re: a ninth transition -- the same origin gives gap 0 and 1 by destination

sylpheed-port confirmed "nothing declared predicts the gap" from their export
independently, and deliberately declined to search combinations: four pairs
against many candidate two-screen functions fits by construction. Right call, and
it applies to me unchanged. So this iteration adds a PAIR rather than a fit.

menu -> a second screen outside GP_TITLE, reached by stepping the cursor two
items before arming. The button is not controlled -- there is no focus readout --
so the destination is identified afterwards by its draw signature: incoming
primitive [255] at 7-9 draws/frame, against the first run's [127] at 12-13.
Different screens.

Outgoing quad rises 25, 51, 102, 229, 255 across frames 37-42, then at frame 44
the new screen is already drawing. NO empty frame anywhere. GAP = 0.

So the menu as origin gives four values across four destinations: title 0,
EXTRAS 1, other-1 1, other-2 0. The same origin yields both 0 and 1 depending on
where it goes, while the two repeated pairs stay internally identical (3,3,3 and
2,2). Further evidence for the ordered pair over the origin.

Recorded as an observation with its counter-example rather than fitted: the
incoming screen's own full-screen primitive is [255] where the gap is 0 and [127]
where it is 1, which suggests a screen beginning from opaque black needs no blank
frame. That FAILS on menu -> EXTRAS, which declares a black backdrop and still
gives 1. Nine transitions against many candidate functions is the construction
the port declined to search, and I am not searching it either.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Wuu56cE8vJGTBtn1ppsk8v

tools/re-capture/fade_decompose.sh

@@ -98,6 +98,18 @@ elif [ "$WHERE" = "menu2other" ]; then
   python3 "$SD/pad.py" tap B 0.5; sleep 6
   case "$w" in extras*) echo "  focus was EXTRAS — stepping once"
                         python3 "$SD/pad.py" dpad UP 0.3; sleep 2;; esac
+  # STEPS=n moves the cursor n further items before arming, so a second run can
+  # leave the menu by a DIFFERENT button. The menu has four non-EXTRAS exits, and
+  # a second distinct destination from the same origin is what separates
+  # "the gap is per ordered pair" from "the gap is per origin plus destination
+  # class". ⚠️ There is no focus readout, so which button this lands on is not
+  # controlled -- it is IDENTIFIED afterwards by the destination's draw
+  # signature, and if the signature matches the previous run it is the same pair
+  # and the run says nothing new.
+  for _ in $(seq 1 "${STEPS:-0}"); do
+    echo "  STEPS: moving the cursor one item"
+    python3 "$SD/pad.py" dpad DOWN 0.3; sleep 2
+  done
   shot "$OUT/armed-on-menu.png"
   echo "  arming on: $(python3 "$SD/which_title_screen.py" "$OUT/armed-on-menu.png")"
   BTN=A