AutoSamplingTheory.SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation

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 cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation :
    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.cycle171_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_lower1

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 171 lower_1 proof-scout/illness-area refiner packet. Classification: rejected-wrapper-churn. Exact missing theorem boundary preserved: hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 from a non-opaque selected weak-test C2_b/bounded-Hessian source interface under sald.general_moving_target_discrete.em_interpolation_fp. Source audit rechecked appendix.tex:984-995, appendix.tex:1379-1387, appendix.tex:1026-1072, main_body.tex:273-305, and a paper-wide original-source search excluding sald_version_2.tex; these sources justify the EM Brownian/Laplacian use and nearby Lipschitz/integrability assumptions but do not state the selected weak-test global bounded-Hessian field. Mathlib/local pieces already cover Brownian coordinate unit direction via SALD.gaussianRealStdOrthonormalBasisUnit and hHessianOpNorm-to-hSecondFDerivOpNorm via SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm. Lower_2 should implement exactly one source-backed theorem only if the source correspondence expands testRegular into the bounded-Hessian field itself; otherwise keep hHessianOpNorm as a source-contract gap and reject wrapper churn.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
SALD.gaussianRealStdOrthonormalBasisUnit
SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
hHessianOpNorm
selected weak-test C2_b/bounded-Hessian source interface
appendix.tex:984-995
appendix.tex:1026-1072
appendix.tex:1379-1387
main_body.tex:273-305
paper-wide original-source search excluding sald_version_2.tex
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.

No SLT theorem was needed, imported, or marked formalized; the configured local SLT clone is absent. The packet records a lower_2-ready theorem shape only when the selected weak-test bounded-Hessian field is source-backed, not when it is merely repackaged as testRegular.

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 cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle171_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_lower1"
  statement := "Cycle 171 lower_1 proof-scout/illness-area refiner packet. Classification: rejected-wrapper-churn. Exact missing theorem boundary preserved: hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 from a non-opaque selected weak-test C2_b/bounded-Hessian source interface under sald.general_moving_target_discrete.em_interpolation_fp. Source audit rechecked appendix.tex:984-995, appendix.tex:1379-1387, appendix.tex:1026-1072, main_body.tex:273-305, and a paper-wide original-source search excluding sald_version_2.tex; these sources justify the EM Brownian/Laplacian use and nearby Lipschitz/integrability assumptions but do not state the selected weak-test global bounded-Hessian field. Mathlib/local pieces already cover Brownian coordinate unit direction via SALD.gaussianRealStdOrthonormalBasisUnit and hHessianOpNorm-to-hSecondFDerivOpNorm via SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm. Lower_2 should implement exactly one source-backed theorem only if the source correspondence expands testRegular into the bounded-Hessian field itself; otherwise keep hHessianOpNorm as a source-contract gap and reject wrapper churn."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
    "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
    "SALD.gaussianRealStdOrthonormalBasisUnit",
    "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
    "hHessianOpNorm",
    "selected weak-test C2_b/bounded-Hessian source interface",
    "appendix.tex:984-995",
    "appendix.tex:1026-1072",
    "appendix.tex:1379-1387",
    "main_body.tex:273-305",
    "paper-wide original-source search excluding sald_version_2.tex",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No SLT theorem was needed, imported, or marked formalized; the configured local SLT clone is absent. The packet records a lower_2-ready theorem shape only when the selected weak-test bounded-Hessian field is source-backed, not when it is merely repackaged as testRegular."

/-- Cycle-171 lower_2 rejection of the unsourced selected-test Hessian
projection route. -/

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