AutoSamplingTheory.SALD.cycle38LsiKlFiLowerObligation

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 cycle38LsiKlFiLowerObligation : 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.lsi_kl_fi.cycle38_lower_finite_sum_fisher_chain

statement : String (explicit)

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

Use AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumScalar and AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumHandoffScalar as the theorem-independent finite-coordinate bridge for main_body.tex lines 208-215: once the analytic backend supplies coordinate derivative identities for sqrt(rho/pi) and log(rho/pi), plus the Dirichlet and Fisher finite-sum identifications, the source input dirichlet=(1/4)*FI follows. Radon-Nikodym density, vector Sobolev gradients, integral transport, admissibility/approximation, zero-density conventions, and finite KL/FI remain obligations.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldKlFiLsiSource — 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.cycle38LsiKlFiUpperPacket
2. SALD.cycle38LsiKlFiMiddleObligation
3. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainScalar
4. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainOfDerivativesScalar
5. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumScalar
6. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumHandoffScalar
7. SALD.lsiKlFiDensityTestBridgeScalar
8. SALD.lsiKlFiDensityTestHalfFisherScalar
9. SALD.saldLsiKlFiDensityTestContract
10. SALD.lsiKlFiDensityTestObligation
11. probability.lsi_to_kl_fi

note : String (explicit)

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

Lower cycle 38 compiles only the finite-coordinate sum and Dirichlet/Fisher handoff after explicit derivative and finite-sum hypotheses are supplied. It does not mark eq:LSI-KL-FI, probability.lsi_to_kl_fi, or the Sobolev/integral density-test backend formalized.

def cycle38LsiKlFiLowerObligation : ProofObligation where
  id := "sald.lsi_kl_fi.cycle38_lower_finite_sum_fisher_chain"
  statement := "Use AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumScalar and AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumHandoffScalar as the theorem-independent finite-coordinate bridge for main_body.tex lines 208-215: once the analytic backend supplies coordinate derivative identities for sqrt(rho/pi) and log(rho/pi), plus the Dirichlet and Fisher finite-sum identifications, the source input dirichlet=(1/4)*FI follows. Radon-Nikodym density, vector Sobolev gradients, integral transport, admissibility/approximation, zero-density conventions, and finite KL/FI remain obligations."
  source := saldKlFiLsiSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle38LsiKlFiUpperPacket",
    "SALD.cycle38LsiKlFiMiddleObligation",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainOfDerivativesScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumHandoffScalar",
    "SALD.lsiKlFiDensityTestBridgeScalar",
    "SALD.lsiKlFiDensityTestHalfFisherScalar",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.lsiKlFiDensityTestObligation",
    "probability.lsi_to_kl_fi"
  ]
  note := "Lower cycle 38 compiles only the finite-coordinate sum and Dirichlet/Fisher handoff after explicit derivative and finite-sum hypotheses are supplied. It does not mark eq:LSI-KL-FI, probability.lsi_to_kl_fi, or the Sobolev/integral density-test backend formalized."

/-- Cycle-43 upper packet for the remaining LSI/KL/FI density-test backend.

This packet follows the current proof-closure sprint after cycle 41 narrowed
Gronwall endpoint calculus and cycle 42 narrowed the selected-test
Donsker--Varadhan backend.  It keeps the active target at item (3),
`eq:LSI-KL-FI`, and assigns lower work to the measure-level bridge that is
still missing after the scalar and finite-coordinate cycle-38 helpers.
-/