AutoSamplingTheory.SALD.cycle118GeneralMovingTargetDiscreteCanonicalBarBDownstreamDag

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 cycle118GeneralMovingTargetDiscreteCanonicalBarBDownstreamDag :
    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.cycle118.middle_packet.direct_canonical_barB_downstream
interface : String (explicit)
Text describing intended mathematical interface.
Middle packet: use the source definition of bar b_{k,s} at appendix.tex:1368-1377 to instantiate the downstream EM state-event interface with the canonical condDistrib guide-plus-score representative, rather than adding 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.cycle117.lower_ready.selected_named_barB_canonical_ae_eq
2. SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib
3. SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib
4. appendix.tex:1368-1377
5. 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.cycle118.lower_ready.direct_canonical_barB_em_state_event_interface
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface instantiates the EM conditional-drift/state-event consumer with barB := canonicalCondDistribBarB and consumes SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib; only if a separate named barB is retained should lower prove pointwise equality to the canonical field via SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq.
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.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
2. SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib
3. SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib
4. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq
5. ASTIS.SALD.cycle117.lower_ready.selected_named_barB_canonical_ae_eq
6. 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. thm:forward-KL-discrete
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — 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 cycle118GeneralMovingTargetDiscreteCanonicalBarBDownstreamDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle118.middle_packet.direct_canonical_barB_downstream"
      interface := "Middle packet: use the source definition of bar b_{k,s} at appendix.tex:1368-1377 to instantiate the downstream EM state-event interface with the canonical condDistrib guide-plus-score representative, rather than adding another hbarBCondExp wrapper."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "ASTIS.SALD.cycle117.lower_ready.selected_named_barB_canonical_ae_eq",
        "SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib",
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib",
        "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.cycle118.lower_ready.direct_canonical_barB_em_state_event_interface"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface instantiates the EM conditional-drift/state-event consumer with barB := canonicalCondDistribBarB and consumes SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib; only if a separate named barB is retained should lower prove pointwise equality to the canonical field via SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
        "SALD.generalMovingTargetDiscreteCanonicalBarBStateEventIntegralAndIntegrableOfCondDistrib",
        "SALD.generalMovingTargetDiscreteCanonicalBarBCondExpOfCondDistrib",
        "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalPointwiseEq",
        "ASTIS.SALD.cycle117.lower_ready.selected_named_barB_canonical_ae_eq",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.formalized
    }
  ]

/-! ### Cycle 119: canonical `barB` weak-FP consumer boundary -/

/-- Cycle-119 middle obligation for consuming the canonical `barB` witness in
the weak-FP generator/source-sign path.

The refreshed illness area after cycle 118 is no longer the representative
choice for `barB`.  This packet fixes `barB` to the canonical `condDistrib`
guide-plus-score field supplied by
`generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface` and narrows the
remaining weak-FP boundary to the EM path derivative, domination, and
source-action identities needed by the dominated generator handoff.
-/

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