Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle202EmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineDependencyNames

Data definition / provenance and workflow record

Meaning and type

The result has data type List String. 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 cycle202EmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineDependencyNames :
    List String

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

  1. SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation
  2. SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Dag
  3. ASTIS.SALD.cycle202.lower_2_packet.selected_endpoint_coordinate_line_source_gap
  4. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
  5. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef
  6. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
  7. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs
  8. AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw
  9. hSelectedEndpointCoordinateLineDef
  10. hSelectedIncrementEndpointDef
  11. hSelectedIncrementCoordinateLineDef
  12. hSourceTaylorIntegrandRawDef
  13. sourceSelectedEndpoint
  14. sourceSelectedLineIncrement
  15. sourceTaylorIntegrand
  16. selectedTest
  17. stdOrthonormalBasis
  18. needed_shape=testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i
  19. leaf=hSelectedEndpointCoordinateLineDef
  20. error_class=source_contract_gap_missing_selected_endpoint_coordinate_line_definition
  21. blocked_by=sourceSelectedEndpoint is an abstract Lean parameter and the original paper source does not provide a Lean-facing endpoint coordinate-line definition
  22. eq:SALD_general_EM
  23. eq:general_moving_target_SALD_frozen_interp
  24. appendix.tex:958-970
  25. appendix.tex:983-996
  26. appendix.tex:1161-1170
  27. appendix.tex:1379-1387
  28. source_contract_gap_missing_selected_endpoint_coordinate_line_definition
  29. sald.general_moving_target_discrete.em_interpolation_fp
  30. sald.general_moving_target_discrete.kl_derivative
  31. divergence/FI/IBP handoff
  32. thm:general-moving-target-SALD-discrete
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 cycle202EmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineDependencyNames :
    List String := [
  "SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation",
  "SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Dag",
  "ASTIS.SALD.cycle202.lower_2_packet.selected_endpoint_coordinate_line_source_gap",
  "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
  "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef",
  "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
  "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs",
  "AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw",
  "hSelectedEndpointCoordinateLineDef",
  "hSelectedIncrementEndpointDef",
  "hSelectedIncrementCoordinateLineDef",
  "hSourceTaylorIntegrandRawDef",
  "sourceSelectedEndpoint",
  "sourceSelectedLineIncrement",
  "sourceTaylorIntegrand",
  "selectedTest",
  "stdOrthonormalBasis",
  "needed_shape=testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i",
  "leaf=hSelectedEndpointCoordinateLineDef",
  "error_class=source_contract_gap_missing_selected_endpoint_coordinate_line_definition",
  "blocked_by=sourceSelectedEndpoint is an abstract Lean parameter and the original paper source does not provide a Lean-facing endpoint coordinate-line definition",
  "eq:SALD_general_EM",
  "eq:general_moving_target_SALD_frozen_interp",
  "appendix.tex:958-970",
  "appendix.tex:983-996",
  "appendix.tex:1161-1170",
  "appendix.tex:1379-1387",
  "source_contract_gap_missing_selected_endpoint_coordinate_line_definition",
  "sald.general_moving_target_discrete.em_interpolation_fp",
  "sald.general_moving_target_discrete.kl_derivative",
  "divergence/FI/IBP handoff",
  "thm:general-moving-target-SALD-discrete"
  ]

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