AutoSamplingTheory.SALD.cycle152GeneralMovingTargetDiscreteEmGeneratorEventSourceFieldStdBasisDag

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 cycle152GeneralMovingTargetDiscreteEmGeneratorEventSourceFieldStdBasisDag :
    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.cycle152.packet.event_source_field_from_stdbasis_fields
interface : String (explicit)
Text describing intended mathematical interface.
Compiled direct-leaf theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields derives hemGeneratorLaplacianEventFieldEqSourceField from hemGeneratorLaplacianEventFieldStdBasisDef plus hweakFpSourceFieldStdBasisDef.
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.cycle152GeneralMovingTargetDiscreteEmGeneratorEventSourceFieldStdBasisLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields
3. hemGeneratorLaplacianEventFieldStdBasisDef
4. hweakFpSourceFieldStdBasisDef
5. appendix.tex:984-995
6. appendix.tex:1368-1387
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
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.cycle152.lower_1_packet.weak_fp_source_field_stdbasis_from_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 scout theorem: SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField derives hweakFpSourceFieldStdBasisDef from hweakFpSourceFieldEqLaplacian plus SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv.
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.cycle152GeneralMovingTargetDiscreteWeakFpSourceFieldStdBasisScoutObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. hweakFpSourceFieldEqLaplacian
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField
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.cycle152.lower_2_packet.weak_fp_source_field_eq_laplacian_pointwise
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpSourceFieldEqLaplacianOfPointwise derives hweakFpSourceFieldEqLaplacian from hweakFpSourceFieldPointwiseEqLaplacian, the pointwise source-field identity for each selected weak test.
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.cycle152GeneralMovingTargetDiscreteWeakFpSourceFieldPointwiseLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceFieldEqLaplacianOfPointwise
3. hweakFpSourceFieldPointwiseEqLaplacian
4. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField
4. sald.general_moving_target_discrete.em_interpolation_fp
5. 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.cycle152.remaining_event_source_field_stdbasis_defs
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 152 lower_2: prove hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field and hweakFpSourceFieldPointwiseEqLaplacian for weakFpLaplacianSourceField; hweakFpSourceFieldEqLaplacian and hweakFpSourceFieldStdBasisDef now follow locally from the latter. Keep htraceFieldEqLaplacian, hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, state-event, and sibling EM leaves explicit.
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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields
2. SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField
3. SALD.generalMovingTargetDiscreteWeakFpSourceFieldEqLaplacianOfPointwise
4. hweakFpSourceFieldPointwiseEqLaplacian
5. appendix.tex:984-995
6. appendix.tex:1368-1387
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. 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

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 cycle152GeneralMovingTargetDiscreteEmGeneratorEventSourceFieldStdBasisDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle152.packet.event_source_field_from_stdbasis_fields"
      interface := "Compiled direct-leaf theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields derives hemGeneratorLaplacianEventFieldEqSourceField from hemGeneratorLaplacianEventFieldStdBasisDef plus hweakFpSourceFieldStdBasisDef."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle152GeneralMovingTargetDiscreteEmGeneratorEventSourceFieldStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields",
        "hemGeneratorLaplacianEventFieldStdBasisDef",
        "hweakFpSourceFieldStdBasisDef",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle152.lower_1_packet.weak_fp_source_field_stdbasis_from_laplacian"
      interface := "Compiled lower_1 scout theorem: SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField derives hweakFpSourceFieldStdBasisDef from hweakFpSourceFieldEqLaplacian plus SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle152GeneralMovingTargetDiscreteWeakFpSourceFieldStdBasisScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "hweakFpSourceFieldEqLaplacian",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle152.lower_2_packet.weak_fp_source_field_eq_laplacian_pointwise"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpSourceFieldEqLaplacianOfPointwise derives hweakFpSourceFieldEqLaplacian from hweakFpSourceFieldPointwiseEqLaplacian, the pointwise source-field identity for each selected weak test."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle152GeneralMovingTargetDiscreteWeakFpSourceFieldPointwiseLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceFieldEqLaplacianOfPointwise",
        "hweakFpSourceFieldPointwiseEqLaplacian",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle152.remaining_event_source_field_stdbasis_defs"
      interface := "Remaining exact theorem boundary after cycle 152 lower_2: prove hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field and hweakFpSourceFieldPointwiseEqLaplacian for weakFpLaplacianSourceField; hweakFpSourceFieldEqLaplacian and hweakFpSourceFieldStdBasisDef now follow locally from the latter. Keep htraceFieldEqLaplacian, hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, state-event, and sibling EM leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields",
        "SALD.generalMovingTargetDiscreteWeakFpSourceFieldStdBasisDefOfLaplacianField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceFieldEqLaplacianOfPointwise",
        "hweakFpSourceFieldPointwiseEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 153: EM generator Laplacian state integral from source functional -/

/-- Cycle-153 direct-leaf narrowing for the selected-test Laplacian state integral. -/

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