AutoSamplingTheory.SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. 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 cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

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.

Ordered data items

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle173.middle_refiner.hessian_source_contract_recheck
interface : String (explicit)
Text describing intended mathematical interface.
Blueprint-guided middle packet: preserve hHessianOpNorm as the exact remaining source-contract boundary after checking that Brownian unit direction and the Hessian-to-iterated-Frechet bridge are already compiled.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
2. SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
3. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
4. SALD.gaussianRealStdOrthonormalBasisUnit
5. hHessianOpNorm
6. appendix.tex:984-995
7. appendix.tex:1026-1072
8. appendix.tex:1379-1387
9. main_body.tex:273-305
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. next source-contract recovery lower packet
2. future source-backed selected weak-test C2_b/bounded-Hessian interface
3. hSecondFDerivOpNorm
4. hDirectionalSecond
5. selected-line Taylor domination
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle173.middle_refiner.reject_unsourced_projection_and_score_hessian
interface : String (explicit)
Text describing intended mathematical interface.
Reject wrapper churn: unexpanded testRegular, unsourced SourceSelectedWeakTestC2bBoundedHessian/SelectedWeakTestC2bBoundedHessian predicates, and iteration_complexity.tex VP score-Hessian regularity do not discharge hHessianOpNorm for sourceTest.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
2. ASTIS.SALD.cycle172.lower_2_refiner.reject_score_or_unsourced_test_hessian_projection
3. hHessianOpNorm
4. sourceTest
5. testRegular
6. SourceSelectedWeakTestC2bBoundedHessian proposed only as source-backed field
7. iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest
8. paper-wide original-source search excluding sald_version_2.tex
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. reviewer wrapper-churn check
2. next lower source-contract recovery packet
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle173.lower_1_refiner.source_hessian_field_proof_route
interface : String (explicit)
Text describing intended mathematical interface.
Lower_1 proof route: reduce hHessianOpNorm to two source-backed fields, hSourceHasHessian and hSourceHessianBound, for a selected weak-test Hessian representative sourceHessian; do not implement this from unexpanded testRegular or an unsourced same-field predicate.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
2. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
3. HasFDerivAt.fderiv
4. hSourceHasHessian
5. hSourceHessianBound
6. hHessianOpNorm
7. appendix.tex:984-995
8. appendix.tex:1026-1072
9. appendix.tex:1379-1387
10. main_body.tex:273-305
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. lower_2 selectedWeakTestHessianOpNormOfSourceHessianField theorem
2. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
3. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
4. reviewer source-contract check
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle173.lower_2_packet.source_hessian_field_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 bridge: SALD.selectedWeakTestHessianOpNormOfSourceHessianField derives hHessianOpNorm from a source-backed Hessian representative sourceHessian plus hSourceHasHessian and hSourceHessianBound, using HasFDerivAt.fderiv.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.selectedWeakTestHessianOpNormOfSourceHessianField
2. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
3. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
4. HasFDerivAt.fderiv
5. hSourceHasHessian
6. hSourceHessianBound
7. sourceHessian
8. hHessianOpNorm
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
2. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
3. selected-line Taylor domination
4. sald.general_moving_target_discrete.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification

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 cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle173.middle_refiner.hessian_source_contract_recheck"
      interface := "Blueprint-guided middle packet: preserve hHessianOpNorm as the exact remaining source-contract boundary after checking that Brownian unit direction and the Hessian-to-iterated-Frechet bridge are already compiled."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305"
      ]
      reusedBy := [
        "next source-contract recovery lower packet",
        "future source-backed selected weak-test C2_b/bounded-Hessian interface",
        "hSecondFDerivOpNorm",
        "hDirectionalSecond",
        "selected-line Taylor domination"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle173.middle_refiner.reject_unsourced_projection_and_score_hessian"
      interface := "Reject wrapper churn: unexpanded testRegular, unsourced SourceSelectedWeakTestC2bBoundedHessian/SelectedWeakTestC2bBoundedHessian predicates, and iteration_complexity.tex VP score-Hessian regularity do not discharge hHessianOpNorm for sourceTest."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "ASTIS.SALD.cycle172.lower_2_refiner.reject_score_or_unsourced_test_hessian_projection",
        "hHessianOpNorm",
        "sourceTest",
        "testRegular",
        "SourceSelectedWeakTestC2bBoundedHessian proposed only as source-backed field",
        "iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest",
        "paper-wide original-source search excluding sald_version_2.tex"
      ]
      reusedBy := [
        "reviewer wrapper-churn check",
        "next lower source-contract recovery packet"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle173.lower_1_refiner.source_hessian_field_proof_route"
      interface := "Lower_1 proof route: reduce hHessianOpNorm to two source-backed fields, hSourceHasHessian and hSourceHessianBound, for a selected weak-test Hessian representative sourceHessian; do not implement this from unexpanded testRegular or an unsourced same-field predicate."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "HasFDerivAt.fderiv",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "hHessianOpNorm",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305"
      ]
      reusedBy := [
        "lower_2 selectedWeakTestHessianOpNormOfSourceHessianField theorem",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
        "reviewer source-contract check"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle173.lower_2_packet.source_hessian_field_bridge"
      interface := "Compiled lower_2 bridge: SALD.selectedWeakTestHessianOpNormOfSourceHessianField derives hHessianOpNorm from a source-backed Hessian representative sourceHessian plus hSourceHasHessian and hSourceHessianBound, using HasFDerivAt.fderiv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestHessianOpNormOfSourceHessianField",
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
        "HasFDerivAt.fderiv",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "sourceHessian",
        "hHessianOpNorm"
      ]
      reusedBy := [
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
        "selected-line Taylor domination",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    }
  ]

/-! ### Cycle 174 middle: Brownian quadratic-variation normalization packet -/

/-- Cycle-174 middle packet after the source-Hessian field audit.

The selected weak-test Hessian representative fields left by cycle 173 are kept
as a source-contract gap.  This packet moves only to the connected scalar
Brownian/Ito leaf named by the EM interpolation source: the quadratic-variation
normalization inside
`generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder`.
-/

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