# Check I: check H re-read with the run-to-run gap instead of comparing labels, the kick's sign carried, and like-for-like runs
Defined after check H's output was seen. Heuremen LLC, 22 Oct 2026. Script check_i_run_gap.py. Replaces check H's reporting rule (check H's output stays published).
Three faults in check H: (1) "runs agree on the label -> report, else CANNOT TELL" compares labels, so a wider run counts as a contradiction;
(2) H1 read distance-1 minus distance-2 ABOVE 0 as "falls off", but the kick is negative, so ABOVE means larger two steps away;
(3) H3 compared run 1 all shots with run 2 clean shots.
Same 39 measured and 117 spectator qubits in both runs (checked). Per spectator, the quantity from run 1 and from run 2.
RUN GAP: median over spectators of run1 - run2, 95 % bootstrap (2000). Interval contains 0 -> no shift between runs resolved; the reading is
the POOLED value (per spectator mean of the two runs). Interval excludes 0 -> the runs differ; both are printed with the gap; reading CANNOT TELL.
SIZE: kick size = -kick when the kick median is below 0 in every group in both runs (printed as a check); otherwise CANNOT TELL for H1.
H1 (N = 8): size(distance 1) - size(distance 2), pooled, bootstrap within groups. ABOVE -> larger next to a measured qubit (falls off).
   BELOW -> larger two steps away. CONSISTENT -> neither resolved; the interval is printed as the bound.
H2: pooled kick(8) - kick(2) and the pooled intercept of total phase gap against N (2, 4, 8). CONSISTENT -> printed as a bound, with the bound
   as a fraction of the pooled kick size.
H3: superposition cost loss(8) - loss(2), all spectators, all shots, in BOTH runs (like for like); run 2's clean-shot value (wired spectators)
   is printed beside it and not mixed in.
Four outcomes: ABOVE / BELOW / CONSISTENT / CANNOT TELL.