AutoSamplingTheory.SALD.dvFiniteLogMgfInterfaceObligation

Data definition / provenance and workflow record

Meaning and type

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

def dvFiniteLogMgfInterfaceObligation : ProofObligation

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.

id : String (explicit)

Stable obligation identifier.

sald.dv_variation.finite_log_mgf_interface

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Formalize the first-layer interface needed to instantiate lem:dv_variation: common measurable probability space for mu and nu, measurable random variable Z, finite log E_mu[exp Z], and the alpha-complexity witness used by SALD squared-velocity tests.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

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

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

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

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. probability.dv_variational_formula
2. SALD.saldDvFiniteLogMgfContract
3. def:alpha-complexity

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

The DV theorem itself remains source-cited. This obligation only exposes the finite-log-mgf and common-space side conditions needed by later theorem-specific DV-energy obligations.

def dvFiniteLogMgfInterfaceObligation : ProofObligation where
  id := "sald.dv_variation.finite_log_mgf_interface"
  statement := "Formalize the first-layer interface needed to instantiate lem:dv_variation: common measurable probability space for mu and nu, measurable random variable Z, finite log E_mu[exp Z], and the alpha-complexity witness used by SALD squared-velocity tests."
  source := saldDvVariationSource
  status := ProofStatus.obligation
  dependsOn := ["probability.dv_variational_formula", "SALD.saldDvFiniteLogMgfContract", "def:alpha-complexity"]
  note := "The DV theorem itself remains source-cited.  This obligation only exposes the finite-log-mgf and common-space side conditions needed by later theorem-specific DV-energy obligations."