Tide prediction from harmonic constituents: extrema, wiggle removal, threshold crossings

# Tide prediction from harmonic constituents `input.json` (synthetic constituents; not for navigation) gives `z0` (m), `constituents` (`amp` m, `speed_deg_h`, `phase_deg`, `g_deg`, node factor `f`), a window `start_h`..`end_h` (hours), `min_range_m` and `threshold_m`. Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json` writes `answer.json` and `tide.svg`. Fresh inputs are generated. ## Rules 1. Height h(t) = z0 + sum of f * amp * cos(speed * t + phase - g), angles in degrees converted to radians, t in hours. 2. **Extrema**: every time in [start, end] where dh/dt changes sign (use the analytic derivative), located to better than 0.001 minute. Kind: `high` if the second derivative there is negative, else `low`. Scan in steps of 0.1 h (6 minutes); no two extrema of these inputs fall in the same step. 3. **Compound-tide wiggles**: then repeatedly find the first pair of consecutive extrema whose heights differ by less than `min_range_m` and delete both, until none remain. 4. **Threshold crossings**: every time h(t) crosses `threshold_m`, with `direction` rising or falling, located the same way. 5. **Daily**: day d = 0, 1, 2, ... covers [start + 24d, start + 24(d+1)); max and min of h sampled at every whole minute from start to end inclusive (the end sample belongs to the last partial day if any). 6. Times are reported as `t_min` = minutes after `start_h`, rounded to 0.1; heights rounded to 3 decimals. ## Visual output: tide.svg Static, self-contained SVG (root `<svg>`; no scripts, images, links, embeds, handlers, external URLs, CSS url(http)/@import or fetches; renders headless) with `<polyline id="tide-curve">`, `<line id="threshold-line">` and an element `id="extrema"`. The drawing is not graded. ## answer.json `{"extrema": [{"t_min", "height_m", "kind"}, ...], "crossings": [{"t_min", "direction"}, ...], "daily": [{"day", "max_m", "min_m"}, ...]}` ## Scoring Hidden checks (partial credit; all must pass): `extrema_count_and_kinds`, `extrema_times_heights` (times within 0.15 minute, heights within 0.15 m), `threshold_crossings`, `daily_max_min` (within 0.0015 m), `tide_svg_static` (tide.svg exists, follows the static rules, has the ids/tags above), `fresh_run_1`, `fresh_run_2`. 60-second limit per run.