AutoSamplingTheory.SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag

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 cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag :
    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.cycle97.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 96 passed reviewer/build, so no recovery is needed. Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill. The single lower packet that reduces the largest remaining risk is the canonical condDistrib disintegration pairing behind appendix.tex:1368-1377, feeding the cycle-96 hcanonical component-action boundary before divergence/no-boundary work.
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.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation
2. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion
3. ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker
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.cycle97.compiled_condDistrib_disintegration_pairing
interface : String (explicit)
Text describing intended mathematical interface.
Compiled local Mathlib-style theorem: AutoSamplingTheory.condDistribIntegralMapIntegral, plus the named-law variant AutoSamplingTheory.condDistribIntegralNamedLawIntegral, disintegrates an integrable paired component test through condDistrib Y X mu and rewrites the conditioning marginal as hatRhoS=mu.map X.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteCondDistribIntegralMathlibSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/Probability.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. AutoSamplingTheory.condDistribIntegralMapIntegral
2. AutoSamplingTheory.condDistribIntegralNamedLawIntegral
3. ProbabilityTheory.compProd_map_condDistrib
4. MeasureTheory.Measure.integral_compProd
5. MeasureTheory.integral_map
6. Mathlib.Probability.Kernel.CondDistrib
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-discrete
5. thm:general-moving-target-SALD-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.cycle97.lower_packet.canonical_condDistrib_component_pairing
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower handoff: SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction instantiates AutoSamplingTheory.condDistribIntegralNamedLawIntegral with f equal to the weak test-gradient pairing against condC or condScore, removes hcanonical as a primitive premise, and feeds SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion. Remaining obligations are paired-integrand integrability and the concrete componentAction/weakGradPairing definition equalities.
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.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation
2. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction
3. AutoSamplingTheory.condDistribIntegralNamedLawIntegral
4. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
6. appendix.tex:1368-1377
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings
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.cycle97.rejected_wrapper_churn_guard
interface : String (explicit)
Text describing intended mathematical interface.
Reject fresh wrappers that merely rename hcanonical, hdriftSource, source signs, KL mass/log-ratio, LSI, DV, Gronwall, or theorem displays. Accept only a compiled use of the condDistrib disintegration theorem, a paired-integrability proof, or one exact missing theorem needed to align the weak-pairing definitions.
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. AutoSamplingTheory.condDistribIntegralNamedLawIntegral
2. ASTIS.SALD.cycle96.lower_packet.condexp_component_generator_pairing
3. ASTIS.SALD.cycle94.remaining_barB_divergence_boundary
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 97 lower
2. cycle 97 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 cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle97.global_phase_judgment"
      interface := "Cycle 96 passed reviewer/build, so no recovery is needed. Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill. The single lower packet that reduces the largest remaining risk is the canonical condDistrib disintegration pairing behind appendix.tex:1368-1377, feeding the cycle-96 hcanonical component-action boundary before divergence/no-boundary work."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
        "ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle97.compiled_condDistrib_disintegration_pairing"
      interface := "Compiled local Mathlib-style theorem: AutoSamplingTheory.condDistribIntegralMapIntegral, plus the named-law variant AutoSamplingTheory.condDistribIntegralNamedLawIntegral, disintegrates an integrable paired component test through condDistrib Y X mu and rewrites the conditioning marginal as hatRhoS=mu.map X."
      source := saldGeneralMovingTargetDiscreteCondDistribIntegralMathlibSource
      targetLean := "AutoSamplingTheory/Probability.lean"
      dependsOn := [
        "AutoSamplingTheory.condDistribIntegralMapIntegral",
        "AutoSamplingTheory.condDistribIntegralNamedLawIntegral",
        "ProbabilityTheory.compProd_map_condDistrib",
        "MeasureTheory.Measure.integral_compProd",
        "MeasureTheory.integral_map",
        "Mathlib.Probability.Kernel.CondDistrib"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
        "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.formalized
    },
    {
      id := "ASTIS.SALD.cycle97.lower_packet.canonical_condDistrib_component_pairing"
      interface := "Compiled lower handoff: SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction instantiates AutoSamplingTheory.condDistribIntegralNamedLawIntegral with f equal to the weak test-gradient pairing against condC or condScore, removes hcanonical as a primitive premise, and feeds SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion. Remaining obligations are paired-integrand integrability and the concrete componentAction/weakGradPairing definition equalities."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction",
        "AutoSamplingTheory.condDistribIntegralNamedLawIntegral",
        "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle97.rejected_wrapper_churn_guard"
      interface := "Reject fresh wrappers that merely rename hcanonical, hdriftSource, source signs, KL mass/log-ratio, LSI, DV, Gronwall, or theorem displays. Accept only a compiled use of the condDistrib disintegration theorem, a paired-integrability proof, or one exact missing theorem needed to align the weak-pairing definitions."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "AutoSamplingTheory.condDistribIntegralNamedLawIntegral",
        "ASTIS.SALD.cycle96.lower_packet.condexp_component_generator_pairing",
        "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary"
      ]
      reusedBy := ["cycle 97 lower", "cycle 97 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 98: `barB` divergence/no-boundary integral boundary -/

/-- Cycle-98 middle obligation for the `barB` weak-divergence boundary.

The active source span is the Fokker--Planck source-sign line
`appendix.tex:1379-1387`.  Cycle 98 keeps the packet on the divergence half of
`ASTIS.SALD.cycle94.remaining_barB_divergence_boundary`: replace the primitive
`hbarBWeakDivergence` input by a law-integral weak-pairing definition and a
no-boundary integration-by-parts theorem for `hatRhoS * barB`.
-/

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