AutoSamplingTheory.SALD.generalMovingTargetDvEnergyCandidateContract

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.SALD.GeneralMovingTargetDvEnergyCandidateContract. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def generalMovingTargetDvEnergyCandidateContract :
    GeneralMovingTargetDvEnergyCandidateContract

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

sourceBlock : AutoSamplingTheory.SourceAnchor (explicit)

Nested provenance data.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDvGronwallSource — audited data reference, not expanded and not a compiled dependency edge

dvMeasure : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

Apply lem:dv_variation with nu=rho_{s(t)} and mu=pi_t.

dvTestFunction : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

Z(x)=alpha*||m_t(x)||^2.

integrabilityRoute : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

The theorem assumes E_{alpha0}(pi_t,m_t)<+infty and alpha in (0,alpha0]; a finite log-mgf monotonicity lemma is needed before invoking DV.

bound : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

||m_t||_{L2(rho_{s(t)})}^2 <= alpha^(-1)*K(t)+E_alpha(pi_t,m_t).

dependencies : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. lem:dv_variation
2. def:alpha-complexity
3. KLContract
4. sald.general_moving_target.dv_finite_log_mgf_witness
5. sald.general_moving_target.dv_positive_alpha_scaling

sourceGaps : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. the appendix applies DV directly; Lean must expose the finite log-mgf witness for m_t

status : AutoSamplingTheory.ProofStatus (explicit)

Stored workflow tag; honor the exact default but do not infer mathematical certification.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

def generalMovingTargetDvEnergyCandidateContract :
    GeneralMovingTargetDvEnergyCandidateContract where
  sourceBlock := saldGeneralMovingTargetDvGronwallSource
  dvMeasure := "Apply lem:dv_variation with nu=rho_{s(t)} and mu=pi_t."
  dvTestFunction := "Z(x)=alpha*||m_t(x)||^2."
  integrabilityRoute := "The theorem assumes E_{alpha0}(pi_t,m_t)<+infty and alpha in (0,alpha0]; a finite log-mgf monotonicity lemma is needed before invoking DV."
  bound := "||m_t||_{L2(rho_{s(t)})}^2 <= alpha^(-1)*K(t)+E_alpha(pi_t,m_t)."
  dependencies := [
    "lem:dv_variation",
    "def:alpha-complexity",
    "KLContract",
    "sald.general_moving_target.dv_finite_log_mgf_witness",
    "sald.general_moving_target.dv_positive_alpha_scaling"
  ]
  sourceGaps := [
    "the appendix applies DV directly; Lean must expose the finite log-mgf witness for m_t"
  ]
  status := ProofStatus.obligation