AutoSamplingTheory.SALD.cycle115GeneralMovingTargetDiscreteNamedBarBSelectedVersionDag

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 cycle115GeneralMovingTargetDiscreteNamedBarBSelectedVersionDag :
    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.cycle115.middle_packet.named_barB_selected_version_to_state_events
interface : String (explicit)
Text describing intended mathematical interface.
Compiled middle theorem: SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq derives Integrable barB hatRhoS and hbarBStateSetIntegral from the selected paper barB being hatRhoS-a.e. equal to the canonical condDistrib guide-plus-score field.
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.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
2. SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq
4. MeasureTheory.ae_eq_comp
5. MeasureTheory.setIntegral_congr_ae
6. 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.cycle115.lower_packet.named_barB_condExp_source_to_state_events
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef discharges the supplied hbarBAe equality in the selected-version bridge by deriving it from the paper sample-space conditional-expectation representative hbarBCondExp, then returns Integrable barB hatRhoS and hbarBStateSetIntegral.
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.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef
3. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
4. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'
5. 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.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle115.remaining_named_barB_condExp_source_representative
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after the cycle-115 lower packet: prove hbarBCondExp, the paper-selected sample-space conditional-expectation representative equality for barB(hatXAtS omega); if not supplied directly, also discharge hbarBEqMeas through the cycle-110 measurable-representative theorem.
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.cycle115.remaining_named_barB_selected_canonical_ae_eq
2. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef
3. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
4. ASTIS.SALD.cycle114.remaining_named_barB_version_after_canonical_state_event_integral
5. 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 cycle115GeneralMovingTargetDiscreteNamedBarBSelectedVersionDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle115.middle_packet.named_barB_selected_version_to_state_events"
      interface := "Compiled middle theorem: SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq derives Integrable barB hatRhoS and hbarBStateSetIntegral from the selected paper barB being hatRhoS-a.e. equal to the canonical condDistrib guide-plus-score field."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq",
        "MeasureTheory.ae_eq_comp",
        "MeasureTheory.setIntegral_congr_ae",
        "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.cycle115.lower_packet.named_barB_condExp_source_to_state_events"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef discharges the supplied hbarBAe equality in the selected-version bridge by deriving it from the paper sample-space conditional-expectation representative hbarBCondExp, then returns Integrable barB hatRhoS and hbarBStateSetIntegral."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
        "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'",
        "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.formalized
    },
    {
      id := "ASTIS.SALD.cycle115.remaining_named_barB_condExp_source_representative"
      interface := "Remaining exact theorem after the cycle-115 lower packet: prove hbarBCondExp, the paper-selected sample-space conditional-expectation representative equality for barB(hatXAtS omega); if not supplied directly, also discharge hbarBEqMeas through the cycle-110 measurable-representative theorem."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle115.remaining_named_barB_selected_canonical_ae_eq",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
        "ASTIS.SALD.cycle114.remaining_named_barB_version_after_canonical_state_event_integral",
        "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 116: canonical `barB` conditional-expectation representative -/

/-- Cycle-116 lower obligation for the canonical conditional-expectation
representative of the named `barB` drift.

This packet stays on
`ASTIS.SALD.cycle115.remaining_named_barB_condExp_source_representative` for
`appendix.tex:1368-1377`.  It compiles the standalone canonical theorem that
proves the old `hbarBCondExp` conclusion when `barB` is chosen as the Mathlib
`condDistrib` guide-plus-score field.  The remaining source boundary is only
the paper-selected named-version equality to that canonical representative.
-/

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