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re: the game interpolates every frame, and its splash is ALSO mostly frozen

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Answers question 1 of the 2026-09-02 play-test: interpolate or hold. It
interpolates, piecewise-linearly, evaluated once per present at one unit
per present.

palogo_sqex_eff gives 28 distinct alphas over 28 consecutive presents,
changing on 26 of 27 adjacent pairs. 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, three
segments with three gradients. Predicted -2.87 and -14.13 per unit against
measured modal steps of -3 (x6) and -14 (x9). The declared keyframes
predict the per-frame steps, which makes this a prediction rather than a
description.

So the port must lerp: hold-to-next-key would emit 3 states where the game
emits 28. And "eased" is the wrong description -- there is no easing
function, the envelope only looks eased because consecutive declared
segments have different gradients.

Alpha lives in the per-vertex k_8_8_8_8 colour, rewritten into a fresh
vertex buffer every frame. Not a PS constant (ps_c[n=0] on 1048/1048), not
a blend factor, not a texture swap.

🔴 And the game's splash is ALSO mostly frozen. Measured with the same
statistic the play-test used on the port: the game moves 21.2% and 27.8%
against the port's 16.4%, and its longest frozen run is 3.34 s against the
port's 3.20 s. The publisher declares 205 of 255 units -- 80% -- as a flat
hold at full opacity.

That refutes the play-test's second clause. "A fade does not hold one
picture for 3.20 s" -- this one does, for 3.34 s. Its first clause stands:
26 states for a 45-unit build-in is too few, the game gives 49 and 51.

The deficit is the state count, not the freeze: ~100 against 26. Acting on
the second clause would have sent the port to remove the one part of its
splash that is already right.

