# SFT Analytic Hypotheses Menu

This menu lists sufficient hypothesis bundles you can choose from when proving or certifying a statement.
It is designed to keep the project honest: if a claim needs an assumption, the assumption appears here explicitly.

## Witness existence bundles

- AWT bundle
  - circle action exists
  - equivariant phase observable exists
  - phase response map is surjective
  - full orbit exists

- ESW bundle
  - embedded subsystem is specified
  - degree or holonomy is nontrivial on that subsystem

## Anti-collapse and quantitative bounds bundles

- MBC bundle (branch-certified)
  - degree-\(|k|\) covering decomposes into \(|k|\) monotone branches
  - upper stretch bound on each branch

- BDH bundle (bounded distortion)
  - two-sided stretch bounds \(0<a\le \partial_\lambda F\le b\)

## Coupled targets bundles

- SOL bundle
  - \(b\ominus a=\Psi(s)\) on the slice
  - free coordinate covers \(\mathbb{T}_P\)

## Robustness bundles

- LCM bundle
  - lift-closeness margin \(<\pi\) on witness loop

- HMR bundle
  - holonomy perturbation \(<P/2\) on witness loop

## Mixing bundles

- DSD bundle
  - phase density diffusion \(\partial_s p=\kappa\partial_{yy}p\)

- SADM bundle
  - advection–diffusion with shear bound \(\|\partial_y u\|_\infty\)
  - mixing certificate \(2\kappa(2\pi/P)^2>\|\partial_y u\|_\infty\)

## Bridge bundles

- NDB bundle (noise-to-diffusion bridge)
  - an explicit modeling choice: phase jitter, random increments, coarse-graining, or measurement noise
  - states how it induces diffusion in the phase-density evolution

Use this menu in reports and in WSC `assumptions` fields.
