Put the frame clock on the 68000, and find that the 12 fps frame does not exist

ROADMAP P3 said "needs MFP timer or VBL" and neither can do it.  The MFP's
timer clock is 16 MHz/4, its prescalers stop at 200 and its data register is 8
bits, so the slowest tick any single timer can make is 78.125 Hz -- 6.5x faster
than a frame -- and 4e6/12 is not an integer, so no setting reaches 12 Hz at
all.  The raster has no whole divide near 12 either: 4 refreshes is 13.86 fps
and 5 is 11.09.  tools/analysis/23_frame_clock.py walks all 7x256 timer settings
rather than asserting it.

src/player/clock.i takes the V-DISP falling edge on MFP GPIP4 -- the start of
vertical blanking, which is when a player would present -- and adds fps*VTOTAL
per edge to a 16-bit accumulator, emitting a tick at 31,500 and keeping the
remainder.  The long-run rate is fps*VTOTAL/VTOTAL = 12.000000 fps exactly, and
both constants are read out of the CRTC at init, so the clock is derived from
the registers that generate the raster it counts.  Measured over 3,000
refreshes: 3,000 interrupts, 649 ticks where 649.1429 were due.

It costs 181.35 clocks per V-DISP, 838 per frame, 0.1006% of the budget -- timed
by the 68000 itself, because the host's granularity is 17.64 ms and the
interrupt is microseconds.  The loop's own cost was calibrated rather than
looked up and landed on 38.000002 clocks, which both licenses the subtraction
and confirms buscost.py's model; the 181.35 then decomposes exactly, leaving
43.99 clocks for the interrupt exception -- the textbook 44, measured.

THE ONE THAT MOVES SOMETHING: 12 fps on a 55.4577 Hz raster is 4.6215 refreshes,
so a frame is shown for 4 refreshes (72.13 ms) or 5 (90.16 ms), 37.9% of them
short.  The 833,333-clock budget every figure in this project is priced against
is the MEAN slot, and the short one is 13.4% under it.  The cadence was already
in the tree unnamed: stream.lua's tick is sampled at frame boundaries, so its
gaps were always 4 or 5, and every host-paced result in FINDINGS 49/51 carried
it.  P3 moved who produces it onto the machine and made it visible.  It is not a
dropped frame -- the pace gate lets an overrun eat the next frame's idle -- and
on the gate container it costs 4 frames of 120 their idle against 1 for the
nominal model, most of that the frame-0 transient at 111% of budget.  stream.s
counts it now, and the rig matches an offline model of the divider exactly.

Also struck: MAME's raster runs 2.22% fast.  refresh_mode() builds the frame
period from scr.max_x*scr.max_y with scr.max_x = m_htotal - 8, one character
cell short and an inclusive bound used as a count, so it runs at 56.6901 Hz
where the registers say 55.4577 -- agreeing to six digits with the arithmetic.
Every "1/55.46 s granularity" note in this tree was wrong and is 1/56.69 s,
corrected in six files with the derivation put once in crtc_mode.lua.  No
conclusion changes and no 68000 cycle figure moves; the CPU clock is unrelated
to the screen.  But anything paced by the raster runs fast under MAME, so the
rig reports both rates and prices the interrupt against the hardware's.

decode.s and frame.i are unchanged; decode.bin is still 1,296 B at the same MD5.
The pace gate's wait loop is byte-for-byte the one FINDINGS 51 measured and the
free-running path executes none of the new code.  check.sh gains two stages: the
clock's own measurement, and 120 frames decoded pixel-exact with nothing outside
the machine deciding when a frame may start.

Claude-Session: https://claude.ai/code/session_01194oWYW8DQXK1SZ2DnChW6

docs/ROADMAP.md

@@ -2,6 +2,7 @@
 
 Written end of session 19 (2026-08-24), against a tree that is ALL GREEN.
 Amended end of session 21: P1 done, P2 half done (FINDINGS 53).
+Amended end of session 22: P3 done (FINDINGS 54).
 
 **THE COMPLETION TARGET IS M3, THE VERTICAL SLICE** (USER DECISION): one scene
 tree — a decision point, two outcomes, a death clip — with audio, streaming from
@@ -124,10 +125,37 @@ re-measurement rather than an edit. Until then the letterbox gets the palette's
 closest thing to black (index 255 on the gate container); `load.i` reports
 whichever index that is and needs no change when it becomes 0.
 
-**P3. A real frame clock.** `stream.s` has `PACE`/`PACEON` (`$18034`/`$18038`)
-but the 12 fps tick comes from the Lua producer. Needs MFP timer or VBL. Keep
-`PACEON=0` free-run working — the wrap gate uses it and every FINDINGS 49 figure
-depends on it.
+~~**P3. A real frame clock.**~~ **DONE, session 22 — FINDINGS 54.**
+`src/player/clock.i` derives the tick from the CRTC's own V-DISP through the
+MFP, with a remainder-keeping divider whose two constants are read out of the
+CRTC at init. **Exactly 12.000000 fps, by construction** — measured at 649 ticks
+over 3,000 refreshes where 649.1429 were due, so the remainder still held and
+nothing accumulated. **181.35 clocks per V-DISP, 838 per frame, 0.1006% of the
+budget**, timed by the 68000 itself because the host's 17.64 ms granularity
+cannot see it. `PACEON=0` free-run is untouched and so is the wait loop; the
+free-running path executes none of the new code.
+
+The item said "MFP timer or VBL" and **neither can do it alone**: 4e6/12 is not
+an integer and no prescale/data pair reaches 12 Hz, while the slowest MFP tick
+of any kind is 78.125 Hz; and the raster's 55.4577 Hz has no whole divide near
+12 either (4 gives 13.86, 5 gives 11.09). `tools/analysis/23_frame_clock.py`
+walks the whole space rather than asserting it.
+
+**What it exposed is bigger than the item.** 12 fps on a 55.4577 Hz raster is
+4.6215 refreshes, so a frame gets **4 refreshes (72.13 ms) or 5 (90.16 ms)** and
+**there is no 83.33 ms frame** — that figure is the mean slot, and 37.9% of slots
+are 13.4% under it. The cadence was ALREADY in every host-paced result in
+FINDINGS 49/51, because `stream.lua`'s tick is sampled at frame boundaries and
+its gaps were always 4 or 5; nothing had named it. On the gate container it
+costs 4 frames of 120 their idle against 1 for the nominal model. **It is not a
+dropped frame** — the pace gate lets an overrun eat the next frame's idle and
+the clock recovers — but it means every budget in this project is priced against
+a slot 37.9% of frames do not get. 54.4.
+
+**Also struck: MAME's raster runs 2.22% fast** (`refresh_mode()` builds the frame
+period from `htotal - 8`), so the tree's "1/55.46 s granularity" was 1/56.69 s
+throughout. No 68000 cycle figure moves — the CPU clock is unrelated to the
+screen — but anything paced by the raster does. 54.5.
 
 **P4. Real transport.** Drive the MB89352 instead of a host file. The `W`
 handshake — clocks stolen per delivered byte, bracketed 5..12 by MC68450 Fig