AutoSamplingTheory.SALD.cycle16UnifiedForwardKlTransportBridgeMiddleObligation

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 cycle16UnifiedForwardKlTransportBridgeMiddleObligation : 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_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-16 middle source-to-Lean map for the unified VA-SALD transport bridge: main_body.tex lines 359-368 must route from prop:guided_path_residual and eq:poisson-eq to u_t+w_t transporting pi_t, then appendix.tex lines 949-951 must specialize thm:general-moving-target-SALD with c_t=u_t and m_t=w_t.

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.cycle16GeneralVaSaldUpperPacket
2. SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract
3. SALD.unifiedForwardKlSpecializationContract
4. sald.guided_path_residual.identity
5. eq:poisson-eq
6. sald.unified_forward_kl.transport_velocity_bridge

note : String (explicit)

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

This is middle-role synchronization data. It selects the transport-velocity bridge as the lower slice and keeps correction-field existence, divergence regularity, DV, Gronwall, and discrete EM work as separate obligations.

def cycle16UnifiedForwardKlTransportBridgeMiddleObligation : ProofObligation where
  id := "sald.unified_forward_kl.transport_bridge_middle"
  statement := "Maintain the cycle-16 middle source-to-Lean map for the unified VA-SALD transport bridge: main_body.tex lines 359-368 must route from prop:guided_path_residual and eq:poisson-eq to u_t+w_t transporting pi_t, then appendix.tex lines 949-951 must specialize thm:general-moving-target-SALD with c_t=u_t and m_t=w_t."
  source := saldUnifiedTransportBridgeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle16GeneralVaSaldUpperPacket",
    "SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.guided_path_residual.identity",
    "eq:poisson-eq",
    "sald.unified_forward_kl.transport_velocity_bridge"
  ]
  note := "This is middle-role synchronization data. It selects the transport-velocity bridge as the lower slice and keeps correction-field existence, divergence regularity, DV, Gronwall, and discrete EM work as separate obligations."