AutoSamplingTheory.SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditDag

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 cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditDag :
    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.cycle158.middle_packet.scalar_event_field_delta_source_gap
interface : String (explicit)
Text describing intended mathematical interface.
Source-contract gap: prove hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian by defining the named frozen EM Laplacian event field from the Brownian generator/Fokker--Planck diffusion term, so that for every selected weak test phi and state x it equals Laplacian.laplacian (selectedTest phi) x.
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.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation
2. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
3. emGeneratorLaplacianEventField
4. eq:general_moving_target_SALD_frozen_interp
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
2. sald.general_moving_target_discrete.em_interpolation_fp
3. 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.cycle158.lower_2_packet.scalar_delta_from_brownian_event_field_def
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef derives hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian from the smaller source-facing Brownian-generator event-field definition hEmGeneratorLaplacianEventFieldBrownianDef by unfolding SALD.emFrozenBrownianLaplacianEventField.
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.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation
2. SALD.emFrozenBrownianLaplacianEventField
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef
4. hEmGeneratorLaplacianEventFieldBrownianDef
5. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian
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.cycle158.remaining_brownian_event_field_def
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact source boundary after lower_2: prove hEmGeneratorLaplacianEventFieldBrownianDef, namely that the named frozen EM Laplacian event field is SALD.emFrozenBrownianLaplacianEventField selectedTest, 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.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation
2. SALD.emFrozenBrownianLaplacianEventField
3. hEmGeneratorLaplacianEventFieldBrownianDef
4. eq:general_moving_target_SALD_frozen_interp
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef
2. sald.general_moving_target_discrete.em_interpolation_fp
3. 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.cycle158.middle_packet.rejected_scalar_delta_wrapper_churn
interface : String (explicit)
Text describing intended mathematical interface.
Rejected wrapper candidates: any theorem that merely takes hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian, a weak-FP source-field equality, a trace-field equality, or a downstream total-event/source-functional consumer and returns the same scalar event-field Delta identity without exposing the Brownian-generator event-field definition.
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.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation
2. ASTIS.SALD.cycle157.remaining_event_field_pointwise_scalar
3. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
4. appendix.tex:984-995
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 158 lower packet selection
2. cycle 158 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 cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle158.middle_packet.scalar_event_field_delta_source_gap"
      interface := "Source-contract gap: prove hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian by defining the named frozen EM Laplacian event field from the Brownian generator/Fokker--Planck diffusion term, so that for every selected weak test phi and state x it equals Laplacian.laplacian (selectedTest phi) x."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation",
        "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
        "emGeneratorLaplacianEventField",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle158.lower_2_packet.scalar_delta_from_brownian_event_field_def"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef derives hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian from the smaller source-facing Brownian-generator event-field definition hEmGeneratorLaplacianEventFieldBrownianDef by unfolding SALD.emFrozenBrownianLaplacianEventField."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation",
        "SALD.emFrozenBrownianLaplacianEventField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef",
        "hEmGeneratorLaplacianEventFieldBrownianDef",
        "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle158.remaining_brownian_event_field_def"
      interface := "Remaining exact source boundary after lower_2: prove hEmGeneratorLaplacianEventFieldBrownianDef, namely that the named frozen EM Laplacian event field is SALD.emFrozenBrownianLaplacianEventField selectedTest, directly from the frozen interpolation and the Fokker--Planck diffusion display."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation",
        "SALD.emFrozenBrownianLaplacianEventField",
        "hEmGeneratorLaplacianEventFieldBrownianDef",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle158.middle_packet.rejected_scalar_delta_wrapper_churn"
      interface := "Rejected wrapper candidates: any theorem that merely takes hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian, a weak-FP source-field equality, a trace-field equality, or a downstream total-event/source-functional consumer and returns the same scalar event-field Delta identity without exposing the Brownian-generator event-field definition."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation",
        "ASTIS.SALD.cycle157.remaining_event_field_pointwise_scalar",
        "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 158 lower packet selection", "cycle 158 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 159: Brownian event-field pointwise definition boundary -/

/-- Cycle-159 middle narrowing of the Brownian event-field definition.

The remaining cycle-158 source boundary was the function equality
`hEmGeneratorLaplacianEventFieldBrownianDef`.  This packet exposes the smaller
pointwise source display that the frozen Brownian-generator Laplacian event
field agrees with `SALD.emFrozenBrownianLaplacianEventField selectedTest` at
each selected weak test and state.
-/

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