Not answered: which function does it. This is the behaviour; the
image-side half of question 1 is still open.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Jc4pciRArGHfxGGhEbwp5t
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# PER-FRAME ALPHA, every splash quad, off the guest's own vertex buffer.
# Alpha lives in the per-vertex k_8_8_8_8 colour, REWRITTEN EVERY FRAME into a
# fresh vertex buffer. Not a PS constant (ps_c[n=0] on every splash draw), not a
# blend factor (the blend register is constant across the whole splash).
# 'present' = one guest swap. Quad names decoded from the disc, 8/8.
## palogo_sqex_eff x[-0.53,0.54] y[-0.13,0.12] presents 4..32 (n=28)
4:34 5:85 7:204 8:221 9:238 10:254 11:249 12:246 13:243 14:237
15:232 16:229 17:226 18:223 19:214 20:211 21:197 22:169 23:141 24:127
25:113 26:98 27:84 28:70 29:56 30:42 31:28 32:14
steps between adjacent presents: {-28: 2, -15: 1, -14: 9, -9: 1, -6: 1, -5: 2, -3: 6, 16: 1, 17: 2, 51: 1}
distinct alphas 28 ; changed on 26 of 27 presents
## palogo_sqex x[-0.52,0.52] y[-0.10,0.08] presents 11..231 (n=221)
11:34 12:51 13:68 14:102 15:136 16:153 17:170 18:187 19:238 20:255
21:255 22:255 23:255 24:255 25:255 26:255 27:255 28:255 29:255 30:255
31:255 32:255 33:255 34:255 35:255 36:255 37:255 38:255 39:255 40:255
41:255 42:255 43:255 44:255 45:255 46:255 47:255 48:255 49:255 50:255
51:255 52:255 53:255 54:255 55:255 56:255 57:255 58:255 59:255 60:255
61:255 62:255 63:255 64:255 65:255 66:255 67:255 68:255 69:255 70:255
71:255 72:255 73:255 74:255 75:255 76:255 77:255 78:255 79:255 80:255
81:255 82:255 83:255 84:255 85:255 86:255 87:255 88:255 89:255 90:255
91:255 92:255 93:255 94:255 95:255 96:255 97:255 98:255 99:255 100:255
101:255 102:255 103:255 104:255 105:255 106:255 107:255 108:255 109:255 110:255
111:255 112:255 113:255 114:255 115:255 116:255 117:255 118:255 119:255 120:255
121:255 122:255 123:255 124:255 125:255 126:255 127:255 128:255 129:255 130:255
131:255 132:255 133:255 134:255 135:255 136:255 137:255 138:255 139:255 140:255
141:255 142:255 143:255 144:255 145:255 146:255 147:255 148:255 149:255 150:255
151:255 152:255 153:255 154:255 155:255 156:255 157:255 158:255 159:255 160:255
161:255 162:255 163:255 164:255 165:255 166:255 167:255 168:255 169:255 170:255
171:255 172:255 173:255 174:255 175:255 176:255 177:255 178:255 179:255 180:255
181:255 182:255 183:255 184:255 185:255 186:255 187:255 188:255 189:255 190:255
191:255 192:255 193:255 194:255 195:255 196:255 197:255 198:255 199:255 200:255
201:255 202:255 203:255 204:255 205:255 206:255 207:255 208:255 209:255 210:255
211:255 212:254 213:249 214:243 215:237 216:231 217:215 218:198 219:181 220:165
221:148 222:131 223:115 224:98 225:81 226:65 227:48 228:31 229:23 230:15
231:7
steps between adjacent presents: {-17: 8, -16: 4, -8: 3, -6: 3, -5: 1, -1: 1, 17: 6, 34: 2, 51: 1}
distinct alphas 30 ; changed on 29 of 220 presents
## palogo_gamearts_eff x[-0.41,0.41] y[0.32,0.57] presents 236..275 (n=40)
236:17 237:34 238:51 239:68 240:85 241:136 242:170 243:187 244:204 245:221
246:238 247:255 248:255 249:255 250:255 251:255 252:255 253:255 254:255 255:255
256:255 257:255 258:255 259:255 260:255 261:254 262:237 263:220 264:203 265:186
266:169 267:152 268:135 269:118 270:101 271:84 272:67 273:50 274:33 275:16
steps between adjacent presents: {-17: 14, -1: 1, 17: 9, 34: 1, 51: 1}
distinct alphas 27 ; changed on 26 of 39 presents
## palogo_seta_eff x[-0.20,0.21] y[-0.15,0.15] presents 236..275 (n=40)
236:17 237:34 238:51 239:68 240:85 241:136 242:170 243:187 244:204 245:221
246:238 247:255 248:255 249:255 250:255 251:255 252:255 253:255 254:255 255:255
256:255 257:255 258:255 259:255 260:255 261:254 262:237 263:220 264:203 265:186
266:169 267:152 268:135 269:118 270:101 271:84 272:67 273:50 274:33 275:16
steps between adjacent presents: {-17: 14, -1: 1, 17: 9, 34: 1, 51: 1}
distinct alphas 27 ; changed on 26 of 39 presents
## palogo_anima_eff x[-0.32,0.31] y[-0.65,-0.22] presents 236..275 (n=40)
236:17 237:34 238:51 239:68 240:85 241:136 242:170 243:187 244:204 245:221
246:238 247:254 248:252 249:249 250:246 251:243 252:240 253:234 254:232 255:229
256:226 257:223 258:220 259:217 260:214 261:211 262:197 263:183 264:169 265:155
266:141 267:127 268:113 269:98 270:84 271:70 272:56 273:42 274:28 275:14
steps between adjacent presents: {-15: 1, -14: 13, -6: 1, -3: 11, -2: 2, 16: 1, 17: 8, 34: 1, 51: 1}
distinct alphas 40 ; changed on 39 of 39 presents
## palogo_gamearts x[-0.39,0.39] y[0.35,0.55] presents 248..416 (n=169)
248:17 249:34 250:51 251:68 252:85 253:119 254:136 255:153 256:170 257:187
