SFT Engine Exhaustiveness: Why Every Declared Claim Produces Either WSC or WOB

SFT treats “universality” as a decision statement: within the declared applicability class, every declared phase-coverage claim resolves to either a certificate or a named obstruction.

Declared inputs and possible outputs

A declared context specifies:

• a slice or subsystem
• a phase observable
• a target rule (including coupling conventions)
• a witness mechanism (how coverage is forced in the declared model class)
• a perturbation model (what stability means)

Within the declared regime, the engine outputs exactly one of:

• WSC (Witness Stability Certificate): coverage on the correct target with explicit robustness margins and an auditable predicate ledger
• WOB (Witness Obstruction): a canonical obstruction code with evidence pointers

This is the operational contract that keeps the theory falsifiable on the page, not only in the abstract.

• Syncré Certificate Engine
• Syncré Form Theory

The first-failure rule

The engine enforces a fixed, finite suite of validator predicates.

• A WSC is admissible only if every required predicate for the declared mechanism and target holds.
• If any required predicate fails, the engine must output a WOB.
• The WOB code is determined by the first failed predicate in a canonical total order.

This is what makes the obstruction catalog exact: it is not a list of possible problems, it is the full list of refusal modes available inside the declared regime.

What this gives you as a reader

• You can tell whether a claim is proved, assumed, or certified by a finite artifact.
• You can see precisely where a universality claim breaks when meaning is underspecified.
• You can reuse the discipline across new arenas without rewriting the philosophy.

Next reading

• SFT Boundary Gallery
• Global Syncré Universality Theorem
• Witness Atlas