# Section 2 equation specification

## Required equations
1. `Re_D=Uref D/nu`; bulk/mean `Uref` for parabolic inflow, uniform speed for uniform inflow, and `Umax ~= 1.5 Uref`. Parabolic inherited labels remain unconverted until source metadata bind `U0`.
2. `(Uw,Vw)=(-omega r_y, omega r_x)`, positive omega counter-clockwise; `s_i=omega_i R/Uref`. Historical source-native `alpha_i=omega_i/U0`; general `s_i=alpha_i R(U0/Uref)`, reducing to `alpha_i R` only when `U0=Uref` is established.
3. Online objective: compact force plus sparse-sensor discrepancy; exact weights optional and run-bound.
4. Mean field L2: area/coordinate-weighted, `Uref`-normalized vector error over declared ROI with roles/comparator explicit.
5. Phase L2: same spatial contract by periodic slot; slots are not repeated-cycle samples.
6. DTW recurrence/path or rigorous prose; state distance/similarity, normalization, channels, aggregation, window and constraints.
7. Comparator-relative reduction optional only under one exact role/ROI/mask/weight/window contract.

## Readiness contract
Authority is frozen Section 2 plus the sensor/field report. Equations 1–2 are configuration definitions; 3–7 require result-local chain/config/case/seed/role/comparator bindings. ROI/mask/weight/window are `N/A: physical/method definition` for 1–3 and mandatory for 4–7. Action sign/order and metric orientation accompany reuse. Implementation constants and rows are `dependency-gated`; no equation implies an artifact. Caption ceiling is definitions only. Fallback retains Reynolds, action, mean L2 and rigorous prose DTW; recurrence/detail may move to supplement.

Plan `specified`; evidence `read`; metric `definition-ready`; render `N/A: typeset equations, not artifact panels`; disposition `retain-with-gates`.