258:204 259:221 260:238 261:255 262:255 263:255 264:255 265:255 266:255 267:255
268:255 269:255 270:255 271:255 272:255 273:255 274:255 275:255 276:255 277:255
278:255 279:255 280:255 281:255 282:255 283:255 284:255 285:255 286:255 287:255
288:255 289:255 290:255 291:255 292:255 293:255 294:255 295:255 296:255 297:255
298:255 299:255 300:255 301:255 302:255 303:255 304:255 305:255 306:255 307:255
308:255 309:255 310:255 311:255 312:255 313:255 314:255 315:255 316:255 317:255
318:255 319:255 320:255 321:255 322:255 323:255 324:255 325:255 326:255 327:255
328:255 329:255 330:255 331:255 332:255 333:255 334:255 335:255 336:255 337:255
338:255 339:255 340:255 341:255 342:255 343:255 344:255 345:255 346:255 347:255
348:255 349:255 350:255 351:255 352:255 353:255 354:255 355:255 356:255 357:255
358:255 359:255 360:255 361:255 362:255 363:255 364:255 365:255 366:255 367:255
368:255 369:255 370:255 371:255 372:255 373:255 374:255 375:255 376:255 377:255
378:255 379:255 380:255 381:255 382:255 383:255 384:255 385:255 386:255 387:255
388:255 389:255 390:255 391:255 392:255 393:255 394:255 395:255 396:255 397:255
398:255 399:255 400:255 401:255 402:255 403:255 404:255 405:255 406:255 407:249
408:237 409:215 410:181 411:148 412:115 413:81 414:48 415:23 416:15
steps between adjacent presents: {-34: 2, -33: 3, -25: 1, -22: 1, -12: 1, -8: 1, -6: 1, 17: 12, 34: 1}
distinct alphas 24 ; changed on 23 of 168 presents
## palogo_seta x[-0.19,0.19] y[-0.12,0.12] presents 248..416 (n=169)
248:17 249:34 250:51 251:68 252:85 253:119 254:136 255:153 256:170 257:187
258:204 259:221 260:238 261:255 262:255 263:255 264:255 265:255 266:255 267:255
268:255 269:255 270:255 271:255 272:255 273:255 274:255 275:255 276:255 277:255
278:255 279:255 280:255 281:255 282:255 283:255 284:255 285:255 286:255 287:255
288:255 289:255 290:255 291:255 292:255 293:255 294:255 295:255 296:255 297:255
298:255 299:255 300:255 301:255 302:255 303:255 304:255 305:255 306:255 307:255
308:255 309:255 310:255 311:255 312:255 313:255 314:255 315:255 316:255 317:255
318:255 319:255 320:255 321:255 322:255 323:255 324:255 325:255 326:255 327:255
328:255 329:255 330:255 331:255 332:255 333:255 334:255 335:255 336:255 337:255
338:255 339:255 340:255 341:255 342:255 343:255 344:255 345:255 346:255 347:255
348:255 349:255 350:255 351:255 352:255 353:255 354:255 355:255 356:255 357:255
358:255 359:255 360:255 361:255 362:255 363:255 364:255 365:255 366:255 367:255
368:255 369:255 370:255 371:255 372:255 373:255 374:255 375:255 376:255 377:255
378:255 379:255 380:255 381:255 382:255 383:255 384:255 385:255 386:255 387:255
388:255 389:255 390:255 391:255 392:255 393:255 394:255 395:255 396:255 397:255
398:255 399:255 400:255 401:255 402:255 403:255 404:255 405:255 406:255 407:249
408:237 409:215 410:181 411:148 412:115 413:81 414:48 415:23 416:15
steps between adjacent presents: {-34: 2, -33: 3, -25: 1, -22: 1, -12: 1, -8: 1, -6: 1, 17: 12, 34: 1}
distinct alphas 24 ; changed on 23 of 168 presents
## palogo_anima x[-0.30,0.30] y[-0.62,-0.25] presents 248..416 (n=169)
248:17 249:34 250:51 251:68 252:85 253:119 254:136 255:153 256:170 257:187
258:204 259:221 260:238 261:255 262:255 263:255 264:255 265:255 266:255 267:255
268:255 269:255 270:255 271:255 272:255 273:255 274:255 275:255 276:255 277:255
278:255 279:255 280:255 281:255 282:255 283:255 284:255 285:255 286:255 287:255
288:255 289:255 290:255 291:255 292:255 293:255 294:255 295:255 296:255 297:255
298:255 299:255 300:255 301:255 302:255 303:255 304:255 305:255 306:255 307:255
308:255 309:255 310:255 311:255 312:255 313:255 314:255 315:255 316:255 317:255
318:255 319:255 320:255 321:255 322:255 323:255 324:255 325:255 326:255 327:255
328:255 329:255 330:255 331:255 332:255 333:255 334:255 335:255 336:255 337:255
338:255 339:255 340:255 341:255 342:255 343:255 344:255 345:255 346:255 347:255
348:255 349:255 350:255 351:255 352:255 353:255 354:255 355:255 356:255 357:255
358:255 359:255 360:255 361:255 362:255 363:255 364:255 365:255 366:255 367:255
368:255 369:255 370:255 371:255 372:255 373:255 374:255 375:255 376:255 377:255
378:255 379:255 380:255 381:255 382:255 383:255 384:255 385:255 386:255 387:255
388:255 389:255 390:255 391:255 392:255 393:255 394:255 395:255 396:255 397:255
398:255 399:255 400:255 401:255 402:255 403:255 404:255 405:255 406:255 407:249
408:237 409:215 410:181 411:148 412:115 413:81 414:48 415:23 416:15
steps between adjacent presents: {-34: 2, -33: 3, -25: 1, -22: 1, -12: 1, -8: 1, -6: 1, 17: 12, 34: 1}
distinct alphas 24 ; changed on 23 of 168 presents

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# ✅ 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.