AutoSamplingTheory.SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation

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 cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation :
    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.cycle84_active_em_backend_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 84 middle keeps appendix.tex:1358-1387 synchronized after the accepted cycle-83 KL handoff: the source route starts with eq:general_KL_derivative_0_discrete, uses the conditional drift definition of bar b_{k,s} from appendix.tex:1368-1377 only through the existing cycle-80/cycle-81 endpoint and conditional readiness packages, uses the weak conditional Fokker-Planck signs of appendix.tex:1379-1387 only through the cycle-82 endpoint source-sign wrapper, and uses the log-ratio weak-FP-to-KL substitution only through the cycle-83 handoff. Since these local bridges compile under supplied hypotheses, middle does not select a new Mathlib/measure fallback; if lower is blocked, the fallback must name exactly one missing conditional-law or generator-to-law weak-FP theorem boundary and keep it below formalized status.

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.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation
2. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
3. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
4. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
5. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
6. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
7. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation
8. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
9. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
10. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
11. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
12. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
13. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
14. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
15. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
16. sald.general_moving_target_discrete.em_interpolation_fp
17. sald.general_moving_target_discrete.kl_derivative
18. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

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

Middle synchronization only. It adds no theorem assumptions, introduces no new cited interface, and leaves conditional law, density/AC, generator-to-law weak FP, KL differentiability, log-ratio admissibility, integration by parts, FI, LSI/KL/FI, DV, Gronwall, theorem status, SLT, and Lake dependencies unpromoted.

def cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle84_active_em_backend_middle"
  statement := "Cycle 84 middle keeps appendix.tex:1358-1387 synchronized after the accepted cycle-83 KL handoff: the source route starts with eq:general_KL_derivative_0_discrete, uses the conditional drift definition of bar b_{k,s} from appendix.tex:1368-1377 only through the existing cycle-80/cycle-81 endpoint and conditional readiness packages, uses the weak conditional Fokker-Planck signs of appendix.tex:1379-1387 only through the cycle-82 endpoint source-sign wrapper, and uses the log-ratio weak-FP-to-KL substitution only through the cycle-83 handoff. Since these local bridges compile under supplied hypotheses, middle does not select a new Mathlib/measure fallback; if lower is blocked, the fallback must name exactly one missing conditional-law or generator-to-law weak-FP theorem boundary and keep it below formalized status."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation",
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Middle synchronization only. It adds no theorem assumptions, introduces no new cited interface, and leaves conditional law, density/AC, generator-to-law weak FP, KL differentiability, log-ratio admissibility, integration by parts, FI, LSI/KL/FI, DV, Gronwall, theorem status, SLT, and Lake dependencies unpromoted."

/-- Cycle-84 lower obligation for the endpoint log-action active-backend
handoff. -/