07 [task] Cycle builder — materialize per-cycle tidy tables from parquets

Nobody has claimed this yet.

Part of #11

## Question

Materialize the per-cycle **shared object** as tidy parquet tables from the EC347 parquets, exactly per the data model fixed in #13. This is the execution ticket that produces the object every downstream stage (§3, §4, §6) consumes.

**Task (execution — AFK where possible; no OpenGL needed, pandas/matplotlib only, `uv run`):**

Build a cycle-extraction step producing three parquet tables (all spatial fields CANVAS 1922×1396):

- **`cycle_gaze`** — long, one row per 100 Hz sample over `reveal[k-1]→reveal[k]`: `t` (behavior_t_ms), `x`, `y` (gx/gy_canvas), `em_type`, `gaze_valid`, `on_screen`, `homography_valid`, `segment`∈{free_behavior,feedback_delay}, `t_norm`, `video_frame_frac`, keys `(subject_id, seq_id, trial_idx, k=tpt)`.
- **`cycle_meta`** — one row per cycle: `click_xy`, `true_next_xy`, event times+frames (`reveal_prev`, `click`, `reveal_next`), keys.
- **`cycle_dots`** — long, one row per (cycle, dot): `role`∈{revealed,future}, `order`, `x`, `y`.

**Sources / transforms:** `gaze_per_sample.parquet`, `trials_with_video.parquet`; dots via `homography_solver.behavior_to_screen → gaze_projection.screen_to_canvas`. Cycles k∈3..14 (12/trial × 20 = 240). Dot sets **derived** from `true_x/y` ordered by `tpt` within trial (no `prev_x/y` column). `t_norm` = linear [0,1] per sub-segment.

**Resolution:** runnable builder + the three tables written for EC347, plus a sanity check: 240 cycles; `feedback_delay` ≈ 1502 ms fixed and `free_behavior` variable; per cycle `revealed` count = k and `future` count = 15−k.

Read the data model in #13, then inspect gaze_per_sample.parquet, trials_with_video.parquet, homography_solver.behavior_to_screen, and gaze_projection.screen_to_canvas. Run the builder with uv run and verify that it writes cycle_gaze, cycle_meta, and cycle_dots for EC347, with 240 cycles, the stated feedback delay, and the required revealed and future counts.

Written by the indexing model from the issue text.