AutoSamplingTheory.SALD.cycle90DiscreteForwardKlMassConservationMiddleObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle90DiscreteForwardKlMassConservationMiddleObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

id : String (explicit)

Stable obligation identifier.

sald.discrete_forward_kl.cycle90_mass_conservation_middle

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 90 middle translates eq:KL-derivative-0-discrete into the smaller Lean boundary for hmass. The compiled theorem SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative proves that a mass term is zero once it is the HasDerivAt derivative of a locally constant total-mass function. SALD.discreteForwardKlDerivativeSplitOfMassDerivativeScalar and SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar then consume that theorem in the cycle-89 raw discrete KL route, replacing the primitive hmass : massTerm = 0 hypothesis by total-mass normalization plus the derivative-under-integral/constant-test witness. Classification: discharges-supplied-hypothesis for the scalar hmass input, while the remaining source-cited boundary is the analytic identification of massTerm with the derivative of the probability-law total mass.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.cycle90DiscreteForwardKlMassConservationUpperObligation
2. SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative
3. SALD.discreteForwardKlDerivativeSplitOfMassDerivativeScalar
4. SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar
5. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
6. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
7. SALD.discreteForwardKlDerivativeObligation
8. sald.discrete_forward_kl.kl_derivative
9. eq:KL-derivative-0-discrete
10. appendix.tex:338-388
11. Mathlib.Analysis.Calculus.Deriv.Basic
12. Mathlib.Analysis.Calculus.ParametricIntegral
13. Mathlib.MeasureTheory.Integral.Bochner.Basic

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Compiled local calculus handoff plus remaining obligation. It removes hmass as a primitive scalar hypothesis under explicit total-mass derivative and local probability-mass-one hypotheses; it does not prove density-to-law mass preservation, differentiation under the integral, weak FP, integration by parts, FI, LSI, DV, Gronwall, or theorem closure.

def cycle90DiscreteForwardKlMassConservationMiddleObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle90_mass_conservation_middle"
  statement := "Cycle 90 middle translates eq:KL-derivative-0-discrete into the smaller Lean boundary for hmass. The compiled theorem SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative proves that a mass term is zero once it is the HasDerivAt derivative of a locally constant total-mass function. SALD.discreteForwardKlDerivativeSplitOfMassDerivativeScalar and SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar then consume that theorem in the cycle-89 raw discrete KL route, replacing the primitive hmass : massTerm = 0 hypothesis by total-mass normalization plus the derivative-under-integral/constant-test witness. Classification: discharges-supplied-hypothesis for the scalar hmass input, while the remaining source-cited boundary is the analytic identification of massTerm with the derivative of the probability-law total mass."
  source := saldForwardKlDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle90DiscreteForwardKlMassConservationUpperObligation",
    "SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative",
    "SALD.discreteForwardKlDerivativeSplitOfMassDerivativeScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar",
    "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
    "SALD.discreteForwardKlDerivativeObligation",
    "sald.discrete_forward_kl.kl_derivative",
    "eq:KL-derivative-0-discrete",
    "appendix.tex:338-388",
    "Mathlib.Analysis.Calculus.Deriv.Basic",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic"
  ]
  note := "Compiled local calculus handoff plus remaining obligation. It removes hmass as a primitive scalar hypothesis under explicit total-mass derivative and local probability-mass-one hypotheses; it does not prove density-to-law mass preservation, differentiation under the integral, weak FP, integration by parts, FI, LSI, DV, Gronwall, or theorem closure."

/-- Cycle-90 lower obligation for mapped-law constant-test mass conservation. -/