named
representative is already the canonical Mathlib `condDistrib` field; instead
it compiles the canonical set-integral theorem and leaves only the smaller
source version-selection/integrability boundary for a non-canonical selected
representative.
-/

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