AutoSamplingTheory.SALD.cycle105GeneralMovingTargetDiscretePureRawKlDerivativeDag

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 cycle105GeneralMovingTargetDiscretePureRawKlDerivativeDag :
    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.cycle105.middle_pure_raw_kl_derivative_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: after finite KL has selected Mathlib llr and the mass term has been removed, isolate the remaining appendix.tex:1358-1366 theorem as pure no-mass KL differentiability for the measure path, without sample-space law or mapped-law mass data.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle105GeneralMovingTargetDiscretePureRawKlDerivativeMiddleObligation
2. SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation
3. eq:general_KL_derivative_0_discrete
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. sald.general_moving_target_discrete.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.cycle105.lower_packet.pure_raw_kl_llr_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower handoff: extract dK = partialS (llr hatRho tildePi) - targetTimeTerm from the pure source-cited package, derive admissibility of that exact llr test through the cycle-88 closure package, and apply the existing weak-FP source-sign-with-log-action theorem.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr
2. SALD.generalMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlrHkl
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfPureNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. thm:forward-KL-discrete
3. 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.cycle105.remaining_pure_raw_kl_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem: prove the pure no-mass finite-KL llr KL differentiability package from Mathlib finite-KL/log-likelihood-ratio regularity, parametric-integral/Bochner differentiation under the KL integral, target-time derivative integrability and formula, and density/time regularity.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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. Mathlib.InformationTheory.KullbackLeibler.Basic
2. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
3. Mathlib.Analysis.Calculus.ParametricIntegral
4. Mathlib.MeasureTheory.Integral.Bochner.Basic
5. appendix.tex:1358-1366
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. sald.general_moving_target_discrete.em_interpolation_fp
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 cycle105GeneralMovingTargetDiscretePureRawKlDerivativeDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle105.middle_pure_raw_kl_derivative_source_map"
      interface := "Middle source map: after finite KL has selected Mathlib llr and the mass term has been removed, isolate the remaining appendix.tex:1358-1366 theorem as pure no-mass KL differentiability for the measure path, without sample-space law or mapped-law mass data."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle105GeneralMovingTargetDiscretePureRawKlDerivativeMiddleObligation",
        "SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation",
        "eq:general_KL_derivative_0_discrete"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle105.lower_packet.pure_raw_kl_llr_handoff"
      interface := "Compiled lower handoff: extract dK = partialS (llr hatRho tildePi) - targetTimeTerm from the pure source-cited package, derive admissibility of that exact llr test through the cycle-88 closure package, and apply the existing weak-FP source-sign-with-log-action theorem."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr",
        "SALD.generalMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlrHkl",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfPureNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle105.remaining_pure_raw_kl_boundary"
      interface := "Remaining exact theorem: prove the pure no-mass finite-KL llr KL differentiability package from Mathlib finite-KL/log-likelihood-ratio regularity, parametric-integral/Bochner differentiation under the KL integral, target-time derivative integrability and formula, and density/time regularity."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "Mathlib.InformationTheory.KullbackLeibler.Basic",
        "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
        "Mathlib.Analysis.Calculus.ParametricIntegral",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic",
        "appendix.tex:1358-1366"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 106: canonical conditional-integral drift regularity -/

/-- Cycle-106 middle obligation for canonical conditional-integral drift
regularity.

This cycle returns to the conditional-drift line `appendix.tex:1368-1377` and
chooses the canonical `condDistrib` representative of `bar b_{k,s}` rather
than adding another supplied-hypothesis wrapper.
-/

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