AutoSamplingTheory.SALD.cycle16UnifiedForwardKlTransportBridgeLowerObligation

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 cycle16UnifiedForwardKlTransportBridgeLowerObligation : 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.unified_forward_kl.transport_bridge_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.

Refine the lower slice for main_body.tex lines 359-368: add the residual equation and correction equation with their source signs, expose the divergence-linearity backend needed to rewrite div(pi_t*(u_t+w_t)), cancel the centered guide residual, and hand v_t=u_t+w_t, c_t=u_t, m_t=w_t to the unified specialization.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldUnifiedTransportBridgeSource — 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.cycle16UnifiedForwardKlTransportBridgeMiddleContract
2. SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract
3. SALD.unifiedForwardKlSpecializationContract
4. sald.guided_path_residual.identity
5. eq:poisson-eq
6. TransportVelocityContract

note : String (explicit)

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

This lower sub-obligation remains inside sald.unified_forward_kl.transport_velocity_bridge. It records only the signed cancellation and divergence-linearity interface; correction-field existence, residual DV, Gronwall, and discrete EM remain separate.

def cycle16UnifiedForwardKlTransportBridgeLowerObligation : ProofObligation where
  id := "sald.unified_forward_kl.transport_bridge_lower"
  statement := "Refine the lower slice for main_body.tex lines 359-368: add the residual equation and correction equation with their source signs, expose the divergence-linearity backend needed to rewrite div(pi_t*(u_t+w_t)), cancel the centered guide residual, and hand v_t=u_t+w_t, c_t=u_t, m_t=w_t to the unified specialization."
  source := saldUnifiedTransportBridgeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract",
    "SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.guided_path_residual.identity",
    "eq:poisson-eq",
    "TransportVelocityContract"
  ]
  note := "This lower sub-obligation remains inside sald.unified_forward_kl.transport_velocity_bridge. It records only the signed cancellation and divergence-linearity interface; correction-field existence, residual DV, Gronwall, and discrete EM remain separate."