AutoSamplingTheory.SALD.cycle124GeneralMovingTargetDiscreteEmBoundIntDag

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 cycle124GeneralMovingTargetDiscreteEmBoundIntDag :
    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.cycle124.lower_packet.em_bound_int_from_joint_law
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated derives hboundInt from a joint-law integrable bound and a.e. equality to the selected sample-space bound, then reuses the cycle-124 derivative-bound 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.cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundDominated
4. MeasureTheory.Integrable.comp_aemeasurable
5. MeasureTheory.Integrable.congr
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. 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.cycle124.remaining_em_path_derivative_domination_after_bound_int
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after hsampleMeas, hsampleInt, hsampleDerivMeas, hsampleDerivBound, and hboundInt are discharged: prove 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated
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.cycle124.reviewer_em_bound_int_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hboundInt, the proof transports a joint-law integrable bound rather than restating hboundInt, and python3 tools/astis.py check passes with no 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.cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated
3. appendix.tex:1368-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 124 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 cycle124GeneralMovingTargetDiscreteEmBoundIntDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle124.lower_packet.em_bound_int_from_joint_law"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated derives hboundInt from a joint-law integrable bound and a.e. equality to the selected sample-space bound, then reuses the cycle-124 derivative-bound theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundDominated",
        "MeasureTheory.Integrable.comp_aemeasurable",
        "MeasureTheory.Integrable.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.cycle124.remaining_em_path_derivative_domination_after_bound_int"
      interface := "Remaining exact theorem after hsampleMeas, hsampleInt, hsampleDerivMeas, hsampleDerivBound, and hboundInt are discharged: prove 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated",
        "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.cycle124.reviewer_em_bound_int_check"
      interface := "Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hboundInt, the proof transports a joint-law integrable bound rather than restating hboundInt, and python3 tools/astis.py check passes with no 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.cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated",
        "appendix.tex:1368-1387"
      ]
      reusedBy := ["cycle 124 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 125: EM path derivative from concrete differentiability -/

/-- Cycle-125 lower obligation for discharging the pointwise path-derivative
input from the EM interval bound-integrability dominated packet.

This packet stays inside the EM path-derivative/domination dynamic leaf.  It
removes only the supplied `hpathDeriv` hypothesis by deriving the selected
`HasDerivAt` input from a.e. differentiability of the concrete weak-test EM
path and the already exposed interval a.e. equality between `sampleDeriv` and
`deriv (fun t => testEval phi (hatX t omega))`.
-/

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