AutoSamplingTheory.SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag

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 cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag :
    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.cycle96.middle_non_em_fallback_rejected
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 96 middle gate: the non-EM LSI/DV/Gronwall fallback is not allowed because the active EM boundary still has named conditional-law and divergence/no-boundary blockers. Keep the packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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.cycle95DiscreteForwardKlClosurePressureLowerObligation
2. ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker
3. ASTIS.SALD.cycle94.remaining_barB_divergence_boundary
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.cycle96.middle_condexp_generator_pairing_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Lower-ready boundary: prove one component conditional-expectation generator pairing for condC or condScore. The theorem should start from Mathlib condDistrib/condexp for X_k^eta | hat X_s=x, named hatRhoS = Law(hatX_s), and the existing component conditional-integral regularity/versioning helpers, then produce the weak test-gradient pairing input consumed by the cycle-95 barB component route.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
4. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
5. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
6. Mathlib.Probability.Kernel.CondDistrib
7. Mathlib.Probability.Kernel.Condexp
8. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib
9. ProbabilityTheory.condExp_ae_eq_integral_condExpKernel
10. 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
4. thm:forward-KL-discrete
5. 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.cycle96.lower_condDistrib_component_pairing_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing handoff: SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion turns a named condC/condScore component pairing into the smaller canonical conditional-integral action theorem, using hatRhoS-a.e. equality with the condDistrib integral and weak-pairing a.e. congruence. Remaining work is the canonical condDistrib/condexp generator identity for one component.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
4. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
5. Mathlib.Probability.Kernel.CondDistrib
6. Mathlib.Probability.Kernel.Condexp
7. appendix.tex:1368-1377
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.em_interpolation_fp
5. thm:forward-KL-discrete
6. 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.cycle96.lower_packet.condexp_component_generator_pairing
interface : String (explicit)
Text describing intended mathematical interface.
Accepted lower packet classification: this cycle narrows-source-cited-boundary by compiling the named-field a.e.-version handoff and exposing the smaller canonical condDistrib/condexp generator identity. It is discharges-supplied-hypothesis only after that canonical component action theorem is proved and removes one component pairing premise from the cycle-95 barB component route. Repackaging source signs, KL, LSI, DV, Gronwall, or display assumptions is rejected-wrapper-churn.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation
2. SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation
3. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion
4. ASTIS.SALD.cycle96.middle_condexp_generator_pairing_boundary
5. ASTIS.SALD.cycle96.lower_condDistrib_component_pairing_handoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
7. ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 96 lower
2. cycle 96 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 cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle96.middle_non_em_fallback_rejected"
      interface := "Cycle 96 middle gate: the non-EM LSI/DV/Gronwall fallback is not allowed because the active EM boundary still has named conditional-law and divergence/no-boundary blockers. Keep the packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle95DiscreteForwardKlClosurePressureLowerObligation",
        "ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker",
        "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle96.middle_condexp_generator_pairing_boundary"
      interface := "Lower-ready boundary: prove one component conditional-expectation generator pairing for condC or condScore. The theorem should start from Mathlib condDistrib/condexp for X_k^eta | hat X_s=x, named hatRhoS = Law(hatX_s), and the existing component conditional-integral regularity/versioning helpers, then produce the weak test-gradient pairing input consumed by the cycle-95 barB component route."
      source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
        "Mathlib.Probability.Kernel.CondDistrib",
        "Mathlib.Probability.Kernel.Condexp",
        "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib",
        "ProbabilityTheory.condExp_ae_eq_integral_condExpKernel",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings",
        "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.cycle96.lower_condDistrib_component_pairing_handoff"
      interface := "Lower proof-producing handoff: SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion turns a named condC/condScore component pairing into the smaller canonical conditional-integral action theorem, using hatRhoS-a.e. equality with the condDistrib integral and weak-pairing a.e. congruence. Remaining work is the canonical condDistrib/condexp generator identity for one component."
      source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
        "Mathlib.Probability.Kernel.CondDistrib",
        "Mathlib.Probability.Kernel.Condexp",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings",
        "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.cycle96.lower_packet.condexp_component_generator_pairing"
      interface := "Accepted lower packet classification: this cycle narrows-source-cited-boundary by compiling the named-field a.e.-version handoff and exposing the smaller canonical condDistrib/condexp generator identity. It is discharges-supplied-hypothesis only after that canonical component action theorem is proved and removes one component pairing premise from the cycle-95 barB component route. Repackaging source signs, KL, LSI, DV, Gronwall, or display assumptions is rejected-wrapper-churn."
      source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation",
        "SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
        "ASTIS.SALD.cycle96.middle_condexp_generator_pairing_boundary",
        "ASTIS.SALD.cycle96.lower_condDistrib_component_pairing_handoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
        "ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker"
      ]
      reusedBy := ["cycle 96 lower", "cycle 96 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 97: canonical `condDistrib` disintegration pairing -/

/-- Cycle-97 middle obligation for the canonical conditional-integral pairing.

This cycle stops adding supplied-hypothesis wrappers and proves the
Mathlib-style map-law disintegration theorem that lower needs for the
canonical `condDistrib` component action.
-/

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