AutoSamplingTheory.SALD.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseDag

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 cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseDag :
    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.cycle156.packet.trace_field_eq_laplacian_from_pointwise
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise derives htraceFieldEqLaplacian from htraceFieldPointwiseEqLaplacian by function extensionality over the selected weak-test index.
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.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise
3. htraceFieldPointwiseEqLaplacian
4. htraceFieldEqLaplacian
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.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
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.cycle156.lower_1_packet.trace_field_pointwise_laplacian_from_stdbasis
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 scout theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis derives htraceFieldPointwiseEqLaplacian from the pointwise standard-basis trace display htraceFieldPointwiseStdBasis 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.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. htraceFieldPointwiseStdBasis
5. htraceFieldPointwiseEqLaplacian
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.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField
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.cycle156.lower_2_packet.trace_field_pointwise_stdbasis_from_event_field
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis derives htraceFieldPointwiseStdBasis from the smaller source-facing pair hemGeneratorLaplacianEventFieldEqTraceField plus hemGeneratorLaplacianEventFieldStdBasisDef.
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.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis
3. htraceFieldPointwiseStdBasis
4. hemGeneratorLaplacianEventFieldEqTraceField
5. hemGeneratorLaplacianEventFieldStdBasisDef
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.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise
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.cycle156.remaining_trace_field_pointwise_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 156 lower_2: prove the event/trace field identification hemGeneratorLaplacianEventFieldEqTraceField and the event-field standard-basis source definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian contribution. Keep 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.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. htraceFieldPointwiseEqLaplacian
6. htraceFieldPointwiseStdBasis
7. hemGeneratorLaplacianEventFieldEqTraceField
8. hemGeneratorLaplacianEventFieldStdBasisDef
9. appendix.tex:984-995
10. appendix.tex:1368-1387
11. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle156.reviewer_trace_field_pointwise_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, htraceFieldEqLaplacian is narrowed to htraceFieldPointwiseEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise, htraceFieldPointwiseStdBasis is narrowed to hemGeneratorLaplacianEventFieldEqTraceField plus hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis, stale trace-law/trace-state 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.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis
4. appendix.tex:984-995
5. appendix.tex:1368-1387
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 156 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 cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle156.packet.trace_field_eq_laplacian_from_pointwise"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise derives htraceFieldEqLaplacian from htraceFieldPointwiseEqLaplacian by function extensionality over the selected weak-test index."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise",
        "htraceFieldPointwiseEqLaplacian",
        "htraceFieldEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle156.lower_1_packet.trace_field_pointwise_laplacian_from_stdbasis"
      interface := "Compiled lower_1 scout theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis derives htraceFieldPointwiseEqLaplacian from the pointwise standard-basis trace display htraceFieldPointwiseStdBasis plus SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "htraceFieldPointwiseStdBasis",
        "htraceFieldPointwiseEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle156.lower_2_packet.trace_field_pointwise_stdbasis_from_event_field"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis derives htraceFieldPointwiseStdBasis from the smaller source-facing pair hemGeneratorLaplacianEventFieldEqTraceField plus hemGeneratorLaplacianEventFieldStdBasisDef."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis",
        "htraceFieldPointwiseStdBasis",
        "hemGeneratorLaplacianEventFieldEqTraceField",
        "hemGeneratorLaplacianEventFieldStdBasisDef",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle156.remaining_trace_field_pointwise_laplacian"
      interface := "Remaining exact theorem boundary after cycle 156 lower_2: prove the event/trace field identification hemGeneratorLaplacianEventFieldEqTraceField and the event-field standard-basis source definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian contribution. Keep hemGeneratorLaplacianStateIntegral, htraceFieldMeas, hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hweakFpSourceFieldPointwiseEqLaplacian, state-event, and sibling EM leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "htraceFieldPointwiseEqLaplacian",
        "htraceFieldPointwiseStdBasis",
        "hemGeneratorLaplacianEventFieldEqTraceField",
        "hemGeneratorLaplacianEventFieldStdBasisDef",
        "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
    },
    {
      id := "ASTIS.SALD.cycle156.reviewer_trace_field_pointwise_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, htraceFieldEqLaplacian is narrowed to htraceFieldPointwiseEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise, htraceFieldPointwiseStdBasis is narrowed to hemGeneratorLaplacianEventFieldEqTraceField plus hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis, stale trace-law/trace-state 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.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 156 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 157: event-field standard-basis definition from pointwise display -/

/-- Cycle-157 narrowing of the EM Laplacian event-field standard-basis boundary. -/

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