AutoSamplingTheory.SALD.cycle25PiVelocityNormLowerObligation

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 cycle25PiVelocityNormLowerObligation : 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_lower

statement : String (explicit)

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

Instantiate the compiled scalar cores for appendix.tex lines 104-129 with genuine weighted-Sobolev data: mean-zero variance identity, PI square-root norm bound, L2 pairing/Cauchy-Schwarz estimate for T_mu(psi), nonnegative L2 norms, and admissibility of the source test functions before the Riesz step.

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.cycle25FirstAppendixPiVelocityNormMiddleObligation
4. SALD.saldPiVelocityNormDependencyContract
5. SALD.piVelocityNormMeanZeroH1UpperScalar
6. SALD.piVelocityNormBoundedFunctionalScalar
7. sald.pi.velocity_norm_backend

note : String (explicit)

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

Cycle 25 lower closes only two theorem-independent real-order substeps: the weighted H1 upper-bound algebra and the Cauchy-Schwarz/PI scalar propagation for T_mu. It does not construct dot H^1(mu), prove the Riesz representation step, interpret the weak PDE, or mark Lemma lem:velocity-norm-bound formalized.

def cycle25PiVelocityNormLowerObligation : ProofObligation where
  id := "sald.first_appendix.cycle25_pi_velocity_norm_lower"
  statement := "Instantiate the compiled scalar cores for appendix.tex lines 104-129 with genuine weighted-Sobolev data: mean-zero variance identity, PI square-root norm bound, L2 pairing/Cauchy-Schwarz estimate for T_mu(psi), nonnegative L2 norms, and admissibility of the source test functions before the Riesz step."
  source := saldPiVelocityNormSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle25FirstAppendixVocabularyPacket",
    "SALD.cycle25FirstAppendixMiddleAuditContract",
    "SALD.cycle25FirstAppendixPiVelocityNormMiddleObligation",
    "SALD.saldPiVelocityNormDependencyContract",
    "SALD.piVelocityNormMeanZeroH1UpperScalar",
    "SALD.piVelocityNormBoundedFunctionalScalar",
    "sald.pi.velocity_norm_backend"
  ]
  note := "Cycle 25 lower closes only two theorem-independent real-order substeps: the weighted H1 upper-bound algebra and the Cauchy-Schwarz/PI scalar propagation for T_mu. It does not construct dot H^1(mu), prove the Riesz representation step, interpret the weak PDE, or mark Lemma lem:velocity-norm-bound formalized."

/-- Cycle-29 upper packet for the first appendix/vocabulary layer.

This returns to the first-DAG source-index layer after the cycle-28 guided
general VA-SALD derivative-side algebra.  It selects the LSI/KL/FI
density-test bridge as the next lower obligation refinement while preserving
all source labels, constants, and non-formalized statuses.
-/