docs: record the millisecond floor as located and closed, and split what stayed open

The retired custom-bounds premise is corrected wherever it was encoded: the tail
bit is the time selection's, not custom bounds'.

docs/COMPLETED.md

@@ -942,3 +942,42 @@ own output, the three folder cases, collapsed-mono placement and summing, both m
 transitions waited out past a panel timer tick, undo, name/colour clone, and
 `GetProjectPathEx` against a non-default recording path — none of it is unit-testable
 and none has been run.
+
+### The offline-render millisecond floor — located and closed (ad-hoc)
+
+Closes the `docs/TODO.md` entry of the same name. REAPER's offline render was
+intermittently refusing an otherwise-valid capture whenever the requested window's end
+carried a sub-millisecond remainder — breaking root `CLAUDE.md`'s "exact bounds — no
+rounding of the requested range" precision invariant.
+
+**Located, not inferred: the floor lives in the `RENDER_BOUNDSFLAG=0` custom-time-bounds
+field, not in REAPER's render engine.** Switching the offline render to
+`RENDER_BOUNDSFLAG=2` (the project's own time selection, driven through
+`GetSet_LoopTimeRange`) escapes it entirely. Confirmed by two live 48 kHz
+`TailMode::None` DAW renders, both landing exactly 97627 frames against the window's own
+count: the first started at the on-grid `0s` and tested only the END edge (a floored end
+would have printed 97584 — 43 frames short); the second, the decisive run, started at
+`2.0338983050847457s` and ended at `4.0677966101694913s`, both edges off the
+millisecond grid, and no millisecond-floored model of either edge alone or both together
+reproduces 97627. No compensation, trimming, or extraction was needed.
+`src/core/capture/render_settings.h`'s `kRenderBoundsTimeSelection` is now the one
+narrative home for the mechanism and the measurement; time selection is the only bounds
+mode the offline render reaches.
+
+**Two hypotheses this track's originating entry previously carried are disproven, not
+merely superseded** — both predicted a shortfall tracking the render's CONTENT: that the
+render bounds itself to the media it can see, and that a trailing-silence trim fires
+despite `RENDER_NORMALIZE`. The measured cause tracks the WINDOW instead — the exact
+millisecond-floored count, independent of what the material does. Recorded so neither is
+re-proposed without a fresh observation.
+
+**Scaffolding removed.** The experiment's apparatus — a two-position
+`RenderBoundsChannel` type, a console verdict line, and a three-checkpoint
+`RENDER_STARTPOS`/`RENDER_ENDPOS` read-back probe — is deleted now that the mechanism is
+settled.
+
+**Left open, filed to `docs/TODO.md`:** `renderHonoredBounds`'s one-frame tolerance
+remains empirical, not proven; and `TailMode::Auto`/`Manual` have no automatic bounds
+observation at all — `render_bounds_gate` judges `TailMode::None` only, so both modes are
+fixed by inference (same bounds path, same floor) rather than by measurement, and only
+the 0-byte gate covers them until a DAW check closes it.