AutoSamplingTheory.SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianDag

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 cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianDag :
    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.cycle146.lower_1_packet.trace_field_std_basis_from_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField derives htraceFieldStdBasis from htraceFieldEqLaplacian by applying the local Mathlib standard-basis Laplacian bridge to each selected 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.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula
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.cycle146.lower_1_packet.weak_fp_source_action_em_generator_trace_laplacian_total_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula feeds the trace-field Laplacian split through the current trace-event total-event route, replacing only htraceFieldStdBasis while keeping hemGeneratorLaplacianTotalEventIntegral and hemGeneratorLaplacianEventFieldEqTraceField 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.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula
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.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle146.lower_1_remaining_total_event_trace_event_and_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 146 lower_1: prove hemGeneratorLaplacianTotalEventIntegral, prove hemGeneratorLaplacianEventFieldEqTraceField, and prove htraceFieldEqLaplacian. The older htraceFieldStdBasis now follows locally from htraceFieldEqLaplacian plus the Mathlib standard-basis Laplacian theorem.
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula
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. 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.cycle146.lower_1_reviewer_trace_field_laplacian_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, htraceFieldStdBasis is narrowed to htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula, sibling EM/weak-FP source leaves remain explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, 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.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
4. SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation
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. cycle 146 lower_1 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 cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle146.lower_1_packet.trace_field_std_basis_from_laplacian"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField derives htraceFieldStdBasis from htraceFieldEqLaplacian by applying the local Mathlib standard-basis Laplacian bridge to each selected test."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle146.lower_1_packet.weak_fp_source_action_em_generator_trace_laplacian_total_event_trace_laplacian"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula feeds the trace-field Laplacian split through the current trace-event total-event route, replacing only htraceFieldStdBasis while keeping hemGeneratorLaplacianTotalEventIntegral and hemGeneratorLaplacianEventFieldEqTraceField explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula",
        "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.formalized
    },
    {
      id := "ASTIS.SALD.cycle146.lower_1_remaining_total_event_trace_event_and_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 146 lower_1: prove hemGeneratorLaplacianTotalEventIntegral, prove hemGeneratorLaplacianEventFieldEqTraceField, and prove htraceFieldEqLaplacian. The older htraceFieldStdBasis now follows locally from htraceFieldEqLaplacian plus the Mathlib standard-basis Laplacian theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula",
        "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.cycle146.lower_1_reviewer_trace_field_laplacian_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, htraceFieldStdBasis is narrowed to htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula, sibling EM/weak-FP source leaves remain explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, wrapper churn, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 146 lower_1 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 146 lower_2: EM pointwise trace-event boundary -/

/-- Cycle-146 lower_2 narrowing for the event-field/trace-field equality
inside the latest trace-event total-event route. -/

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