re: a keyframe time is worth half a rendered frame, and the ramp is linear

Q1 of the menu port, measured against the running game rather than reasoned
about. The developer-logo splash is the cheap target: it is the first thing the
guest draws and its bundle declares short, unambiguous ramps.

Two results, both frame-exact and both emulator-speed-independent (frame numbers
are VdSwap counts, the guest's own frames):

  * the ramp is LINEAR. A declared 15-unit fade lands on round(255*k/15) for all
    seven of its samples with zero error, k stepping 2,4,6,8,10,12,14. No ease
    can reproduce a constant step of 34 at both ends.
  * the animation clock advances 2.000 time units per submitted frame, over six
    consecutive intervals with no residual, with 1 unit as the quantum
    underneath (one frame in the fade-out advances by 1).

The conversion to seconds is one step further and is flagged as such: 300 frames
took 10.87 s = 27.6 present-frames/second, which reads as a 30 Hz title at 92 %
under the emulator and gives 1 unit = 1/60 s -- the title build 4.2 s, the main
menu build 1.1 s. That reading is not proven, because the rate was measured
while the guest was still streaming from the ISO; the page names the one test
that would settle it and says what changes if it goes the other way.

Committed beside it: the raw draw capture and the per-frame quad CSV, so the
numbers can be re-derived without a disc or an emulator.

docs/port/HANDOFF.md

@@ -27,7 +27,7 @@ authored version can be deleted.
 
 | | Question | State | Answer / link |
 |---|---|---|---|
-| Q1 | keyframe time unit + ramp shape | ❔ open | blocks all animation |
+| Q1 | keyframe time unit + ramp shape | ✅ answered | ramp is **linear**; the clock advances **2 units per rendered frame**; working conversion **1 unit = 1/60 s** — [`ui-keyframe-time-unit.md`](../re/ui-keyframe-time-unit.md) |
 | Q2 | which build is which screen state | 🟡 partial | build 4 title, 5 main menu, 6/8/9 submenus, `palogo` splash — unconfirmed against captures |
 | Q3 | paint order for the six screens | ❔ open | runtime-solved only; declaration table is refuted |
 | Q4 | button → GamePart | ❔ open | labels are baked into sprites |
@@ -57,6 +57,16 @@ authored version can be deleted.
 * **The resting pose is the hold**, not the first, last or longest-dwell keyframe;
   a keyframe is the **start of a ramp**.
   [`ui-resting-pose.md`](../re/structures/ui-resting-pose.md). ✅
+* **That ramp is linear, and it runs at 2 keyframe time units per rendered
+  frame.** Measured frame-by-frame off the running game's own draw stream: a
+  declared 15-unit fade lands on `round(255·k/15)` for all seven of its samples,
+  with `k` stepping 2, 4, 6, 8, 10, 12, 14 on seven consecutive submitted frames.
+  **measured**, not decoded — the disc says `t=30`, it does not say what a `t` is.
+  The seconds conversion (`1 unit = 1/60 s`, so a 30 fps screen) rests on a
+  measured 27.6 present-frames/second and is the one part still worth re-testing;
+  [`ui-keyframe-time-unit.md`](../re/ui-keyframe-time-unit.md) names the test.
+  If it turns out the game presents at 60 Hz, every duration halves — nothing
+  else on this page changes.
 * **The GamePart id table** — 29 entries at `.rdata 0x820A1630`, confirmed by the
   executable's own registration strings. ✅ This is the screen vocabulary; which
   button reaches which entry is Q4 and is *not* part of it.

docs/re/INDEX.md

@@ -134,6 +134,7 @@ files, which is how the same ground got covered twice.
 | [`structures/stage-definition-table.md`](structures/stage-definition-table.md) | Stage definition table and the squadron (`UnitGroup`) roster | ✅ for the record vocabulary and the stage→table wiring; |
 | [`structures/stage-mission-tables.md`](structures/stage-mission-tables.md) | The stage table set — phases, routes, sub-objectives and AI parameters | ✅ the table set and how the stage record reaches it, validated across; **`AIParams` disc-wide: 23 objects, one shared 34-profile roster (782 records), loader `sub_8233C368`; `Type`→field-count holds except the two `_Test` templates** |
 | [`structures/texture-color-k8888.md`](structures/texture-color-k8888.md) | Texture colour interpretation — `k_8_8_8_8` (32bpp UI/HUD textures) | — |
+| [`ui-keyframe-time-unit.md`](ui-keyframe-time-unit.md) | What a keyframe time is worth, and what shape the ramp has |  ✅ CONFIRMED from the running game's own draw stream — the ramp is **linear** (a declared 15-unit fade lands on `round(255·k/15)` for all seven samples) and the animation clock advances **2 time units per submitted frame**. 🟡 the seconds conversion (`1 unit = 1/60 s`) rests on a measured 27.6 present-frames/second |
 | [`structures/ui-composable-bundles.md`](structures/ui-composable-bundles.md) | A screen build is not the only thing `compose` can draw |  ✅ CONFIRMED by measurement over the disc, with the artifact to |
 | [`structures/ui-focus-and-effect-elements.md`](structures/ui-focus-and-effect-elements.md) | `_eff` glow layers are not focused-state records |  ✅ CONFIRMED by measurement over all 965 screen builds on the disc, |
 | [`structures/ui-paint-order-key.md`](structures/ui-paint-order-key.md) | The paint order comes from a layer key in the T8aD sprite header |  ✅ CONFIRMED on both screens whose paint order has been measured — |

