BusyBeaverWiki - User contributions [en]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2026-01-02T08:36:38Z

Atoms: grammar

{{machine|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}}
{{TM|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}} is a [[holdout]] [[BB(6)]] TM.

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
'''step 83 params (2, 2, 5)'''
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
'''step 2391 params (2, 2, 17)'''
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
'''step 8224 params (2, 19, 10)'''
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
'''step 18088 params (2, 19, 12)'''
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
'''step 36576 params (2, 19, 14)'''
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
'''step 72990 params (2, 19, 16)'''
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
'''step 145562 params (2, 19, 18''')
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
'''step 288850 params (2, 20, 19''')
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
'''step 575574 params (2, 20, 21)'''
'''step 1146640 params (2, 41, 2)'''
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
'''step 1146679 params (2, 2, 41)'''
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)
step 2304485 params (2, 45, 8)
step 3451146 params (2, 45, 8)
step 5753106 params (2, 43, 12)

I think the things I've bolded may be the key because they doubles every time and all the start of the new cycle.

NOW :
step 5753237 params (2, 45, 10)

Interval (last to now): 131
Interval (first to now): 5753157

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt. The macro recurrence y(n+1) = 2y(n) + 7 induces rapidly increasing execution times, with empirical evidence suggesting super-exponential growth between successive f(x) events.

For sufficiently large g(c, d) at step k, regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2) at approx (2 +- 0.1)k. c+d then will be x in the g() function. Then after a deterministic conveyor of length x-2: it will be g(2, y) and starts another chain of patten of +3 steps between g() and f()

The y values in successive g(2, y) appearances seem to follow the recurrence:y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made

[[Category:BB(6)]]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2026-01-02T03:19:58Z

Atoms: bold keys

{{machine|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}}
{{TM|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}} is a [[holdout]] [[BB(6)]] TM.

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
'''step 83 params (2, 2, 5)'''
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
'''step 2391 params (2, 2, 17)'''
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
'''step 8224 params (2, 19, 10)'''
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
'''step 18088 params (2, 19, 12)'''
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
'''step 36576 params (2, 19, 14)'''
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
'''step 72990 params (2, 19, 16)'''
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
'''step 145562 params (2, 19, 18''')
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
'''step 288850 params (2, 20, 19''')
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
'''step 575574 params (2, 20, 21)'''
'''step 1146640 params (2, 41, 2)'''
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
'''step 1146679 params (2, 2, 41)'''
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)
step 2304485 params (2, 45, 8)
step 3451146 params (2, 45, 8)
step 5753106 params (2, 43, 12)

I think the thinks I've bolded may be the key because they doubles every time and all the start of the new cycle.

NOW :
step 5753237 params (2, 45, 10)

Interval (last to now): 131
Interval (first to now): 5753157

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt. The macro recurrence y(n+1) = 2y(n) + 7 induces rapidly increasing execution times, with empirical evidence suggesting super-exponential growth between successive f(x) events.

For sufficiently large g(c, d) at step k, regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2) at approx (2 +- 0.1)k. c+d then will be x in the g() function. Then after a deterministic conveyor of length x-2: it will be g(2, y) and starts another chain of patten of +3 steps between g() and f()

The y values in successive g(2, y) appearances seem to follow the recurrence:y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made

[[Category:BB(6)]]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2026-01-01T03:41:54Z

Atoms:

{{machine|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}}
{{TM|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}} is a [[holdout]] [[BB(6)]] TM.

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)
step 2304485 params (2, 45, 8)
step 3451146 params (2, 45, 8)
step 5753106 params (2, 43, 12)

NOW :
step 5753237 params (2, 45, 10)

Interval (last to now): 131
Interval (first to now): 5753157

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt. The macro recurrence y(n+1) = 2y(n) + 7 induces rapidly increasing execution times, with empirical evidence suggesting super-exponential growth between successive f(x) events.

For sufficiently large g(c, d) at step k, regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2) at approx (2 +- 0.1)k. c+d then will be x in the g() function. Then after a deterministic conveyor of length x-2: it will be g(2, y) and starts another chain of patten of +3 steps between g() and f()

The y values in successive g(2, y) appearances seem to follow the recurrence:y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made

[[Category:BB(6)]]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2026-01-01T03:03:10Z

Atoms: small proof

{{machine|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}}
{{TM|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}} is a [[holdout]] [[BB(6)]] TM.

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)

NOW :
step 2304485 params (2, 45, 8)

Interval (last to now): 131
Interval (first to now): 2304405

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt. The macro recurrence y(n+1) = 2y(n) + 7 induces rapidly increasing execution times, with empirical evidence suggesting super-exponential growth between successive f(x) events.

For sufficiently large g(c, d) at step k, regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2) at approx (2 +- 0.1)k. c+d then will be x in the g() function. Then after a deterministic conveyor of length x-2: it will be g(2, y) and starts another chain of patten of +3 steps between g() and f()

The y values in successive g(2, y) appearances seem to follow the recurrence:y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made

[[Category:BB(6)]]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2026-01-01T02:56:48Z

Atoms: more proof

{{machine|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}}
{{TM|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}} is a [[holdout]] [[BB(6)]] TM.

