AutoSamplingTheory.SALD.cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Obligation

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 cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Obligation :
    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.cycle197_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_bound_def_lower2

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 197 lower_2 dynamic-leaf worker packet. Classification: rejected-wrapper-churn / narrows-source-cited-boundary fallback. Exact missing theorem boundary narrowed: hNormalizedRemainderBoundDef would need the source-backed equality remainderBound phi x i z = remainderBoundC phi x i * z ^ 2. Lean inspection shows remainderBound and remainderBoundC are parameters of SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound, not reducible local definitions, and the original SALD source excluding sald_version_2.tex does not define these names or the quadratic equality at appendix.tex:958-996, appendix.tex:1161-1170, appendix.tex:1358-1387, or appendix.tex:1422-1434. The existing compiled bridge SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound remains valid only after this equality and the normalized scalar coordinate law are supplied. No source-Hessian, testRegular repackaging, VP score-Hessian substitution, direct SLT dependency, broad route audit, or new integrability wrapper is introduced.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — 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. hNormalizedRemainderBoundDef
2. remainderBound
3. remainderBoundC
4. SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound
5. AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound
6. AutoSamplingTheory.TechnicalLemmas.Gaussian.integrable_const_mul_sq_gaussianReal_zero
7. gaussian.quadratic-bound-integrable
8. sald.normalized-remainder-bound-int-quadratic
9. appendix.tex:958-996
10. appendix.tex:1161-1170
11. appendix.tex:1358-1387
12. appendix.tex:1422-1434
13. paper-wide original-source search excluding sald_version_2.tex
14. source-contract-gap_missing_remainder_bound_definition
15. sald.general_moving_target_discrete.em_interpolation_fp
16. sald.general_moving_target_discrete.kl_derivative
17. divergence/FI/IBP handoff
18. thm:general-moving-target-SALD-discrete

note : String (explicit)

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

typed_verifier_feedback: leaf=hNormalizedRemainderBoundDef; error_class=source_contract_gap_missing_remainder_bound_definition; needed_shape=remainderBound phi x i z = remainderBoundC phi x i * z ^ 2; source_lines=appendix.tex:958-996; appendix.tex:1161-1170; appendix.tex:1358-1387; appendix.tex:1422-1434; blocked_by=no original-paper definition of remainderBound/remainderBoundC outside sald_version_2.tex and no existing Lean definitional unfolding; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet.

def cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle197_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_bound_def_lower2"
  statement := "Cycle 197 lower_2 dynamic-leaf worker packet. Classification: rejected-wrapper-churn / narrows-source-cited-boundary fallback. Exact missing theorem boundary narrowed: hNormalizedRemainderBoundDef would need the source-backed equality remainderBound phi x i z = remainderBoundC phi x i * z ^ 2. Lean inspection shows remainderBound and remainderBoundC are parameters of SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound, not reducible local definitions, and the original SALD source excluding sald_version_2.tex does not define these names or the quadratic equality at appendix.tex:958-996, appendix.tex:1161-1170, appendix.tex:1358-1387, or appendix.tex:1422-1434. The existing compiled bridge SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound remains valid only after this equality and the normalized scalar coordinate law are supplied. No source-Hessian, testRegular repackaging, VP score-Hessian substitution, direct SLT dependency, broad route audit, or new integrability wrapper is introduced."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.obligation
  dependsOn := [
    "hNormalizedRemainderBoundDef",
    "remainderBound",
    "remainderBoundC",
    "SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound",
    "AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound",
    "AutoSamplingTheory.TechnicalLemmas.Gaussian.integrable_const_mul_sq_gaussianReal_zero",
    "gaussian.quadratic-bound-integrable",
    "sald.normalized-remainder-bound-int-quadratic",
    "appendix.tex:958-996",
    "appendix.tex:1161-1170",
    "appendix.tex:1358-1387",
    "appendix.tex:1422-1434",
    "paper-wide original-source search excluding sald_version_2.tex",
    "source-contract-gap_missing_remainder_bound_definition",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "divergence/FI/IBP handoff",
    "thm:general-moving-target-SALD-discrete"
  ]
  note := "typed_verifier_feedback: leaf=hNormalizedRemainderBoundDef; error_class=source_contract_gap_missing_remainder_bound_definition; needed_shape=remainderBound phi x i z = remainderBoundC phi x i * z ^ 2; source_lines=appendix.tex:958-996; appendix.tex:1161-1170; appendix.tex:1358-1387; appendix.tex:1422-1434; blocked_by=no original-paper definition of remainderBound/remainderBoundC outside sald_version_2.tex and no existing Lean definitional unfolding; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet."

/-- Cycle-197 proof-DAG pane for the normalized remainder bound-definition gap. -/