AutoSamplingTheory.SALD.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasDag

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 cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasDag :
    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.middle_named_barB_eq_meas_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: after cycle 109, the exact removable supplied side condition is hbarBEqMeas for the canonical guide-plus-score field and named barB. This supports the source representative route needed before appendix.tex:1379-1387 weak-FP source signs use barB.
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.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasMiddleObligation
2. SALD.cycle109GeneralMovingTargetDiscreteNamedBarBCondExpSourceLowerObligation
3. appendix.tex:1368-1377
4. 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.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle110.lower_named_barB_eq_meas
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: strongly measurable canonical condDistrib guide-plus-score field and strongly measurable named barB imply the equality set required by ae_map_iff is measurable.
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.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasLowerObligation
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
3. MeasureTheory.StronglyMeasurable.measurableSet_eq_fun
4. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. ASTIS.SALD.cycle109.remaining_condExp_source_representative_for_named_barB
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
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_condExp_source_representative_after_eq_meas
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after equality-set measurability: prove the selected sample-space conditional-expectation representative hbarBCondExp for the guide-plus-score frozen drift, and supply strong measurability of the canonical and named representatives if the lower route uses the cycle-110 measurable-set helper.
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.cycle109.remaining_condExp_source_representative_for_named_barB
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
3. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef
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
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_named_barB_eq_meas_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the compiled theorem removes hbarBEqMeas under measurable representatives, the packet is classified as discharges-supplied-hypothesis, and no direct hbarBAe wrapper, generator-to-law wrapper churn, weak-FP/no-boundary/KL/LSI/DV/Gronwall promotion, theorem-status change, SLT import, Lake dependency change, fake closure, or sald_version_2 use appears.
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.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasLowerObligation
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
3. appendix.tex:1368-1377
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 cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle110.middle_named_barB_eq_meas_boundary"
      interface := "Middle source map: after cycle 109, the exact removable supplied side condition is hbarBEqMeas for the canonical guide-plus-score field and named barB. This supports the source representative route needed before appendix.tex:1379-1387 weak-FP source signs use barB."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasMiddleObligation",
        "SALD.cycle109GeneralMovingTargetDiscreteNamedBarBCondExpSourceLowerObligation",
        "appendix.tex:1368-1377",
        "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.obligation
    },
    {
      id := "ASTIS.SALD.cycle110.lower_named_barB_eq_meas"
      interface := "Compiled lower theorem: strongly measurable canonical condDistrib guide-plus-score field and strongly measurable named barB imply the equality set required by ae_map_iff is measurable."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
        "MeasureTheory.StronglyMeasurable.measurableSet_eq_fun",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef"
      ]
      reusedBy := [
        "ASTIS.SALD.cycle109.remaining_condExp_source_representative_for_named_barB",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle110.remaining_condExp_source_representative_after_eq_meas"
      interface := "Remaining exact theorem after equality-set measurability: prove the selected sample-space conditional-expectation representative hbarBCondExp for the guide-plus-score frozen drift, and supply strong measurability of the canonical and named representatives if the lower route uses the cycle-110 measurable-set helper."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle109.remaining_condExp_source_representative_for_named_barB",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef",
        "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"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle110.reviewer_named_barB_eq_meas_check"
      interface := "Reviewer check: accept only if the compiled theorem removes hbarBEqMeas under measurable representatives, the packet is classified as discharges-supplied-hypothesis, and no direct hbarBAe wrapper, generator-to-law wrapper churn, weak-FP/no-boundary/KL/LSI/DV/Gronwall promotion, theorem-status change, SLT import, Lake dependency change, fake closure, or sald_version_2 use appears."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle110GeneralMovingTargetDiscreteNamedBarBEqMeasLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
        "appendix.tex:1368-1377"
      ]
      reusedBy := ["cycle 110 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 110: dominated generator-to-law weak-FP transport -/

/-- Cycle-110 lower obligation for the dominated parametric-integral
generator-to-law step.

This is the assigned appendix.tex:1379-1387 packet: it does not add another
source-sign wrapper.  Instead it derives the sample-space weak-test derivative
from Mathlib's dominated parametric-integral theorem, then reuses the cycle-79
law-map transport and cycle-104 named-law route to remove the supplied
integral-level `hsampleGenerator` premise.
-/

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