Samplinglib
Lean gate not recorded for this source state main · 994992ba220c

AutoSamplingTheory.SALD.cycle180EmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentDependencyNames

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 cycle180EmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentDependencyNames :
    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.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation
  2. SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPolynomialIntegrabilityLower1Obligation
  3. SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoDominatedRemainderLower2Obligation
  4. SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentDag
  5. ASTIS.SALD.cycle180.middle_packet.source_hessian_gap_preserved
  6. ASTIS.SALD.cycle180.middle_packet.taylor_moment_integral_split
  7. ASTIS.SALD.cycle180.lower_1_packet.polynomial_summand_integrability
  8. ASTIS.SALD.cycle180.lower_2_packet.dominated_remainder_integrability
  9. ASTIS.SALD.cycle180.remaining_taylor_integral_source_boundary
  10. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefs
  11. SALD.gaussianRealLinearQuadraticTaylorSummandsIntegrable
  12. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndGaussianPolynomialIntegrability
  13. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder
  14. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
  15. SALD.gaussianRealZeroOneDimTaylorMomentContribution
  16. hFrozenScalarBrownianItoTaylorMomentDecomposition
  17. hBrownianCoordinateGeneratorTaylorIntegralDef
  18. hLinearInt
  19. hQuadraticInt
  20. hLinearInt discharged by Gaussian polynomial integrability
  21. hQuadraticInt discharged by Gaussian polynomial integrability
  22. hRemainderInt
  23. hRemainderInt discharged by dominated remainder integrability
  24. hRemainderMeas
  25. hRemainderBound
  26. hRemainderBoundInt
  27. hRemainderGeneratorLimitDef
  28. normalizedRemainder
  29. remainderBound
  30. brownianCoordinateGenerator
  31. linearCoeff
  32. quadraticCoeff
  33. remainderGeneratorLimit
  34. MeasureTheory.integral_add
  35. MeasureTheory.integral_const_mul
  36. MeasureTheory.Integrable.mono'
  37. MeasureTheory.Integrable.const_mul
  38. ProbabilityTheory.integrable_exp_mul_gaussianReal
  39. ProbabilityTheory.integrable_pow_of_integrable_exp_mul
  40. hScalarLineTaylorCoeffDef
  41. hNormalizedVectorLaw
  42. hCoordinateLawDef
  43. hVarianceDef
  44. hSecondCoeff
  45. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
  46. hFrozenScalarBrownianItoEventFieldCoordinateSum
  47. hSourceHasHessian
  48. hSourceHessianBound
  49. source-contract-gap for selected weak-test Hessian fields
  50. eq:general_moving_target_SALD_frozen_interp
  51. appendix.tex:984-995
  52. appendix.tex:1170-1176
  53. appendix.tex:1379-1387
  54. sald.general_moving_target_discrete.em_interpolation_fp
  55. sald.discrete_forward_kl.em_interpolation_fp
  56. 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 cycle180EmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentDependencyNames :
    List String := [
  "SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation",
  "SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPolynomialIntegrabilityLower1Obligation",
  "SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoDominatedRemainderLower2Obligation",
  "SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentDag",
  "ASTIS.SALD.cycle180.middle_packet.source_hessian_gap_preserved",
  "ASTIS.SALD.cycle180.middle_packet.taylor_moment_integral_split",
  "ASTIS.SALD.cycle180.lower_1_packet.polynomial_summand_integrability",
  "ASTIS.SALD.cycle180.lower_2_packet.dominated_remainder_integrability",
  "ASTIS.SALD.cycle180.remaining_taylor_integral_source_boundary",
  "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefs",
  "SALD.gaussianRealLinearQuadraticTaylorSummandsIntegrable",
  "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndGaussianPolynomialIntegrability",
  "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder",
  "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
  "SALD.gaussianRealZeroOneDimTaylorMomentContribution",
  "hFrozenScalarBrownianItoTaylorMomentDecomposition",
  "hBrownianCoordinateGeneratorTaylorIntegralDef",
  "hLinearInt",
  "hQuadraticInt",
  "hLinearInt discharged by Gaussian polynomial integrability",
  "hQuadraticInt discharged by Gaussian polynomial integrability",
  "hRemainderInt",
  "hRemainderInt discharged by dominated remainder integrability",
  "hRemainderMeas",
  "hRemainderBound",
  "hRemainderBoundInt",
  "hRemainderGeneratorLimitDef",
  "normalizedRemainder",
  "remainderBound",
  "brownianCoordinateGenerator",
  "linearCoeff",
  "quadraticCoeff",
  "remainderGeneratorLimit",
  "MeasureTheory.integral_add",
  "MeasureTheory.integral_const_mul",
  "MeasureTheory.Integrable.mono'",
  "MeasureTheory.Integrable.const_mul",
  "ProbabilityTheory.integrable_exp_mul_gaussianReal",
  "ProbabilityTheory.integrable_pow_of_integrable_exp_mul",
  "hScalarLineTaylorCoeffDef",
  "hNormalizedVectorLaw",
  "hCoordinateLawDef",
  "hVarianceDef",
  "hSecondCoeff",
  "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
  "hFrozenScalarBrownianItoEventFieldCoordinateSum",
  "hSourceHasHessian",
  "hSourceHessianBound",
  "source-contract-gap for selected weak-test Hessian fields",
  "eq:general_moving_target_SALD_frozen_interp",
  "appendix.tex:984-995",
  "appendix.tex:1170-1176",
  "appendix.tex:1379-1387",
  "sald.general_moving_target_discrete.em_interpolation_fp",
  "sald.discrete_forward_kl.em_interpolation_fp",
  "thm:general-moving-target-SALD-discrete"
  ]

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