AutoSamplingTheory.SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDag

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 cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDag :
    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.cycle159.middle_packet.brownian_event_field_def_from_pointwise
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise derives hEmGeneratorLaplacianEventFieldBrownianDef from the smaller pointwise Brownian-generator event-field display hEmGeneratorLaplacianEventFieldBrownianPointwiseDef by function extensionality over selected tests and states.
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.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise
3. SALD.emFrozenBrownianLaplacianEventField
4. hEmGeneratorLaplacianEventFieldBrownianPointwiseDef
5. hEmGeneratorLaplacianEventFieldBrownianDef
6. appendix.tex:984-995
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle159.lower_2_packet.brownian_pointwise_def_from_stdbasis
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis derives hEmGeneratorLaplacianEventFieldBrownianPointwiseDef from the smaller coordinate Brownian-generator Hessian-trace display hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef, using SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv to rewrite the trace as SALD.emFrozenBrownianLaplacianEventField selectedTest.
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.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. SALD.emFrozenBrownianLaplacianEventField
5. hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef
6. hEmGeneratorLaplacianEventFieldBrownianPointwiseDef
7. appendix.tex:984-995
8. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle159.remaining_brownian_event_field_pointwise_stdbasis_def
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact source boundary after the lower_2 split: prove hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef, namely that the named frozen EM Brownian-generator Laplacian event field is the coordinate Hessian trace of each selected weak test at each state point, directly from the frozen interpolation and the Fokker--Planck diffusion display.
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.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation
2. hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef
3. eq:general_moving_target_SALD_frozen_interp
4. appendix.tex:984-995
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.em_interpolation_fp
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.cycle159.reviewer_brownian_event_field_pointwise_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hEmGeneratorLaplacianEventFieldBrownianPointwiseDef is narrowed to hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis, stale weak-FP source-field/trace-field/consumer wrappers are rejected, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, downstream wrapper churn, or sald_version_2 use.
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.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation
2. SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise
5. SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation
6. appendix.tex:984-995
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 159 reviewer
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — 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 cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle159.middle_packet.brownian_event_field_def_from_pointwise"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise derives hEmGeneratorLaplacianEventFieldBrownianDef from the smaller pointwise Brownian-generator event-field display hEmGeneratorLaplacianEventFieldBrownianPointwiseDef by function extensionality over selected tests and states."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise",
        "SALD.emFrozenBrownianLaplacianEventField",
        "hEmGeneratorLaplacianEventFieldBrownianPointwiseDef",
        "hEmGeneratorLaplacianEventFieldBrownianDef",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle159.lower_2_packet.brownian_pointwise_def_from_stdbasis"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis derives hEmGeneratorLaplacianEventFieldBrownianPointwiseDef from the smaller coordinate Brownian-generator Hessian-trace display hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef, using SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv to rewrite the trace as SALD.emFrozenBrownianLaplacianEventField selectedTest."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "SALD.emFrozenBrownianLaplacianEventField",
        "hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef",
        "hEmGeneratorLaplacianEventFieldBrownianPointwiseDef",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle159.remaining_brownian_event_field_pointwise_stdbasis_def"
      interface := "Remaining exact source boundary after the lower_2 split: prove hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef, namely that the named frozen EM Brownian-generator Laplacian event field is the coordinate Hessian trace of each selected weak test at each state point, directly from the frozen interpolation and the Fokker--Planck diffusion display."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation",
        "hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle159.reviewer_brownian_event_field_pointwise_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hEmGeneratorLaplacianEventFieldBrownianPointwiseDef is narrowed to hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis, stale weak-FP source-field/trace-field/consumer wrappers are rejected, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, downstream wrapper churn, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation",
        "SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise",
        "SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 159 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 160: frozen scalar Brownian Ito generator event-field boundary -/

/-- Cycle-160 middle narrowing of the Brownian coordinate-trace boundary.

The remaining cycle-159 source boundary was the pointwise coordinate
Hessian-trace display
`hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef`.  This packet
exposes one smaller named stochastic-generator interface for the frozen scalar
Brownian increment in `eq:general_moving_target_SALD_frozen_interp`: identify
the abstract EM Laplacian event field with
`SALD.emFrozenScalarBrownianItoGeneratorEventField selectedTest`.
-/

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