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Closes the open half of Q3. `ui-paint-order-derived-check.md` bounded WHERE a wrong tie-break could show -- overlapping same-key pairs -- and said outright that nobody had measured how many change a pixel. At the instant the player sees, the answer is: at most 1 px at max channel difference 1, on the JAPANESE title only (`ptlogo2` x `ptlogo_tm`, 5 px of shared ink). Exactly 0 px on all five port screens. The earlier 24-pair bound was counted at `rest()`, and 10 of the title's 11 overlapping tied pairs are between `ptlogo_back2eff1`..`eff5` -- the five transient flashes from the settle-time finding, transparent on the settled screen. A tie between two invisible elements cannot cost a pixel. Not a knife-edge. Sweeping every keyframe time and every midpoint between keyframe times, the live-pair count is flat across the ENTIRE settle window: 1 on the EN title, 2 on the JP title, 0 on all four loading bundles -- whose tie is live only at t17..t33, during the build-in, which matters because their settle windows are narrow enough to deserve little trust otherwise. Controls: every entry reporting zero also swaps an overlapping DIFFERENT-key pair, which must and does move pixels (25 310 / 268 698 / ~765 000 px). Zeros are explained by shared-ink counts rather than asserted -- the `ptframe` pairs overlap by bounding box and share 0 px of ink. Entries 0/1/12/15 have NO live control and their zeros rest on keyframe data rather than a render; recorded as the weaker claim it is. Refutation attempt on the corpus's "24 overlapping pairs": it SURVIVES as a rest-pose count -- an independent recount reproduces entry 7's 16 exactly. What is overturned is its interpretation as the risk surface. `tie_break_pixel_cost` gains a settle-time case and an alpha/scale filter on its rect test; `tie_cost_over_time` is new. Also strips 611 bytes of captured cargo warnings from the head of the committed tie census. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01QsEPXWVaEpyfudtR6re1Pd
119 lines
5.6 KiB
Markdown
119 lines
5.6 KiB
Markdown
# What the paint-order tie-break actually costs: one pixel, on one screen
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**Classification: decoded.** Both terms come from the disc — the pairs from the
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keyframe table, the pixels from rendering the same bundle twice with two
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elements swapped. No capture is involved, and none is needed: this measures how
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much a *wrong* answer could cost, not which answer is right.
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## The question this closes
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[`ui-paint-order-derived-check.md`](ui-paint-order-derived-check.md) bounds
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*where* a wrong tie-break could show — same-layer-key pairs whose rects overlap —
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and says outright that **nobody has measured how many of them change a pixel**.
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That was the last open half of Q3.
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## The answer
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**At the instant the player actually sees, the tie-break costs at most one pixel,
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at a maximum channel difference of 1, and only on the Japanese title. On all five
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port screens it is exactly zero.**
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| entry | screen | live tied pairs at settle | measured cost |
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|---|---|---|---|
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| 4 | title (EN) | 1 | **0 px** — the pair is `ptloop01`×`ptloop02`, not both drawn |
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| 5 | main menu | 2 | **0 px** — `ptframe1`×`ptframe2` share **no ink**; the other is undrawn |
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| 6 | submenu | 2 | **0 px** — same shape |
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| 8 | submenu | 2 | **0 px** — same shape |
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| 9 | submenu | 2 | **0 px** — same shape |
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| 7 | title (JP) | 2 | **1 px, max Δ 1** — `ptlogo2`×`ptlogo_tm`, 5 px of shared ink |
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| 0, 1, 12, 15 | loading | **0** | no pair is live at all |
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Full run: [`tie-break-pixel-cost-gp_title.txt`](../data/tie-break-pixel-cost-gp_title.txt).
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## Why the number moved: `rest()` was counting elements that are not there
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The census that produced the earlier bound posed every element at `rest()`, its
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own last hold keyframe. That draws **transients at their peak**
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([`ui-settle-time.md`](ui-settle-time.md)), and the title's ties are almost
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entirely *between transients*: `ptlogo_back2eff1`…`eff5` are five staggered
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two-frame flashes, all extinguished by t110, and they account for 10 of the
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title's 11 overlapping tied pairs.
