AutoSamplingTheory.SALD.cycle25FirstAppendixPiVelocityNormMiddleObligation

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 cycle25FirstAppendixPiVelocityNormMiddleObligation : 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.first_appendix.cycle25_pi_velocity_norm_middle

statement : String (explicit)

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

Maintain the cycle 25 lower-ready map for appendix.tex lines 96-129: define the weighted mean-zero Sobolev interface dot H^1(mu), expose the mean-zero/variance bridge and PI norm equivalence, and state the bounded-functional T_mu step before the Riesz representation theorem is used.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldPiVelocityNormSource — 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. SALD.cycle25FirstAppendixVocabularyPacket
2. SALD.cycle25FirstAppendixMiddleAuditContract
3. SALD.saldPIContract
4. SALD.piDefinitionContract
5. SALD.saldPiVelocityNormDependencyContract
6. SALD.piVelocityNormBackendObligation
7. sald.pi.velocity_norm_backend

note : String (explicit)

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

This is a middle-role synchronization obligation. It preserves PI as contract-only, keeps the velocity-norm bound as an obligation, and records line 119 notation plus the line 130-138 operator-norm/Riesz continuation as source-contract gaps rather than theorem assumptions.

def cycle25FirstAppendixPiVelocityNormMiddleObligation : ProofObligation where
  id := "sald.first_appendix.cycle25_pi_velocity_norm_middle"
  statement := "Maintain the cycle 25 lower-ready map for appendix.tex lines 96-129: define the weighted mean-zero Sobolev interface dot H^1(mu), expose the mean-zero/variance bridge and PI norm equivalence, and state the bounded-functional T_mu step before the Riesz representation theorem is used."
  source := saldPiVelocityNormSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle25FirstAppendixVocabularyPacket",
    "SALD.cycle25FirstAppendixMiddleAuditContract",
    "SALD.saldPIContract",
    "SALD.piDefinitionContract",
    "SALD.saldPiVelocityNormDependencyContract",
    "SALD.piVelocityNormBackendObligation",
    "sald.pi.velocity_norm_backend"
  ]
  note := "This is a middle-role synchronization obligation. It preserves PI as contract-only, keeps the velocity-norm bound as an obligation, and records line 119 notation plus the line 130-138 operator-norm/Riesz continuation as source-contract gaps rather than theorem assumptions."

/-- Cycle-25 lower obligation after compiling the scalar PI/Cauchy--Schwarz core. -/