# Witness Atlas Families

The witness atlas is organized into families so entries read as reductions under a small set of templates.

## Rotation & periodic forcing

- Template: a cyclic action on a slice plus an equivariant phase observable with nondegenerate response.
- Output: WSC with action witness, circle target, Haar baseline.
- Typical predicates: V01, V08, V09.

## Embedded loops & defects

- Template: a loop subsystem (ring, defect circuit, closed path) where the phase observable has nonzero degree or nonzero holonomy multiple.
- Output: WSC on an embedded target (induced circle), Haar baseline on that embedded target.
- Typical predicates: V01, V02, V04, with V05 when holonomy is used.

## Coupled targets (CST)

- Template: multi-cycle integer relations restrict the image to a coupled subtorus.
- Output: WSC on CST with coupled Haar baseline, plus explicit target-correctness assertions.
- Typical predicates: V01, V06, with inference predicates V13–V15 when CST is inferred from data.

## Torus drives & equidistribution

- Template: independent drives generate a torus target.
- Output: WSC for coverage, with RNF evidence recorded only when explicitly declared.
- Typical predicates: V01, V08, V09, with boundary codes for resonance and coupling mistakes.

## Noise-to-diffusion mixing upgrades

- Template: an explicit noise-to-diffusion bridge plus a declared mixing certificate.
- Output: WSC that carries a mixing upgrade, with baseline discipline enforced.
- Typical predicates: V01, V07, and V06 on CST targets.

## Boundary obstructions

- Template: missing cyclic observability, wrong target/baseline, equivariance defects, resonance, disconnected evidence domains, or ill-posed inference.
- Output: WOB with a canonical code and evidence.

