# Units per SECOND: is the animation clock frame-counted or time-integrated?

**Pre-registration. Written 2026-09-01 BEFORE the capture was taken**, per
[`../agents/TEMPORAL-VERIFICATION.md`](../agents/TEMPORAL-VERIFICATION.md).
Committed first so the prediction cannot be edited afterwards.

## The question, and why the last answer did not close it

[`h3-units-per-frame-measured.md`](h3-units-per-frame-measured.md) pinned **2
declared units per guest frame**. The port needs **units per second**, and
`units/s = (units/frame) × (frames/s)`. That is only a valid decomposition if the
game's animation clock counts **frames**. If it integrates **elapsed time**, then
units/second is the invariant, units/frame is an artefact of whatever rate the
host managed, and multiplying by an assumed 30 fps is meaningless.

There is already evidence it is time-integrated, and it is the anomaly the last
page had to quote as a caveat: across the empty label 5376 the plate's alpha
moved **+82** where three adjacent labels each moved **+23**. `82 / 23 = 3.57` —
**not an integer number of ticks**. A fixed per-frame increment cannot produce a
fractional multiple of itself. That is suggestive and it is one observation.

## The instrument, and why it is not a wall clock

The draw logger now stamps every frame boundary with
`Clock::QueryGuestTickCount()` and `Clock::guest_tick_frequency()` — the timebase
the **guest** reads, 50 MHz (`emulator.cc:225`), with `guest_time_scalar_ = 1.0`
(`clock.cc:37`, unchanged by any flag this harness passes). A duration computed
from those is the duration **the game experienced**, which is the only one its own
integrator could have used. No host wall clock enters the calculation.

⟨canary-source⟩ for the scalar and the frequency; ⟨capture⟩ for everything
measured with them.

## The discriminator — within one run, no second capture needed

For every consecutive pair of frame labels on `ptbtn00`'s ramp, compute the
label's **guest duration** and the **alpha step** across it. Then:

| if the clock is | Δα vs guest duration | what it means |
|---|---|---|
| **frame-counted** | **flat** — Δα ≈ 23 whatever the frame took | units/frame is the invariant; the port multiplies by an assumed fps |
| **time-integrated** | **proportional, through the origin** | units/second is the invariant; **units/frame is not a property of the game at all** |

The slope of that line, if it is one, is the answer: `slope × 22 / 255` =
**units per guest second**.

Frame durations under this emulator vary by a factor of several — the previous
capture's labels ran from nominal to 3.5× nominal — so the regressor has real
dynamic range and this is not a null test.

## The predictions, stated before the run

1. **The clock is time-integrated.** Δα correlates with guest frame duration,
   r > 0.9.
2. **The rate is 60 units per guest second.** I accept **55–65**. This is *not*
   independent: it is what the previous capture's run-average implies (27.2
   labels/s × 2.0–2.25 units/label ≈ 54–61), so it is a consistency prediction,
   not a blind one, and I say so. What is new is that this measurement is
   per-label rather than a run average, in guest time rather than host time, and
   carries a shape test the average cannot.
3. **120 units/s and 30 units/s are both excluded** if 1 and 2 hold.

**If prediction 1 fails** — Δα flat against duration — then the clock *is*
frame-counted, `units/s` genuinely depends on the console's frame rate, and the
+82 anomaly needs another explanation. That outcome is reportable and I will
report it.

## The control that removes the test's own subject

The plate's ramp is short. The same regression is run **independently** on
`ptcopyright`'s ramp in the same capture — a different element, a different
declared segment, a different part of the screen. Two elements must give the
**same** units/second under the time-integrated model and need not under any
other. Disagreement between them fails the test regardless of either slope.

## What this still will not answer

The **console's** frame rate. Even a confirmed 60 units/s says nothing about
whether the retail game ran at 30 or 60 fps; it says the port should not need to
know, because it should drive its clock in seconds and not in frames.