AutoSamplingTheory.SALD.cycle116GeneralMovingTargetDiscreteCanonicalBarBCondExpDag

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 cycle116GeneralMovingTargetDiscreteCanonicalBarBCondExpDag :
    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.cycle116.lower_packet.canonical_barB_condExp
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib proves hbarBCondExp for the canonical condDistrib guide-plus-score representative composed with 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.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib
2. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'
3. MeasureTheory.integral_add
4. MeasureTheory.integral_smul
5. appendix.tex:1368-1377
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib
2. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.em_interpolation_fp
5. 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.cycle116.lower_packet.canonical_barB_condExp_to_state_events
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib specializes the cycle-115 selected bridge to the canonical condDistrib field, discharging hbarBCondExp and hbarBEqMeas for that representative and returning Integrable canonical barB hatRhoS plus 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.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib
2. SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib
3. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef
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.cycle116.remaining_named_barB_selected_version_after_canonical_condExp
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after the canonical hbarBCondExp narrowing: identify the paper-selected named barB with the canonical condDistrib guide-plus-score field, or instantiate downstream EM obligations with the canonical representative.
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_condExp_source_representative
2. SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib
3. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
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
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 cycle116GeneralMovingTargetDiscreteCanonicalBarBCondExpDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle116.lower_packet.canonical_barB_condExp"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib proves hbarBCondExp for the canonical condDistrib guide-plus-score representative composed with hatXAtS."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib",
        "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'",
        "MeasureTheory.integral_add",
        "MeasureTheory.integral_smul",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef",
        "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.cycle116.lower_packet.canonical_barB_condExp_to_state_events"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib specializes the cycle-115 selected bridge to the canonical condDistrib field, discharging hbarBCondExp and hbarBEqMeas for that representative and returning Integrable canonical barB hatRhoS plus hbarBStateSetIntegral."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib",
        "SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef",
        "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.cycle116.remaining_named_barB_selected_version_after_canonical_condExp"
      interface := "Remaining exact theorem after the canonical hbarBCondExp narrowing: identify the paper-selected named barB with the canonical condDistrib guide-plus-score field, or instantiate downstream EM obligations with the canonical representative."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle115.remaining_named_barB_condExp_source_representative",
        "SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
        "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 117: selected named `barB` version-selection boundary -/

/-- Cycle-117 middle obligation for the selected paper `barB` version step.

The refreshed blueprint illness area is not another conditional-expectation
wrapper.  Cycle 116 already proves the old `hbarBCondExp` input for the
canonical Mathlib `condDistrib` representative.  The remaining lower-ready
boundary is the faithful source version-selection step: either identify the
paper-selected named `barB` with that canonical field, or use the canonical
representative downstream if the paper's definition supports that choice.
-/

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