SFT Boundary Gallery: How Syncré Claims Fail When Meaning Is Underspecified

This page is a quick guide to the most common ways phase-coverage claims go wrong.

Each item corresponds to a boundary obstruction in the engine. The point is not merely that “coverage fails,” but that the claim is not yet meaningful in an auditable way.

Missing phase (no cycle-valued observable)

A claim cannot be checked if it does not name a phase.

Symptoms:

• the observable is a scalar with no cyclic interpretation
• the phase is described only in words (“periodic behavior”) with no declared mapping to a circle

Engine meaning:

• the correct output is a WOB in the “no phase observable” family

No slice or subsystem (nothing to observe)

Coverage is a statement about where the phase is measured.

Symptoms:

• the claim says “somewhere in the system” but never names a slice
• the phase is defined only along trajectories, not on a declared slice or subsystem

Engine meaning:

• the correct output is a WOB in the “no subsystem” family

Wrong target (asserting coverage on the ambient product instead of the coupled target)

This is the most common universality mistake in multi-cycle problems.

Symptoms:

• multiple phases are present and the claim asserts coverage on a full torus
• a physical or structural constraint locks them together (resonance, conservation, geometry, or imposed coupling law)

Engine meaning:

• the correct target is a coupled subtorus coset (CST)
• the correct output is either a WSC on the CST or a WOB explaining why CST identification is not justified

Baseline mismatch (using the wrong “uniform” reference)

When statistical language is used, the baseline must match the correct target.

Symptoms:

• “uniform on the torus” is asserted even when coupling reduces the target
• “uniform on the circle” is asserted when the correct target is a quotient or an embedded target

Engine meaning:

• mixing upgrades are allowed only when the baseline is declared and target-correct

Witness not declared (no forcing route)

SFT does not allow “coverage must happen” without a declared reason.

Symptoms:

• the claim is presented as obvious or intuitive
• no symmetry, winding, holonomy, or coupling template is specified

Engine meaning:

• the correct output is a WOB in the “no witness mechanism” family

Overclaiming outside the declared regime

The applicability class exists to keep universality claims honest and checkable.

Symptoms:

• no admissible witness mechanism can be declared
• the target cannot be identified in a stable way under perturbations
• the needed regularity assumptions fail in the declared tolerance model

Engine meaning:

• the correct output is a boundary obstruction, not a coverage certificate

Next reading

• SFT Engine Exhaustiveness (WSC or WOB)
• Syncré Certificate Engine
• Syncré Canonical Equation Reference