# Worked example: Earth local time and SOL coupling

## Purpose

Provide one fully audited, copy-ready example that demonstrates the SFT engine discipline:

- define the witness context
- produce WSC artifacts for global and coupled tiers
- record assumptions explicitly (AWT, SOL, FEQ, LCM)
- point to audit instructions

This example is designed for inclusion in a paper appendix.

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## Example context

- Slice: Earth surface at global instant \(s\)
- Subsystem loop: latitude circle \(E\cong S^1\) (embedded witness)
- Phase observable: local solar phase (time-of-day) modulo \(P=86400\)

Model:
\[
\Phi_s(\lambda,\varphi)=c_s(\varphi)\oplus \frac{P}{2\pi}\lambda.
\]
On the latitude loop at \(\varphi_0\), this restricts to degree-1 wrapping.

Coupled extension (SOL-style):
- solar phase \(a=\Phi_\odot\)
- lunar phase \(b=\Phi_{\leftmoon}\)
- coupling \(b\ominus a=\Psi(s)\)
- target CST\(_s\) is the diagonal translate.

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## Artifacts

- Global witness (AWT) example WSC: `engine/artifacts/WSC-G-AWT-0001.json`
- Coupled witness (CMT-SOL) example WSC: `engine/artifacts/WSC-C-CMT-0001.json`

Audit:

- `engine/audit/audit_wsc.py engine/artifacts/WSC-G-AWT-0001.json`
- `engine/audit/audit_wsc.py engine/artifacts/WSC-C-CMT-0001.json`

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## Notes on diagnostics

- In the uncoupled setting, the target baseline is Haar on \(\mathbb{T}_P\).
- Under SOL, the target baseline is coupled Haar on CST\(_s\).

Rate and threshold reminders appear in `engine/contracts/constants_thresholds.md`.

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## Acceptance gates

- example can be pasted into a paper appendix with no missing definitions
- artifact pointers and audit commands are explicit
