# 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<=∂_λ F<=b

## Coupled targets bundles

- SOL bundle
  - b⊖a=Ψ(s) on the slice
  - free coordinate covers T_P

## Robustness bundles

- LCM bundle
  - lift-closeness margin < π on witness loop

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

## Ergodic bundles

- RNF bundle (nonresonant torus translation)
  - the increment vector ω has no nontrivial integer relation (nonresonant)
  - the induced translation on the correct target (torus or CST) is uniquely ergodic
  - time averages converge to Haar on the correct target
  - optional empirical diagnostics of low Fourier modes may be recorded as evidence, but are not used as proofs

## Mixing bundles

- DSD bundle
  - phase density diffusion ∂_s p = κ ∂_yy p

- SADM bundle
  - advection–diffusion with shear bound ||∂_y u||_∞
  - mixing certificate 2κ(2π/P)^2 > ||∂_y u||_∞

## 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.
