[cbaucom]

Closes #14

Approach

Two pure functions added to the Beat Grid module, plus a schema field for persistence.

tapToBpm(tapTimestampsMs) — takes ≥8 tap timestamps (ms from track start), computes inter-tap intervals, takes their median (robust against one mis-tap), and derives BPM + first-beat offset. Requires ≥8 taps to match the AC minimum; throws on non-positive medianMs (duplicate/stuck timestamps).

manualBeatGridFromBpm(bpm, firstBeatOffsetSecs) — numeric-entry path that constructs a BeatGrid directly. Throws on bpm ≤ 0. Produces results identical to tapToBpm with perfectly-spaced taps at the same tempo (AC3 by construction).

resolveEffectiveBeatGrid(manual, cache) — manual ?? cache priority logic: manual override always wins; re-analysis (cache update) never evicts it; clearing is explicit (pass undefined).

SlideshowJson.manualBeatGrid — schema field for persistence across project reopens. Wiring into slidesToJson and the editor shell is intentional follow-on work (the UI detection slice).

Acceptance criteria

• Given at least 8 taps, when applied, derived BPM/offset replace the detected grid and plan re-nudges — tapToBpm produces a BeatGrid accepted by plan(..., beatGrid) from the prior slice
• Given a manual correction, when the project reopens or the track is re-analyzed, manual values still win until explicitly cleared — resolveEffectiveBeatGrid + SlideshowJson.manualBeatGrid schema field; persistence wiring is a follow-up
• Given numeric entry of BPM and offset, when applied, behavior is identical to tapping — manualBeatGridFromBpm produces the same BPM/interval/offset as tapToBpm with perfect taps (tested directly)

Code review findings fixed

• Guard raised from ≥2 to ≥8 taps (AC minimum)
• medianMs ≤ 0 guard added (duplicate timestamps → throw instead of Infinity BPM)
• bpm ≤ 0 guard added in manualBeatGridFromBpm (prevents Infinity beatIntervalSecs)

Follow-ups

• Wire tapToBpm / manualBeatGridFromBpm into the editor UI (tap button + BPM/offset fields)
• Persist manualBeatGrid through slidesToJson and read it back in the Project Store
• Expose "clear manual override" action in the UI