AutoSamplingTheory.SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation

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 cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation :
    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.general_moving_target_discrete.cycle87_kl_log_ratio_boundary_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 87 middle translates appendix.tex lines 1358-1366 into a lower-ready KL/log-ratio theorem boundary. The old supplied post-mass-drop hkl hypothesis dK=partialS(logRatioTest)-targetTimeTerm is now split into: a raw KL differentiation theorem with an explicit mass term dK=partialS(logRatioTest)+massTerm-targetTimeTerm, the mass-conservation identity massTerm=0 corresponding to integral partial_s hat rho_s dx=0, log-ratio measurability/integrability/admissibility for log(hat rho_s/tilde pi_s), and target-time derivative integrability for integral (hat rho_s/tilde pi_s) partial_s tilde pi_s. The lower packet should compile the scalar mass-conservation handoff and leave the remaining analytic boundary as raw KL differentiation plus log-ratio regularity, not as another post-mass-drop hkl wrapper. Classification: narrows-source-cited-boundary unless the raw KL differentiation or log-ratio regularity theorem is actually proved.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation
2. eq:general_KL_derivative_0_discrete
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
4. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
5. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
6. Mathlib.MeasureTheory.Integral.Bochner.Basic
7. Mathlib.Analysis.Calculus.ParametricIntegral
8. sald.general_moving_target_discrete.kl_derivative
9. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

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

Middle boundary only. It names the smaller analytic theorem split and keeps KL differentiability, density/AC, log-ratio admissibility, target-time integrability, and mass conservation unpromoted.

def cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle87_kl_log_ratio_boundary_middle"
  statement := "Cycle 87 middle translates appendix.tex lines 1358-1366 into a lower-ready KL/log-ratio theorem boundary. The old supplied post-mass-drop hkl hypothesis dK=partialS(logRatioTest)-targetTimeTerm is now split into: a raw KL differentiation theorem with an explicit mass term dK=partialS(logRatioTest)+massTerm-targetTimeTerm, the mass-conservation identity massTerm=0 corresponding to integral partial_s hat rho_s dx=0, log-ratio measurability/integrability/admissibility for log(hat rho_s/tilde pi_s), and target-time derivative integrability for integral (hat rho_s/tilde pi_s) partial_s tilde pi_s. The lower packet should compile the scalar mass-conservation handoff and leave the remaining analytic boundary as raw KL differentiation plus log-ratio regularity, not as another post-mass-drop hkl wrapper. Classification: narrows-source-cited-boundary unless the raw KL differentiation or log-ratio regularity theorem is actually proved."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation",
    "eq:general_KL_derivative_0_discrete",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "sald.general_moving_target_discrete.kl_derivative",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle boundary only. It names the smaller analytic theorem split and keeps KL differentiability, density/AC, log-ratio admissibility, target-time integrability, and mass conservation unpromoted."

/-- Cycle-87 lower scalar handoff for the KL/log-ratio mass-conservation drop. -/