docs/re/METHOD.md

@@ -103,3 +103,17 @@ agent's loop prompt, i.e. nowhere durable. See [`README.md`](README.md) for the
   out of noise.
 * **A probe that never performs the action will "prove" the action does not
   exist.**
+* **The container's Canary binary can be older than the Canary source tree, and
+  the failure mode is a hang, not an error.** After a merge into `sylpheed-re`
+  the prebuilt `xenia_canary` had no `log_ui_draws`, no `mem_watch`, no
+  `create_profile_if_none` — and an unknown cvar makes xenia open an SDL message
+  box before logging is up, which headless is an unexplained freeze. Check before
+  trusting a harness flag: `nm -C <binary> | grep cvars::<flag>`, and
+  `build-canary Release` if it is missing.
+* **A capture armed *at* a screen only ever sees the steady state.** Anything
+  about how a screen is built or animated has to be armed *before* it exists.
+  Re-arming every few seconds and keeping every log tiles the approach: each F10
+  opens a new numbered file and closes the previous one complete.
+* **Measure animation in submitted frames, not in seconds.** `VdSwap` counts are
+  the guest's own frames, so an emulator at 80 % of real time does not move them;
+  a stopwatch reading does, silently and by an unknown factor.

docs/re/captures/ui-timing/splash-build-quads.csv

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docs/re/ui-keyframe-time-unit.md

