AutoSamplingTheory.SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle57GuidedGeneralDerivativeSplitLowerObligation : 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.cycle57_derivative_split_lower

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 57 lower compiles the source-shaped scalar handoff for appendix.tex:765-884: from the raw KL derivative split with a mass-conservation term, the general VA-SALD Fokker-Planck first-term evaluation, the target-transport second-term evaluation, and the residual identity m_t=v_t-c_t, SALD.generalMovingTargetKlDerivativeResidualSplitScalar derives the residual derivative display; SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar then feeds that display into the existing Young, LSI, and time-change scalar pipeline. The analytic mass conservation, KL differentiation, Fokker-Planck, integration-by-parts, target transport, residual Young, LSI density-test, sigma positivity, and inverse-schedule backends remain obligations.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDerivativeSource — 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

SALD.cycle57GuidedGeneralSkeletonMiddleContract
SALD.cycle57GuidedGeneralSkeletonMiddleObligation
SALD.generalMovingTargetDerivativeCandidateContract
SALD.generalMovingTargetDerivativeObligation
SALD.generalMovingTargetKlDerivativeResidualSplitScalar
SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar
SALD.generalMovingTargetPostYoungDerivativeBoundScalar
SALD.generalMovingTargetLsiDerivativeBoundScalar
SALD.generalMovingTargetTimeChangedDerivativeBoundScalar
SALD.generalMovingTargetPreDvDerivativeBoundScalar
sald.general_moving_target.kl_derivative
probability.lsi_to_kl_fi
sald.forward_kl.schedule_time_change

note : String (explicit)

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

Proof-producing scalar/order core only. It does not promote sald.general_moving_target.kl_derivative, the general Fokker-Planck/KL derivative identity, LSI/KL/FI, schedule calculus, residual DV, Gronwall, or thm:general-moving-target-SALD.

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 cycle57GuidedGeneralDerivativeSplitLowerObligation : ProofObligation where
  id := "sald.general_moving_target.cycle57_derivative_split_lower"
  statement := "Cycle 57 lower compiles the source-shaped scalar handoff for appendix.tex:765-884: from the raw KL derivative split with a mass-conservation term, the general VA-SALD Fokker-Planck first-term evaluation, the target-transport second-term evaluation, and the residual identity m_t=v_t-c_t, SALD.generalMovingTargetKlDerivativeResidualSplitScalar derives the residual derivative display; SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar then feeds that display into the existing Young, LSI, and time-change scalar pipeline. The analytic mass conservation, KL differentiation, Fokker-Planck, integration-by-parts, target transport, residual Young, LSI density-test, sigma positivity, and inverse-schedule backends remain obligations."
  source := saldGeneralMovingTargetDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle57GuidedGeneralSkeletonMiddleContract",
    "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "SALD.generalMovingTargetKlDerivativeResidualSplitScalar",
    "SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar",
    "SALD.generalMovingTargetPostYoungDerivativeBoundScalar",
    "SALD.generalMovingTargetLsiDerivativeBoundScalar",
    "SALD.generalMovingTargetTimeChangedDerivativeBoundScalar",
    "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
    "sald.general_moving_target.kl_derivative",
    "probability.lsi_to_kl_fi",
    "sald.forward_kl.schedule_time_change"
  ]
  note := "Proof-producing scalar/order core only. It does not promote sald.general_moving_target.kl_derivative, the general Fokker-Planck/KL derivative identity, LSI/KL/FI, schedule calculus, residual DV, Gronwall, or thm:general-moving-target-SALD."

/-- Cycle-57 proof-DAG pane for the guided/general upper route and selected lower
backend. -/

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