# 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 below corresponds to a canonical boundary obstruction in the engine: the point is not 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 single most common universality mistake in multi-cycle problems.

Symptoms:

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

Engine meaning:

- the correct target is a coupled subtorus (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” distribution)

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 target is a quotient or 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 regime (trying to use SFT where its predicates do not apply)

COC is the class where the question is well-posed under the SFT contract.

Symptoms:

- the context cannot declare any admissible witness mechanism
- the system’s automorphism class does not support cyclic forcing
- the target cannot be identified in a stable way under perturbations

Engine meaning:

- the correct output is a boundary obstruction, not a coverage certificate.

## Where the engine draws these lines

- Contract overview: `engine/contracts/engine_contract.md`
- Predicate spec: `engine/contracts/VALIDATOR_PREDICATE_SPEC.md`
- WOB codebook: `engine/contracts/wob_codebook.json`