@@ -0,0 +1,131 @@
+# What a keyframe time is worth, and what shape the ramp has
+
+**Status:** ✅ `CONFIRMED` for the two things the port is blocked on — the ramp is
+**linear**, and the animation clock advances **2 keyframe time units per frame the
+game submits**. 🟡 the conversion to *seconds* rests on one further step: the game
+was measured presenting **27.6 frames/second**, which reads as a 30 Hz title
+running at ~92 % under the emulator, giving **1 unit = 1/60 s**. That last step is
+reasoning over a measurement, not a measurement — see *the reach of the negative*
+below.
+
+This answers `docs/port/MISSION.md` **Q1**. Everything animated downstream — the
+title wordmark zoom, the main menu's staggered buttons, every fade — is scaled by
+this number.
+
+## The measurement
+
+The question cannot be asked of a screen that is sitting still, and
+`log_ui_draws` armed *at* a screen only ever sees the steady state. So arm it
+repeatedly through the boot and keep every log: each F10 opens a new numbered
+file and **closes** the previous one, which stays on disk complete. Re-arming
+every 3 s tiles the whole approach to a screen, and whichever file straddles the
+build contains it. `tools/re-capture/screen_build_capture.sh` does this; it sends
+no pad input at all, because Ⓐ during the boot has ended a run on a permanent
+black screen (`canary-scripted-input-traps.md`).
+
+The developer-logo splash is the cheap target: it is the first thing the guest
+draws, roughly ten seconds in, and its bundle (`GP_TITLE.pak`, `--all --build 11`
+/ `14` — the `palogo` group) declares short, unambiguous ramps.
+
+The capture is committed: [`captures/ui-timing/splash-build-draws.log`](captures/ui-timing/splash-build-draws.log)
+(the raw draw stream) and [`captures/ui-timing/splash-build-quads.csv`](captures/ui-timing/splash-build-quads.csv)
+(`tools/re-capture/kf_time_probe.py`, one row per quad per frame: pixel rect and
+the per-vertex colour whose high byte is the element's fade).
+
+Frame numbers are the emulator's **VdSwap count** — frames the guest submitted —
+so an emulator running at 80 % of real time does not move them. That is the whole
+reason to measure in this unit rather than with a stopwatch.
+
+### The quads are the splash, by position and size
+
+Every sprite in the capture lands on its declared placement:
+
+| capture quad | declared element (build 11) | declared placement |
+|---|---|---|
+| `666x65 @ (307,331)` | `palogo_sqex.t32` 666×68 | (309,330) |
+| `525x90 @ (378,155)` | `palogo_gamearts_eff.t32` 521×91 | (379,154) |
+| `262x108 @ (512,306)` | `palogo_seta_eff.t32` 261×110 | (511,305) |
+| `499x72 @ (390,162)` | `palogo_gamearts.t32` 500×71 | (390,164) |
+| `243x86 @ (518,317)` | `palogo_seta.t32` 240×89 | (521,316) |
+
+(A quad runs a few pixels under its sprite; that offset is already recorded in
+`ui-title-paint-order-capture.md` and is not what is being measured here.)
+
+## Result 1 — the ramp is linear, exactly
+
+`palogo_gamearts_eff` and `palogo_seta_eff` declare a fade-in of
+`t=15 a=0 → t=30 a=255`: a **15-unit** ramp. Their fade alpha, frame by frame,
+straight out of the capture:
+
+| frame | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 |
+|---|---|---|---|---|---|---|---|---|
+| alpha | `0x22` 34 | `0x44` 68 | `0x66` 102 | `0x88` 136 | `0xAA` 170 | `0xCC` 204 | `0xEE` 238 | `0xFF` 255 |
+| ⇒ units into the ramp *k* | 2 | 4 | 6 | 8 | 10 | 12 | 14 | ≥15 |
+
+`round(255·k/15) = 17k` reproduces **all seven samples with zero error**. An eased
+ramp cannot do that: any ease-in/ease-out would bend the first and last steps, and
+these are a constant 34 throughout. **Linear interpolation, refuted-nothing-left.**
+
+The same element's fade-*out* gives the same law with a one-count offset —
+`255·(1−k/15) − 1` = 254, 220, 186, 152, 118, 84, 67, 33 for
+*k* = 0, 2, 4, 6, 8, 10, 11, 13, which is exactly what the capture holds on frames
+108–115.
+
+## Result 2 — 2 time units per submitted frame
+
+Read *k* off the row above: 2, 4, 6, 8, 10, 12, 14 on seven consecutive submitted
+frames. **The clock advances 2.000 units per frame, over six consecutive
+intervals, with no residual.** The fade-out shows the same 2-per-frame step with
+one single-unit frame (*k* goes 10 → 11 → 13), so the quantum underneath is 1 unit
+and the normal step is two of them.
+
+Cross-checks in the same capture, all consistent:
+
+* the declared hold `t=30 → t=45` (15 units) is held for frames 101–107, **7
+  frames** ≈ 14 units;
+* `palogo_sqex`'s fade-out steps in multiples of 17 per frame (−34 with the odd
+  −17), the same 255/15 quantum;
+* the `gamearts`/`seta` pair holds full alpha for frames 116–198 and fades out
+  over frames 199–211.
+
+## Result 3 — the conversion to seconds, and how far it reaches
+
+300 submitted frames took **10.87 s** wall-clock, measured by arming one bounded
+capture over the splash and timing it to its own `[UI-CAP] done` line:
+**27.6 frames/second**.
+
+With 2 units per frame that is **55 units/second measured**. The two readings that
+fit are:
+
+* **30 Hz present, 60-unit-per-second timeline** — the emulator running at 92 % of
+  real time. A 30 Hz renderer stepping a 60 Hz timeline is exactly the 2-units-
+  per-frame quantum that was measured, and 92 % is an ordinary number for this
+  container.
+* 60 Hz present at 46 % of real time, giving a 120-unit-per-second timeline. This
+  requires the emulator to be running at *less than half speed* while drawing four
+  quads over a black screen, and it requires the game's timeline to tick at 120 Hz.
+
+**Taking the first**: `1 unit = 1/60 s`. The title build (`GP_TITLE.pak` build 4,
+t = 16 … 269) is then **4.2 s**, and the main menu build (build 5, t = 12 … 80)
+**1.1 s**.
+
+**The reach of this negative:** the present rate was measured *during the boot
+splash*, where the guest is also streaming from the ISO, so it is a lower bound on
+the emulator's speed and cannot by itself exclude the 60 Hz reading. What would
+settle it is the same 300-frame timing taken on the **idle title screen**, where
+nothing is loading — if that also comes out near 28 fps the game is 30 Hz and the
+unit is 1/60 s; if it doubles to ~55 fps the game is 60 Hz and every duration on
+this page halves. Until then the port should treat **2 units per rendered frame**
+as the measured fact and `1/60 s` as the working conversion.
+
+## What this does not say
+
+* Nothing here is a *decode*: no field on the disc says "sixtieths of a second".
+  The number is measured from the running game, and the port is transcribing a
+  measurement, not a disc value.
+* The splash drew `palogo_sqex`, then `palogo_gamearts` + `palogo_seta` with their
+  `_eff` sprites — but **not** `palogo_anima` (declared at 388×136 @ (446,449)) and
+  not `palogo_sqex_eff`, in the ~7 s of capture after the pair faded out. The
+  `_sqex_eff` absence is explainable (the capture joined the SQUARE ENIX logo
+  mid-hold); the missing studio-anima logo is not, and is left as an open
+  observation for Q2 rather than a claim.