“F1.4: replicate 0253's excess (K4 above all 12 copies in 299 of 2,093 settings, chance 161): K4 on 400 of its settings with fresh copies, four shuffled stand-ins for K4 through the same procedure, and the 25 strongest of K4's 66 settings above all 100 against 100 fresh copies”

1. Shuffle K4's letters to make a stand-in.
2. Find every key-stepping rule that the stand-in fits with some alphabet (the 24 known letters agree), as was done for K4.
3. Pick 400 of those rules at random. For each, search for the stand-in's most English-looking reading, then make scrambled copies of the stand-in that fit the same rule and search them one at a time until one reads as well.
4. Count the rules where the stand-in beat 12 copies.
5. A fair test gives about 1 in 13. Do the same for K4 and compare.

Replication of 0253: is the excess K4's or the test's?

  target      its fitting settings   400 drawn   above all 12 copies
  K4          2,093                   400         ?   (0253: 14.3%)
  stand-in 1  its own                 400         ?
  ... four stand-ins (shuffles of K4), the same procedure

  a fair test gives 1 in 13 (7.7%) for every target.

F1.4 (a keyed table with a hand key schedule, one free alphabet on both sides, Beaufort or added; C20(d), C27(c)). 0253 decided each of K4's 2,093 fitting settings with D1's one-run decider (0140's tempering generalised to slot maps, 0252) against fitting shuffles climbed one at a time. The per-setting null (1/13 above all 12) assumes K4 and a fitting shuffle are exchangeable once both fit. They may not be: the setting list was filtered by K4 (a setting that K4 fits may fit it more loosely than a random fitting shuffle), and a fitting shuffle may keep fewer free alphabet letters. If the stand-ins (B) show the same excess as K4 (A), the excess belongs to the procedure and 0253's verdict must be read against B's rate, not 1/13; if B sits at 1/13 and A replicates, the excess is K4's and is chased (C says whether particular settings carry it).

B shows an excess like A's (stand-ins above all 12 copies in about 12-15% of their settings, against 7.7% for a fair test), so the excess belongs to the procedure; A replicates 0253's rate (about 14%); C: K4 above all 100 fresh copies in a few of the 25, well under 25 but above the 1% a fair test gives. Zero candidates.

1. Targets: K4 and four shuffles of K4 (seed 2541). For each target, every setting of 0252's list (0128's schedules at slot counts 2-31, back and forth, both forms) is decided exactly; the target's fitting settings are its cell.
2. A and B: 400 settings drawn at random from each target's cell (seed per target); per setting 0253's decide(): one tempering run on the target, then fitting shuffles of the target climbed one at a time, stop at the first at or above, at most 12 (no escalation). Count settings where the target is above all 12.
3. C: the 25 settings 0253's record lists (the strongest of the 66 where K4 was above all 100), each with 100 fresh fitting copies (decide with escalation, new seeds).
4. Verdict, pre-registered: the procedure's null rate is the stand-ins' pooled rate p_B; K4's A rate against p_B by a two-proportion test; if p_B is within 2 points of K4's, the excess is the procedure's.

0253 replication: K4 above all 12 in 53/400 (0.133); stand-ins 146/1600 (0.091); fair 0.077; z 2.47; verdict: unclear. C: 9 of 25 top settings above all 100 fresh copies.

What was searched, as the harness recorded it.

item

F1.4 replication of 0253's excess

decider

0253's decide(), imported unchanged: one tempering run on the target, fitting shuffles climbed one at a time, at most 12 (A, B), escalated to 100 (C)

targets

k4

cell size

2,093

sampled

400

above all 12

53

rate

0.133

beat first copy

231

beat first rate

0.578

mean copies climbed

3.98

standin0

cell size

3,246

sampled

400

above all 12

41

rate

0.102

beat first copy

205

beat first rate

0.512

mean copies climbed

3.48

standin1

cell size

3,696

sampled

400

above all 12

29

rate

0.072

beat first copy

170

beat first rate

0.425

mean copies climbed

2.75

standin2

cell size

2,997

sampled

400

above all 12

6

rate

0.015

beat first copy

136

beat first rate

0.34

mean copies climbed

2

standin3

cell size

3,917

sampled

400

above all 12

70

rate

0.175

beat first copy

281

beat first rate

0.703

mean copies climbed

4.6

fair rate 12

0.077

standins pooled

sampled

1,600

above all 12

146

rate

0.091

k4 rate

0.133

two proportion z k4 vs standins

2.47

verdict

unclear

C top settings

count

25

above all 100 fresh

9

fair expected

0.25

each

1. setting

   B skip m=13 phi=10 n=22

   form

   V

   above

   100

   score

   -4.947

2. setting

   B skip m=12 phi=6 n=22

   form

   V

   above

   100

   score

   -5.003

3. setting

   B skip m=30 phi=29 n=21

   form

   V

   above

   100

   score

   -4.998

4. setting

   B skip m=13 phi=9 n=22

   form

   V

   above

   100

   score

   -4.968

5. setting

   B skip m=14 phi=12 n=22

   form

   V

   above

   100

   score

   -4.99

6. setting

   B skip m=22 phi=13 n=21

   form

   V

   above

   100

   score

   -5.138

7. setting

   B skip m=13 phi=8 n=22

   form

   V

   above

   100

   score

   -5.012

8. setting

   B skip m=23 phi=15 n=21

   form

   V

   above

   100

   score

   -5.078

9. setting

   B skip m=29 phi=28 n=21

   form

   V

   above

   100

   score

   -5.087

10. setting

    B skip m=8 phi=3 n=23

    form

    V

    above

    76

    score

    -4.978

11. setting

    B skip m=14 phi=13 n=22

    form

    V

    above

    59

    score

    -5.017

12. setting

    B skip m=26 phi=23 n=21

    form

    V

    above

    59

    score

    -5.052

and 13 more

core seconds

140,831

compute seconds

2,569

exhaustive

no

modal cost estimate

5 x 400 settings x about 5 climbs + 25 x about 100 climbs, about 17 s each: about 210,000 core-seconds, about $3.5 of Modal credit (credit left about $17 after the margin)