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)

NOW :
step 2304485 params (2, 45, 8)

Interval (last to now): 131
Interval (first to now): 2304405

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt. The macro recurrence y(n+1) = 2y(n) + 7 induces rapidly increasing execution times, with empirical evidence suggesting super-exponential growth between successive f(x) events.

For sufficiently large g(c, d) at step k, regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2) at approx (2 +- 0.1)k

The y values in successive g(2, y) appearances seem to follow the recurrence:
y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made)

[[Category:BB(6)]]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2026-01-01T02:42:30Z

Atoms: Adding ".", ","

{{machine|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}}
{{TM|1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---}} is a [[holdout]] [[BB(6)]] TM.

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)

NOW :
step 2304485 params (2, 45, 8)

Interval (last to now): 131
Interval (first to now): 2304405

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt

For sufficiently large g(c, d), regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2)

The y values in successive g(2, y) appearances seem to follow the recurrence:
y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made)

[[Category:BB(6)]]

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2025-12-31T11:25:44Z

Atoms:

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)

NOW :
step 2304485 params (2, 45, 8)

Interval (last to now): 131
Interval (first to now): 2304405

Call g(x,y) := $ 0^2 1^x 0^y 1 $
Since there's a lot of them, I'll sort out the pair
And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y)
The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g()
We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397
I found the pattern:
g(2, y) at step a
f(4+y) at step a+3
g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!!
g(2, 41) at step 1146679
f(41+4) or f(45) at step 1146682 = 1146679 + 3
g(3, 40) at step 1146685 = 1146682 + 3
CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt

For sufficiently large g(c, d), regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2)

The y values in successive g(2, y) appearances seem to follow the recurrence:
y(n+1) = 2y(n) + 7
CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made)

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2025-12-31T11:22:44Z

Atoms: Fix many grammar bugs

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 4 params (2)
THEN:
step 14 params (4)
step 86 params (9)
NOW:
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST:
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)

NOW :
step 2304485 params (2, 45, 8)

Interval (last to now): 131
Interval (first to now): 2304405

Call g(x,y) := $ 0^2 1^x 0^y 1 $
Since there's a lot of them, I'll sort out the pair
And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y)
The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g()
We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397
I found the pattern:
g(2, y) at step a
f(4+y) at step a+3
g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!!
g(2, 41) at step 1146679
f(41+4) or f(45) at step 1146682 = 1146679 + 3
g(3, 40) at step 1146685 = 1146682 + 3
CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt

For sufficiently large (2, c, d), regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces (2, c+d, 2)

The y values in successive g(2, y) appearances seem to follow the recurrence:
y(n+1) = 2y(n) + 7
CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made)

1RB0LE 1LC1LB 0RD0LC 1RA0RE 1RF1RD 0LA---

2025-12-31T11:16:33Z

Atoms: Created page with "SAME CONFIG (#4) State : D Head run : 1 Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None)) FIRST : step 4 params (2) THEN : step 14 params (4) step 86 params (9) NOW : step 2394 params (21) Call f(x) := $ 0^x 1 $ Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394 SAME CONFIG (#64) State : C Head run : 2 Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None)) FIRST : step 80 params (2, 5, 2) TH..."

