video-mode: flatten cursorExpression so ffmpeg 8's eval depth cap can't kill long renders

[mmkal]

Problem

ffmpeg 8 (homebrew's current: 8.0.1) added a recursion-depth cap (~100) to its expression parser. video-mode's pointer overlay builds the cursor's x/y as one nested if(between(t,a,b), value, <rest>) level per cursor waypoint segment — depth O(actions). Any spec with roughly 35+ pointer-highlighted actions now dies at render time:

[Parsed_overlay_351] [Eval] Missing ')' or too many args in 'if(between(t,49.123,49.423),(184+...
Error: Command failed: ffmpeg -hide_banner ... <several kilobytes of -filter_complex> ...

Empirically: nesting depth 90 parses, 100 fails. ffmpeg ≤7 has no limit, which is why short specs and older installs never noticed. First seen rendering iterate's specs/mobile/approvals.spec.ts (~350 filter nodes).

Fix

The waypoint segments are sequential and disjoint, so the nested chain is just a first-match lookup. Flatten it to a constant-depth sum:

Σ (gte(t,aᵢ)*lt(t,bᵢ))·valueᵢ(t)  +  (1 − gte(t,first)·lt(t,last))·base

Half-open windows (instead of inclusive-both-ends between) keep a shared segment boundary from firing two terms and doubling the coordinate; at a boundary the successor term yields the same position the nested version picked. base is the last waypoint's coordinate, matching the old fallback outside all segments. Depth stays ~10 no matter how long the spec gets.

Tests

spec/video-mode-cursor-expression.spec.ts (node-only, 400 segments — 4× the cap):

• nesting depth stays < 32 at any waypoint count (the cross-version guard: CI's older ffmpeg can't repro the parse failure itself)
• the installed ffmpeg parses and evaluates the expression through the real overlay quoting (fails on ffmpeg 8 with the old nested form)
• values match the waypoint smoothstep interpolation at every segment boundary and midpoint — mutation-checked: inclusive windows (the coordinate-doubling trap) fail this test

Verification

Full suite on ffmpeg 8.0.1 (the strict parser): 157 passed, 3 skipped (llm-recover, needs credentials). spec/todo-app.spec.ts rendered baseline:

video-rendered.webm

The originally-failing iterate mobile approvals spec (48s, 100+ waypoint segments), rendered green against this branch's build:

video-rendered.webm

Review notes

Riskiest part: the boundary semantics of the flattened sum (double-fire / gap edge cases) — that's what the value test pins down, boundaries included. The complement term assumes segments are contiguous, which is structural (segments are consecutive waypoint pairs). Review order: src/plugins/video-mode.ts (cursorExpression, one function), then the spec. On merge: rendered output is pixel-identical in intent; only the filter string shape changes.

🤖 Generated with Claude Code

https://claude.ai/code/session_01WZz4ydAhbRixWwJLpUEnSj

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