AutoSamplingTheory.SALD.cycle90DiscreteForwardKlMassConservationUpperObligation

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 cycle90DiscreteForwardKlMassConservationUpperObligation :
    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_upper

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 upper records the reviewed theorem-route exception after the cycle-89 pressure test. The shared EM backend remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1358-1387, but the next lower packet is the smallest blocker inside SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative: prove or sharply isolate hmass : massTerm = 0 from eq:KL-derivative-0-discrete, where the paper drops integral partial_s hat rho_s dx by mass conservation. Lower must either discharge this supplied hypothesis using local Mathlib/probability-law ingredients or name one exact missing theorem; wrappers around hmass are rejected.

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.cycle90DiscreteForwardKlMassConservationUpperPacket
2. SALD.cycle89DiscreteForwardKlClosurePressureLowerObligation
3. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
4. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
5. SALD.discreteForwardKlDerivativeObligation
6. SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
7. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
8. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
9. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
10. sald.discrete_forward_kl.kl_derivative
11. sald.general_moving_target_discrete.em_interpolation_fp
12. eq:KL-derivative-0-discrete
13. eq:general_KL_derivative_0_discrete
14. appendix.tex:338-388
15. appendix.tex:1358-1387

note : String (explicit)

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

Upper routing record only. It selects the mass-conservation theorem boundary before hfirst and htarget; it does not prove KL differentiability, weak FP, integration by parts, FI identification, LSI, DV, Gronwall, or theorem closure.

def cycle90DiscreteForwardKlMassConservationUpperObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle90_mass_conservation_upper"
  statement := "Cycle 90 upper records the reviewed theorem-route exception after the cycle-89 pressure test. The shared EM backend remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1358-1387, but the next lower packet is the smallest blocker inside SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative: prove or sharply isolate hmass : massTerm = 0 from eq:KL-derivative-0-discrete, where the paper drops integral partial_s hat rho_s dx by mass conservation. Lower must either discharge this supplied hypothesis using local Mathlib/probability-law ingredients or name one exact missing theorem; wrappers around hmass are rejected."
  source := saldForwardKlDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle90DiscreteForwardKlMassConservationUpperPacket",
    "SALD.cycle89DiscreteForwardKlClosurePressureLowerObligation",
    "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
    "SALD.discreteForwardKlDerivativeObligation",
    "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "sald.discrete_forward_kl.kl_derivative",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "eq:KL-derivative-0-discrete",
    "eq:general_KL_derivative_0_discrete",
    "appendix.tex:338-388",
    "appendix.tex:1358-1387"
  ]
  note := "Upper routing record only. It selects the mass-conservation theorem boundary before hfirst and htarget; it does not prove KL differentiability, weak FP, integration by parts, FI identification, LSI, DV, Gronwall, or theorem closure."

/-- Cycle-90 middle obligation for the compiled mass-derivative route. -/