AutoSamplingTheory.SALD.cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasDag

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 cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasDag :
    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.cycle123.lower_packet.em_sample_deriv_meas_from_concrete_deriv
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated derives hsampleDerivMeas from AEStronglyMeasurable of the concrete derivative fun omega => deriv (fun t => testEval phi (hatX t omega)) s0 plus ae equality to sampleDeriv phi s0, then reuses the cycle-122 EM interval 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.cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated
4. MeasureTheory.AEStronglyMeasurable.congr
5. 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. thm:forward-KL-discrete
3. thm:general-moving-target-SALD-discrete
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.cycle123.remaining_em_path_derivative_domination_after_deriv_meas
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after hsampleMeas, hsampleInt, and hsampleDerivMeas are discharged: prove hsampleDerivBound, hboundInt, and hpathDeriv for each admissible weak test on the source EM interval, then separately prove hderivValue and the canonical barB source-action identities.
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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated
2. ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative
3. Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le
4. eq:general_moving_target_SALD_frozen_interp
5. 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. thm:general-moving-target-SALD-discrete
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.cycle123.reviewer_em_sample_deriv_meas_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hsampleDerivMeas, the proof uses a concrete EM derivative representative and ae-congruence rather than a wrapper around hsampleDerivMeas, and python3 tools/astis.py check passes with no hbarBCondExp wrapper churn, non-EM fallback, SLT/Lake change, source-index rebaseline, theorem-status promotion, fake closure, 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.cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated
3. appendix.tex:1368-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 123 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 cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle123.lower_packet.em_sample_deriv_meas_from_concrete_deriv"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated derives hsampleDerivMeas from AEStronglyMeasurable of the concrete derivative fun omega => deriv (fun t => testEval phi (hatX t omega)) s0 plus ae equality to sampleDeriv phi s0, then reuses the cycle-122 EM interval theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated",
        "MeasureTheory.AEStronglyMeasurable.congr",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle123.remaining_em_path_derivative_domination_after_deriv_meas"
      interface := "Remaining exact theorem after hsampleMeas, hsampleInt, and hsampleDerivMeas are discharged: prove hsampleDerivBound, hboundInt, and hpathDeriv for each admissible weak test on the source EM interval, then separately prove hderivValue and the canonical barB source-action identities."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated",
        "ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative",
        "Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle123.reviewer_em_sample_deriv_meas_check"
      interface := "Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hsampleDerivMeas, the proof uses a concrete EM derivative representative and ae-congruence rather than a wrapper around hsampleDerivMeas, and python3 tools/astis.py check passes with no hbarBCondExp wrapper churn, non-EM fallback, SLT/Lake change, source-index rebaseline, theorem-status promotion, fake closure, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated",
        "appendix.tex:1368-1387"
      ]
      reusedBy := ["cycle 123 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 124: EM sample derivative bound from concrete derivative representative -/

/-- Cycle-124 lower obligation for discharging the sample derivative bound input
from the EM interval measurable/integrable/derivative-measurable dominated
packet.

This packet stays inside the cycle-123 EM path-derivative/domination dynamic
leaf.  It removes only the supplied `hsampleDerivBound` hypothesis by requiring
a source-facing concrete derivative bound on the EM interval and an a.e.
interval equality between the concrete derivative representative and the chosen
`sampleDeriv` representative.  It leaves bound integrability, pointwise path
derivatives, derivative-value splitting, and source-action facts explicit.
-/

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