AutoSamplingTheory.SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessObligation

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 generalMovingTargetDiscreteDvFiniteLogMgfWitnessObligation : 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.general_moving_target_discrete.dv_finite_log_mgf_witness

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 discrete residual DV side interface for appendix lines 1544-1552: with nu=hat rho_s, mu=tilde pi_s=pi_{t(s)}, and Z=alpha*||m_{t(s)}||^2, reuse the continuous residual alpha0-to-alpha finite-log-mgf witness, expose EM-interpolation common-space and absolute-continuity, divide by alpha>0, and preserve the doubled coefficient 2*sigma_eta^(-2)*dot t(s)^2 before time change.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteResidualDvSource — 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. def:alpha-complexity
3. SALD.saldDvFiniteLogMgfContract
4. sald.dv_variation.finite_log_mgf_interface
5. sald.general_moving_target.dv_finite_log_mgf_witness
6. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
7. sald.general_moving_target_discrete.em_interpolation_fp
8. sald.general_moving_target_discrete.derivative_side_conditions

note : String (explicit)

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

This narrows the Cycle 12 upper target to the residual m_t DV witness under the general EM interpolation. It does not add hypotheses to the discrete theorem or mark DV formalized.

def generalMovingTargetDiscreteDvFiniteLogMgfWitnessObligation : ProofObligation where
  id := "sald.general_moving_target_discrete.dv_finite_log_mgf_witness"
  statement := "Formalize the discrete residual DV side interface for appendix lines 1544-1552: with nu=hat rho_s, mu=tilde pi_s=pi_{t(s)}, and Z=alpha*||m_{t(s)}||^2, reuse the continuous residual alpha0-to-alpha finite-log-mgf witness, expose EM-interpolation common-space and absolute-continuity, divide by alpha>0, and preserve the doubled coefficient 2*sigma_eta^(-2)*dot t(s)^2 before time change."
  source := saldGeneralMovingTargetDiscreteResidualDvSource
  status := ProofStatus.obligation
  dependsOn := [
    "probability.dv_variational_formula",
    "def:alpha-complexity",
    "SALD.saldDvFiniteLogMgfContract",
    "sald.dv_variation.finite_log_mgf_interface",
    "sald.general_moving_target.dv_finite_log_mgf_witness",
    "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.derivative_side_conditions"
  ]
  note := "This narrows the Cycle 12 upper target to the residual m_t DV witness under the general EM interpolation. It does not add hypotheses to the discrete theorem or mark DV formalized."