AutoSamplingTheory.SALD.cycle117GeneralMovingTargetDiscreteNamedBarBVersionSelectionDag

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 cycle117GeneralMovingTargetDiscreteNamedBarBVersionSelectionDag :
    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.cycle117.middle_packet.named_barB_version_selection
interface : String (explicit)
Text describing intended mathematical interface.
Middle packet: the current lower-ready boundary is the source version-selection theorem identifying the paper-selected named barB with the canonical condDistrib guide-plus-score representative, not another hbarBCondExp wrapper.
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.cycle116.remaining_named_barB_selected_version_after_canonical_condExp
2. SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib
3. SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib
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.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle117.lower_packet.selected_barB_pointwise_canonical
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq discharges the selected-to-canonical hbarBAe premise when the paper-selected barB is pointwise the canonical condDistrib guide-plus-score field, then reuses the cycle-115 selected-version bridge to return Integrable barB hatRhoS and the state-event set-integral identity.
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.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq
2. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq
4. SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib
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.cycle117.lower_ready.selected_named_barB_canonical_ae_eq
interface : String (explicit)
Text describing intended mathematical interface.
Remaining source choice after the lower packet: either use the canonical condDistrib guide-plus-score representative directly downstream, as supported by the pointwise definition at appendix.tex:1368-1377, or prove the pointwise/canonical equality for a separately retained named barB version.
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.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq
2. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq
4. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
5. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'
6. Mathlib.Probability.Kernel.CondDistrib
7. appendix.tex:1368-1377
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
2. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef
3. sald.general_moving_target_discrete.em_interpolation_fp
4. 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 cycle117GeneralMovingTargetDiscreteNamedBarBVersionSelectionDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle117.middle_packet.named_barB_version_selection"
      interface := "Middle packet: the current lower-ready boundary is the source version-selection theorem identifying the paper-selected named barB with the canonical condDistrib guide-plus-score representative, not another hbarBCondExp wrapper."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle116.remaining_named_barB_selected_version_after_canonical_condExp",
        "SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib",
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib",
        "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.obligation
    },
    {
      id := "ASTIS.SALD.cycle117.lower_packet.selected_barB_pointwise_canonical"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq discharges the selected-to-canonical hbarBAe premise when the paper-selected barB is pointwise the canonical condDistrib guide-plus-score field, then reuses the cycle-115 selected-version bridge to return Integrable barB hatRhoS and the state-event set-integral identity."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq",
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib",
        "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.cycle117.lower_ready.selected_named_barB_canonical_ae_eq"
      interface := "Remaining source choice after the lower packet: either use the canonical condDistrib guide-plus-score representative directly downstream, as supported by the pointwise definition at appendix.tex:1368-1377, or prove the pointwise/canonical equality for a separately retained named barB version."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
        "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'",
        "Mathlib.Probability.Kernel.CondDistrib",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 118: direct canonical `barB` downstream instantiation -/

/-- Cycle-118 middle obligation for direct canonical downstream use.

The refreshed illness area is no longer a request for another
`hbarBCondExp` bridge.  The source definition at `appendix.tex:1368-1377`
allows the lower route to choose the canonical Mathlib `condDistrib`
guide-plus-score field as the `barB` representative consumed by the EM
state-event interface at `appendix.tex:1379-1387`.  If a separate named
representative is retained, the only remaining boundary is its pointwise
equality to that canonical field.
-/

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