AutoSamplingTheory.SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDag

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 cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDag :
    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.cycle157.packet.event_field_stdbasis_from_pointwise
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise derives hemGeneratorLaplacianEventFieldStdBasisDef from the smaller pointwise standard-basis source display hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef by function extensionality over selected weak tests.
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.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise
3. hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef
4. hemGeneratorLaplacianEventFieldStdBasisDef
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.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields
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.cycle157.lower_1_packet.event_field_pointwise_stdbasis_from_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian derives hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef from the smaller pointwise source Delta identity hemGeneratorLaplacianEventFieldEqLaplacian 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.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseLaplacianScoutObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. hemGeneratorLaplacianEventFieldEqLaplacian
5. hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef
6. appendix.tex:984-995
7. appendix.tex:1368-1387
8. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise
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.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle157.lower_2_packet.event_field_laplacian_from_pointwise_scalar
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar derives hemGeneratorLaplacianEventFieldEqLaplacian from the smaller statewise source display hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian by function extensionality over the state variable.
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.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
3. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
4. hemGeneratorLaplacianEventFieldEqLaplacian
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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian
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.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle157.remaining_event_field_pointwise_scalar
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after the lower_2 split: prove hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian, the scalar source Delta identity for the named frozen EM Laplacian event field at each selected weak test and state point, directly from the frozen EM interpolation and Fokker--Planck Laplacian display. Do not close it via the cycle-151/152 source-field or trace-field consumers. Keep hemGeneratorLaplacianEventFieldEqTraceField, hemGeneratorLaplacianStateIntegral, htraceFieldMeas, hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hweakFpSourceFieldPointwiseEqLaplacian, 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
2. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
3. appendix.tex:984-995
4. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian
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.cycle157.reviewer_event_field_pointwise_stdbasis_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldStdBasisDef is narrowed to hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise, hemGeneratorLaplacianEventFieldEqLaplacian is narrowed to hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar, stale htraceFieldEqLaplacian/downstream total-event 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.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisLowerObligation
2. SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 157 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 cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle157.packet.event_field_stdbasis_from_pointwise"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise derives hemGeneratorLaplacianEventFieldStdBasisDef from the smaller pointwise standard-basis source display hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef by function extensionality over selected weak tests."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise",
        "hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef",
        "hemGeneratorLaplacianEventFieldStdBasisDef",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqSourceFieldOfStdBasisFields",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle157.lower_1_packet.event_field_pointwise_stdbasis_from_laplacian"
      interface := "Compiled lower_1 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian derives hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef from the smaller pointwise source Delta identity hemGeneratorLaplacianEventFieldEqLaplacian plus SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseLaplacianScoutObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "hemGeneratorLaplacianEventFieldEqLaplacian",
        "hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle157.lower_2_packet.event_field_laplacian_from_pointwise_scalar"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar derives hemGeneratorLaplacianEventFieldEqLaplacian from the smaller statewise source display hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian by function extensionality over the state variable."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
        "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
        "hemGeneratorLaplacianEventFieldEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle157.remaining_event_field_pointwise_scalar"
      interface := "Remaining exact theorem boundary after the lower_2 split: prove hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian, the scalar source Delta identity for the named frozen EM Laplacian event field at each selected weak test and state point, directly from the frozen EM interpolation and Fokker--Planck Laplacian display. Do not close it via the cycle-151/152 source-field or trace-field consumers. Keep hemGeneratorLaplacianEventFieldEqTraceField, hemGeneratorLaplacianStateIntegral, htraceFieldMeas, hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hweakFpSourceFieldPointwiseEqLaplacian, state-event, and sibling EM leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
        "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle157.reviewer_event_field_pointwise_stdbasis_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldStdBasisDef is narrowed to hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise, hemGeneratorLaplacianEventFieldEqLaplacian is narrowed to hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar, stale htraceFieldEqLaplacian/downstream total-event 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.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisLowerObligation",
        "SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 157 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 158: scalar event-field Delta source audit -/

/-- Cycle-158 middle audit for the remaining scalar event-field Delta identity.

This is an explicit wrapper-churn rejection for the current illness area.  Lean
still sees the named frozen EM Laplacian event field as an abstract field, so a
theorem that simply assumes `hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian`
and returns an equivalent field identity would not reduce the paper boundary.
The next lower packet must instead expose the source definition of the Brownian
generator/Fokker--Planck Laplacian event field, or narrow exactly that source
definition further.
-/

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