AutoSamplingTheory.SALD.generalMovingTargetDiscreteFrozenDeltaObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def generalMovingTargetDiscreteFrozenDeltaObligation : 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.frozen_delta_cross_lip

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 Lemma lem:frozen_delta_cross_lip, appendix lines 1026-1307: under the source c_t/score space-time Lipschitz assumptions, exponential-complexity assumptions, and step-size condition, bound the VA frozen-field cross term by (sigma_eta^2/8)*FI + 2*eta^2*alpha'^(-1)*Gamma*K + 2*eta*Delta.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldFrozenDeltaCrossLipGeneralSource — 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

eq:SALD_general_EM
eq:general_discrete_delta_def
lem:dv_variation
def:alpha-complexity

note : String (explicit)

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

generalFrozenDeltaCrossLipContract records the source proof split through the joint law, increment estimate, DV bounds for c_t/score/1+M, and Gamma/Delta collection.

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 generalMovingTargetDiscreteFrozenDeltaObligation : ProofObligation where
  id := "sald.general_moving_target_discrete.frozen_delta_cross_lip"
  statement := "Formalize Lemma lem:frozen_delta_cross_lip, appendix lines 1026-1307: under the source c_t/score space-time Lipschitz assumptions, exponential-complexity assumptions, and step-size condition, bound the VA frozen-field cross term by (sigma_eta^2/8)*FI + 2*eta^2*alpha'^(-1)*Gamma*K + 2*eta*Delta."
  source := saldFrozenDeltaCrossLipGeneralSource
  status := ProofStatus.obligation
  dependsOn := ["eq:SALD_general_EM", "eq:general_discrete_delta_def", "lem:dv_variation", "def:alpha-complexity"]
  note := "generalFrozenDeltaCrossLipContract records the source proof split through the joint law, increment estimate, DV bounds for c_t/score/1+M, and Gamma/Delta collection."

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