AutoSamplingTheory.SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag

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 cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag :
    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.cycle99.middle_raw_kl_derivative_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: appendix.tex:1358-1366 differentiates KL(hat rho_s||tilde pi_s) at the log-ratio weak test. Cycle 99 narrows the old hklRaw scalar display to a source-cited raw-KL finite-KL llr package with explicit regularity, target-time, and mass-derivative fields.
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.cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation
2. SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation
3. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
4. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
5. 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
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.cycle99.raw_kl_derivative_at_finite_kl_llr
interface : String (explicit)
Text describing intended mathematical interface.
Source-cited analytic theorem boundary: prove SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr from Mathlib KL/llr regularity, ParametricIntegral/Bochner differentiation under the KL integral, target-time derivative integrability and formula, and the mapped-law constant-test mass derivative for hat rho_s=Law(hat X_s).
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlLogRatioMathlibSource — 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.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr
2. Mathlib.InformationTheory.KullbackLeibler.Basic
3. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
4. Mathlib.Analysis.Calculus.ParametricIntegral
5. Mathlib.MeasureTheory.Integral.Bochner.Basic
6. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
7. appendix.tex:1358-1366
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction
3. sald.general_moving_target_discrete.kl_derivative
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.sourceCited — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle99.no_mass_raw_kl_derivative_at_finite_kl_llr
interface : String (explicit)
Text describing intended mathematical interface.
Strictly smaller source-cited analytic theorem boundary: prove SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr, i.e. the no-mass derivative display dK = partialS (llr hatRho tildePi) - targetTimeTerm from finite-KL llr regularity, endpoint-safe KL integral differentiation, and target-time integrability/formula. The mapped-law constant-test derivative is proved locally in the compiled handoff.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlLogRatioMathlibSource — 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.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr
2. SALD.generalMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlrHkl
3. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
4. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
5. Mathlib.InformationTheory.KullbackLeibler.Basic
6. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
7. Mathlib.Analysis.Calculus.ParametricIntegral
8. Mathlib.MeasureTheory.Integral.Bochner.Basic
9. appendix.tex:1358-1366
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction
2. sald.general_moving_target_discrete.kl_derivative
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.sourceCited — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle99.lower_packet.raw_kl_llr_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Compiled local handoff: derive hklRaw from the source-cited finite-KL llr package and compose it with the existing finite-KL admissibility, mapped-law mass, and weak-FP source-sign theorem. The no-mass variant additionally proves the mapped-law constant-test derivative internally and removes the mass-derivative field from the exact llr route. It does not prove the KL differentiation package fields.
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.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation
2. SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction
4. SALD.generalMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlrHkl
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction
7. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
8. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. sald.discrete_forward_kl.kl_derivative
3. thm:forward-KL-discrete
4. thm:general-moving-target-SALD-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 cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle99.middle_raw_kl_derivative_source_map"
      interface := "Middle source map: appendix.tex:1358-1366 differentiates KL(hat rho_s||tilde pi_s) at the log-ratio weak test.  Cycle 99 narrows the old hklRaw scalar display to a source-cited raw-KL finite-KL llr package with explicit regularity, target-time, and mass-derivative fields."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation",
        "SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation",
        "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
        "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
        "eq:general_KL_derivative_0_discrete"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle99.raw_kl_derivative_at_finite_kl_llr"
      interface := "Source-cited analytic theorem boundary: prove SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr from Mathlib KL/llr regularity, ParametricIntegral/Bochner differentiation under the KL integral, target-time derivative integrability and formula, and the mapped-law constant-test mass derivative for hat rho_s=Law(hat X_s)."
      source := saldGeneralMovingTargetDiscreteKlLogRatioMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr",
        "Mathlib.InformationTheory.KullbackLeibler.Basic",
        "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
        "Mathlib.Analysis.Calculus.ParametricIntegral",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "appendix.tex:1358-1366"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      status := ProofStatus.sourceCited
    },
    {
      id := "ASTIS.SALD.cycle99.no_mass_raw_kl_derivative_at_finite_kl_llr"
      interface := "Strictly smaller source-cited analytic theorem boundary: prove SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr, i.e. the no-mass derivative display dK = partialS (llr hatRho tildePi) - targetTimeTerm from finite-KL llr regularity, endpoint-safe KL integral differentiation, and target-time integrability/formula. The mapped-law constant-test derivative is proved locally in the compiled handoff."
      source := saldGeneralMovingTargetDiscreteKlLogRatioMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr",
        "SALD.generalMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlrHkl",
        "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "Mathlib.InformationTheory.KullbackLeibler.Basic",
        "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
        "Mathlib.Analysis.Calculus.ParametricIntegral",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic",
        "appendix.tex:1358-1366"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      status := ProofStatus.sourceCited
    },
    {
      id := "ASTIS.SALD.cycle99.lower_packet.raw_kl_llr_handoff"
      interface := "Compiled local handoff: derive hklRaw from the source-cited finite-KL llr package and compose it with the existing finite-KL admissibility, mapped-law mass, and weak-FP source-sign theorem. The no-mass variant additionally proves the mapped-law constant-test derivative internally and removes the mass-derivative field from the exact llr route. It does not prove the KL differentiation package fields."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation",
        "SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction",
        "SALD.generalMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlrHkl",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction",
        "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
        "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.discrete_forward_kl.kl_derivative",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    }
  ]

/-! ### Cycle 100: `barB` weak-pairing definition alignment -/

/-- Cycle-100 middle obligation for the `barB` weak-pairing definition
alignment inside the no-boundary drift source route. -/

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