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A tie between two elements that are transparent cannot cost a pixel however much
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their rects overlap. Posing at the settle time instead:
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| | entry 4 | entry 7 | entries 0/1/12/15 |
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|---|---|---|---|
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| overlapping tied pairs at `rest()` | 11 | 13 | 1 each |
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| **still live at the settle time** | **1** | **2** | **0** |
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## It is not a knife-edge
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The obvious objection is that "at the settle time" picks one instant, and a
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different instant might give a different count. Sweeping every keyframe time and
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every midpoint between keyframe times
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([`tie-break-live-over-time-gp_title.txt`](../data/tie-break-live-over-time-gp_title.txt)):
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| entry | peak live pairs over the whole timeline | **max anywhere in the settle window** |
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|---|---|---|
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| 4 | 6 | **1** |
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| 7 | 6 | **2** |
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| 5 / 6 / 8 / 9 | 2 | 2 |
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| 0 / 1 / 12 / 15 | 1 | **0** |
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The count is **flat across the entire window**, not just at its midpoint. The four
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loading bundles are the sharpest case: their tie is live only at t17–t33 — during
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the build-in — and dead everywhere else, which matters because their settle
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windows are narrow (4 and 8 units) and would otherwise deserve little trust.
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## Controls
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* ✅ **A live control on every entry that reports a zero.** Each run also swaps an
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overlapping pair with **different** keys — an order the game demonstrably does
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care about — and requires it to move pixels. It moves 25 310 px on the title,
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268 698 px on the JP title, and ~765 000 px on the four menu screens.
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* ⚠️ **Entries 0, 1, 12, 15 have no live control** ("no overlapping different-key
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pair is drawn"). Their zeros rest on the *keyframe data* — no tied pair has both
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elements opaque at any instant in the window — not on a render, so a dead
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control does not undermine them. But nothing here demonstrates the renderer
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would notice a swap on those bundles.
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* ✅ **Shared-ink accounting.** A zero is only meaningful with an explanation. The
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`ptframe` pairs overlap by bounding box and share **0 px** of actual ink; the
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JP title's 1 px comes from 5 px of shared ink between `ptlogo2` and
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`ptlogo_tm`.
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## 🟡 Refutation attempt: the corpus's "24 overlapping pairs" — it survives
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Recounted independently. Without the alpha/scale filter this document adds, the
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per-entry counts are `e0:1 e1:1 e4:13 e5:2 e6:2 e7:16 e8:2 e9:2 e12:1 e15:1`,
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total 41 — and **entry 7's 16 reproduces the corpus's figure exactly**. The 24 is
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that population scoped to the entries without a measured order. Adding the filter
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takes the total to 36.
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So the count stands as a **rest-pose upper bound**. What this document overturns
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is its *interpretation*: 24 was being read as the surface on which a wrong
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tie-break could show, and at the instant the player sees, that surface is one
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pixel.
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## Reach and what is still open
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❔ **Why the game orders ties as it does is still unknown**, and this does not
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touch it — eight candidate rules remain refuted in
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[`ui-paint-order-derived-check.md`](ui-paint-order-derived-check.md). What changes
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is that the question is no longer worth much: getting it wrong costs one pixel on
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a screen the port does not ship.
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⚠️ **`GP_TITLE` only.** Other paks were not swept. The method is bundle-agnostic
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but the numbers are not.
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⚠️ **Rect overlap is still an approximation** (pivot doubled, placed at the pose).
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It is used only to *choose candidate pairs*; every reported cost is a real render
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diff, so the approximation can add candidates but cannot invent a cost.
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## Reproducing
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```bash
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cargo run -p sylpheed-formats --example tie_break_pixel_cost -- "$SYLPHEED_DISC/dat/GP_TITLE.pak"
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cargo run -p sylpheed-formats --example tie_cost_over_time -- "$SYLPHEED_DISC/dat/GP_TITLE.pak"
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```
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