. . . . "analysis.py computed partial quotients of sqrt(2) (Decimal.sqrt), e (series), pi (Machin) and cbrt(2) (Newton) at 4000 and 8000 decimal digits, kept the agreeing prefix, and classified the first 300 terms. Classes: {'sqrt(2)': 'purely_repetitive', 'e': 'intermediate', 'pi': 'complicated', 'cbrt(2)': 'complicated'}. Purely repetitive means a period p<=40 with preperiod s<=5 covering the rest of the prefix. Otherwise the lzma-9 size of the comma-separated terms is divided by the mean size of 20 shuffles (PCG64 seed 20261102). Thresholds 0.55 and 0.80 are the pre-registered ones." . . "Measured: 3 constants matching the locked class (sqrt(2) purely repetitive, e regular, pi and cbrt(2) complicated) (n = 4, exact on the agreeing 300-term prefix). Interpretation: Wolfram's page 143 statement is that square roots have purely repetitive continued fractions, that e (and its roots) shows definite regularity, and that pi and cube roots look essentially random. 'Purely repetitive' is eventual periodicity of the partial quotients with preperiod at most 5. 'Definite regularity' is order that an LZMA compressor exploits far beyond the multiset of terms. 'Essentially random' is the absence of that order. A finite prefix does not prove that pi or cbrt(2) is non-periodic, and it does not say anything about organisms. Fourth roots and roots of e are outside this locked set." . "Claim test of wolfram2002-ch04-16: mixed, confidence 0.55" . . . "Partial quotients generated in this directory by integer/decimal arithmetic at two precisions, with only the agreeing prefix used. No external table." . "claim-test/0.1.0" . "computational" . "sqrt(2) is not periodic on the prefix, e compresses no better than a complicated sequence, or pi or cbrt(2) is periodic on the prefix." . "A finite prefix cannot prove that pi or cbrt(2) never becomes periodic, and it does not prove a theorem about all cube roots or fourth roots." . "The four arithmetic programs say nothing about organisms." . "sqrt(2) was purely periodic with period 1 after the first term. pi and cbrt(2) had compression ratios 1.021 and 1.003 against shuffles of their own terms. e began 2, 1, 2, 1, 1, 4, 1, 1, 6 and compressed to 0.634 of a shuffle, which is between the locked cutoffs 0.55 and 0.80, so the pre-registered test calls e intermediate rather than regular." . "Among 300 partial quotients, sqrt(2) is eventually periodic with preperiod <= 5 and period <= 40, e is not, but compresses to at most 55% of a shuffle of its own terms, and pi and cbrt(2) compress to at least 80% of a shuffle and are not periodic on this prefix." . "Pre-registered. Refutes if sqrt(2) is not purely repetitive, or e is complicated, or pi or cbrt(2) is purely repetitive. Mixed if sqrt(2) is purely repetitive but e, pi or cbrt(2) falls strictly between the two compression thresholds (ratio in (0.55, 0.80)). Inconclusive with reason underpowered if fewer than 300 partial quotients agree across the two precisions." . "0.55"^^ . . "mixed" . "The first 300 continued-fraction partial quotients of sqrt(2) are purely repetitive, those of e are regular but not purely repetitive, and those of pi and cbrt(2) are neither periodic nor substantially more compressible than a shuffle of the same terms." . "Classify each of the four sequences by the locked periodicity test and, if that fails, by the lzma-to-shuffle ratio with thresholds 0.55 and 0.80. The claim is supported only if all four classifications match the hypothesis." . "Pre-registered. Compute partial quotients of sqrt(2), e, pi and cbrt(2) from Decimal series (sqrt via Decimal.sqrt; e via sum 1/n!; pi via Machin 16*arctan(1/5)-4*arctan(1/239); cbrt(2) via Newton). Keep the longest prefix on which precisions 4000 and 8000 decimal digits agree, and require at least 300 agreeing terms; otherwise the test is inconclusive (underpowered). Regularity statistic, locked before the run: a sequence a[0..n) is purely repetitive if there exist a period p in 1..40 and a start s <= 5 such that n - s >= 250 and a[i] == a[i+p] for every i in s..n-p-1. Otherwise form the comma-separated decimal text of the 300 terms and let compression_ratio be its lzma-9 size divided by the mean lzma-9 size of 20 shuffles of those terms (numpy Generator PCG64 seed 20261102). Regular means compression_ratio <= 0.55. Complicated means compression_ratio >= 0.80. Supports if sqrt(2) is purely repetitive, e is regular, and both pi and cbrt(2) are complicated." . "false"^^ . . "the four continued fractions named in the pre-registration" . "generated" . . "Dataset: 300 agreeing partial quotients of sqrt(2), e, pi and cbrt(2)" . . . "delphisci claim tester (grok-4.7; cursor/wolfram-programs-c-b6e6)" . . . "grok-4.7" . . . . . . . . . "2026-11-08T16:24:31.924Z"^^ . . . . . "Claim test of wolfram2002-ch04-16: mixed, confidence 0.55" . . "RSA" . 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