SAME CONFIG (#4)
State : D
Head run : 1
Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None))
FIRST :
step 4 params (2)
THEN :
step 14 params (4)
step 86 params (9)
NOW :
step 2394 params (21)
Call f(x) := $ 0^x 1 $
Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64)
State : C
Head run : 2
Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None))
FIRST :
step 80 params (2, 5, 2)
THEN :
step 81 params (2, 4, 3)
step 82 params (2, 3, 4)
step 83 params (2, 2, 5)
step 89 params (2, 3, 4)
step 1226 params (2, 5, 12)
step 1243 params (2, 7, 10)
step 1286 params (2, 7, 10)
step 1309 params (2, 9, 8)
step 1374 params (2, 9, 8)
step 2376 params (2, 17, 2)
step 2377 params (2, 16, 3)
step 2378 params (2, 15, 4)
step 2379 params (2, 14, 5)
step 2380 params (2, 13, 6)
step 2381 params (2, 12, 7)
step 2382 params (2, 11, 8)
step 2383 params (2, 10, 9)
step 2384 params (2, 9, 10)
step 2385 params (2, 8, 11)
step 2386 params (2, 7, 12)
step 2387 params (2, 6, 13)
step 2388 params (2, 5, 14)
step 2389 params (2, 4, 15)
step 2390 params (2, 3, 16)
step 2391 params (2, 2, 17)
step 2397 params (2, 3, 16)
step 2430 params (2, 6, 13)
step 2450 params (2, 8, 11)
step 8224 params (2, 19, 10)
step 8283 params (2, 21, 8)
step 10656 params (2, 21, 8)
step 18088 params (2, 19, 12)
step 18147 params (2, 21, 10)
step 20520 params (2, 21, 10)
step 36576 params (2, 19, 14)
step 36635 params (2, 21, 12)
step 39008 params (2, 21, 12)
step 72990 params (2, 19, 16)
step 73049 params (2, 21, 14)
step 75422 params (2, 21, 14)
step 145562 params (2, 19, 18)
step 145621 params (2, 21, 16)
step 147994 params (2, 21, 16)
step 288794 params (2, 18, 21)
step 288850 params (2, 20, 19)
step 573322 params (2, 5, 36)
step 573339 params (2, 7, 34)
step 573382 params (2, 7, 34)
step 573405 params (2, 9, 32)
step 573470 params (2, 9, 32)
step 575518 params (2, 18, 23)
step 575574 params (2, 20, 21)
step 1146640 params (2, 41, 2)
step 1146641 params (2, 40, 3)
step 1146642 params (2, 39, 4)
step 1146643 params (2, 38, 5)
step 1146644 params (2, 37, 6)
step 1146645 params (2, 36, 7)
step 1146646 params (2, 35, 8)
step 1146647 params (2, 34, 9)
step 1146648 params (2, 33, 10)
step 1146649 params (2, 32, 11)
step 1146650 params (2, 31, 12)
step 1146651 params (2, 30, 13)
step 1146652 params (2, 29, 14)
step 1146653 params (2, 28, 15)
step 1146654 params (2, 27, 16)
step 1146655 params (2, 26, 17)
step 1146656 params (2, 25, 18)
step 1146657 params (2, 24, 19)
step 1146658 params (2, 23, 20)
step 1146659 params (2, 22, 21)
step 1146660 params (2, 21, 22)
step 1146661 params (2, 20, 23)
step 1146662 params (2, 19, 24)
step 1146663 params (2, 18, 25)
step 1146664 params (2, 17, 26)
step 1146665 params (2, 16, 27)
step 1146666 params (2, 15, 28)
step 1146667 params (2, 14, 29)
step 1146668 params (2, 13, 30)
step 1146669 params (2, 12, 31)
step 1146670 params (2, 11, 32)
step 1146671 params (2, 10, 33)
step 1146672 params (2, 9, 34)
step 1146673 params (2, 8, 35)
step 1146674 params (2, 7, 36)
step 1146675 params (2, 6, 37)
step 1146676 params (2, 5, 38)
step 1146677 params (2, 4, 39)
step 1146678 params (2, 3, 40)
step 1146679 params (2, 2, 41)
step 1146685 params (2, 3, 40)
step 1146718 params (2, 6, 37)
step 1146738 params (2, 8, 35)
step 1148978 params (2, 18, 25)
step 1149034 params (2, 20, 23)
step 2304354 params (2, 43, 10)

NOW :
step 2304485 params (2, 45, 8)

Interval (last ? now) : 131
Interval (first ? now): 2304405

Call g(x,y) := $ 0^2 1^x 0^y 1 $
Since there's a lot of them, I'll sort out the pair
And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y)
The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g()
We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89
f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397
I found the pattern:
g(2, y) at step a
f(4+y) at step a+3
g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!!
g(2, 41) at step 1146679
f(41+4) or f(45) at step 1146682 = 1146679 + 3
g(3, 40) at step 1146685 = 1146682 + 3
CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt

If I am missing, feel free to contribute

For sufficiently large (2, c, d), regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces (2, c+d, 2)

The y values in successive g(2, y) appearances seem to follow the recurrence:
y(n+1) = 2y(n) + 7
CAUTIOUS: y(1) = 5, not 2

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made)

Talk:1RB1RA 0RC1RC 1LD0LF 0LE1LE 1RA0LB ---0LC

2025-12-30T03:49:34Z

Atoms: I don't know when it will come to that config again, but I do know that I found a config

This is my analysis:
SAME CONFIG (PARAMETRIC)
State : C
Head run : 1
Template : (('0', None), ('1', 'n'), ('0', 'n'), ('1', 'n'), ('0', 1), ('1', 1), ('0', None))
Old params: (2, 2, 5) at step 48
New params: (2, 8, 4) at step 99
Interval : 51 steps

SAME CONFIG (PARAMETRIC)
State : F
Head run : 1
Template : (('0', None), ('1', 1), ('0', 'n'), ('1', 'n'), ('0', 1), ('1', 1), ('0', None))
Old params: (3, 5) at step 49
New params: (9, 4) at step 100
Interval : 51 steps

As you can see that
Step 48: $ 1^2 0^2 1^5 0 1 $
Step 49: $ 1 0^3 1^5 0 1 $
Let me this easier:
Step 48: $ 11 00 11111 0 1 $
Step 49: $ 10 00 11111 0 1 $
The differ is 1 and 0 and 2nd position
We can infer:
f(x, y, z) := $ 1^x 0^y 1^z 0 1 $
Then f(x, y, z) after 1 steps will be f(x-1, y+1, z)
Checking again:
Step 99: f(2, 8, 4)
Step 100: f(1, 9, 4)