# Pass 08 — Dynamics Boundary and Margins (WPD/WBD as Certificate Conditions)

## Purpose

Push dynamics-related scores to 10 by making the boundary between:

- witness preservation (WPD)
- witness breaking (WBD)

explicit, checkable, and tied to WSC margins (DMG fields).

This is the “referee hard” version of the dynamics story.

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## WPD (witness-preserving dynamics)

### WPD-1 Degree preservation on loops

Under sufficient regularity and periodic compatibility, winding/degree on a witness loop is preserved.

Certificate linkage:
- store a dynamics margin ensuring lift closeness remains within LCM < \(\pi\) on the loop.

### WPD-2 Holonomy preservation under \(d\omega=0\)

If forcing \(\omega\) is spatially constant (or \(d\omega=0\)), holonomy classes are preserved.

Certificate linkage:
- store a dynamics margin ensuring loop-integral perturbation remains within HMR < \(P/2\).

### WPD-3 Coupled persistence under structural constraints

If coupling constraints are structurally enforced by the model (SOL/affine/matrix coupling), then CST target selection persists through time.

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## WBD (witness-breaking dynamics)

SFT explicitly does not claim witness persistence when:

- discontinuities or tears appear (degree/holonomy become undefined)
- coupling constraints drift without a controlled model (CST target changes unpredictably)
- slicing leaves the admissible FEQ class without a phase-controlled relation

These become WOB outputs, not failures of the theory.

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## DMG (dynamics margin) fields for WSC

Add optional `margins.DMG` fields:

- `max_lift_drift` (must stay < \(\pi\))
- `max_holonomy_drift` (must stay < \(P/2\))
- `regularity_class` (e.g., Lipschitz, C1)
- `time_horizon` (interval where certification applies)

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## Acceptance gates

- WPD vs WBD boundary is explicit and linked to certificate margin fields
- dynamics conditions are phrased as checklists
- failure modes map to WOB codes (tear, coupling mismatch, mixing not justified)
