# ✅ The game **interpolates piecewise-linearly, every frame** — and its splash is *also* mostly frozen

**Status: ✅ measured, and the declared keyframes predict the measured steps.**
2026-09-02. Instrument: ⟨capture⟩ — per-frame vertex alpha off the guest's own
vertex buffer; ⟨disc⟩ for the keyframes that predict it.
Series: [`data/splash-per-frame-alpha-series.txt`](data/splash-per-frame-alpha-series.txt).

Answers question 1 of [`../agents/PLAYTEST-2026-09-02.md`](../agents/PLAYTEST-2026-09-02.md)
— *"what does it do BETWEEN keyframes — interpolate, or hold to the next key?
That single answer decides whether the port should lerp at all."*

---

## 1 — it interpolates. Every frame. Piecewise-linearly.

`palogo_sqex_eff`, 28 consecutive presents, **28 distinct alphas**, changing on
**26 of 27** adjacent pairs:

```
34  85 204 221 238 254 249 246 243 237 232 229 226 223 214 211 197 169 141
127 113  98  84  70  56  42  28  14
```

**It is not one slope, and the disc says why.** That element declares
`0:a=0 → 15:a=255 → 30:a=212 → 45:a=0`, which is three segments with three
different gradients. Predicted against measured, per unit:

| declared segment | predicted Δα/unit | measured modal step |
|---|---|---|
| `15 → 30` (255 → 212) | **−2.87** | **−3** ×6 |
| `30 → 45` (212 → 0) | **−14.13** | **−14** ×9 |

**The declared keyframes predict the per-frame steps.** That is the whole answer:
the game evaluates a linear interpolation between the two bracketing keyframes,
once per present, at one unit per present.

> **The port must lerp.** Hold-to-next-key would emit 3 states where the game
> emits 28.

⚠️ **And "eased" is the wrong description**, which matters because a port that
believes it will fit a curve. There is no easing function — the *envelope* looks
eased only because consecutive declared segments have different gradients. Every
segment is straight.

## 2 — where the alpha lives, so it can be watched

**The per-vertex `k_8_8_8_8` colour**, in a vertex buffer the guest rewrites into
a fresh address every frame. Ruled out by the same captures:

* **not a PS constant** — `ps_c[n=0]` on 1 048 / 1 048 splash draws;
* **not a blend factor** — the blend register is constant across the whole splash;
* **not a texture swap** — one texture is bound throughout.

## 3 — 🔴 the game's splash is ALSO mostly frozen, and the port's 3.2 s hold is CORRECT

Measured with the same statistic the play-test applied to the port:

| | **game** publisher | **game** developer | **port** (both) |
|---|---|---|---|
| moving | **21.2 %** | **27.8 %** | 16.4 % |
| longest frozen run | **3.34 s** | **2.50 s** | 3.20 s |
| distinct states | **49** | **51** | **26 total** |

📌 **The play-test's inference does not hold, though its observation does.** It
reads *"a fade does not hold one picture for 3.20 s"* as proof of breakage. **The
game holds one picture for 3.34 s.** The publisher's declared timeline is
`0:a=0 → 15:a=0 → 30:a=255 → 235:a=255 → …`, i.e. **205 of 255 units — 80 % — is
a flat hold at full opacity.** A splash that is static most of the time is what
the disc describes.

🔴 **So the deficit is not the freeze. It is the state count: ~100 against 26.**
The game changes alpha on *every present* during a ramp — 15 distinct values for
a 15-unit ramp — and the port produces roughly a quarter of that across both
splashes. **Fixing the hold would make it worse; the ramps are where the states
are missing.**

## What the port should do

1. **Lerp between bracketing keyframes, evaluated once per frame** — not
   hold-to-next-key, and not an easing function.
2. **Keep the long hold.** ~3.3 s of genuinely identical frames is correct.
3. Expect **~15 distinct alphas per 15-unit ramp**, ~100 across both splashes.
4. Alpha is a **per-quad scalar**, uniform across the quad's four vertices.

## Refutation attempt, recorded per the adversarial duty

**Target:** the play-test's *"A 45-unit build-in cannot be drawn in 26 states, and
a fade does not hold one picture for 3.20 s."*

**Result: the first clause SURVIVES, the second is REFUTED.** 26 states for a
45-unit build-in is indeed too few — the game gives 49 and 51. But the game holds
one picture for **3.34 s**, longer than the port's 3.20 s, and the disc declares
80 % of the publisher splash as a flat hold. Recorded because acting on the second
clause would have sent the port to remove the one part of its splash that is
right.

## Reach

⟨capture⟩, one boot, both splashes, English locale. The interpolation law is
checked against ⟨disc⟩ keyframes on one element with three gradients, which is
what makes it a prediction rather than a description — **it has not been checked
on the title or the menus**, and doing so is the obvious next step.

❔ **Not answered here: which function does it.** This is the *behaviour*, measured.
The image-side half of question 1 — the function that advances the clock and
evaluates the segment — is not found yet.