https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/Head https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/assertion https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/provenance https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/pubinfo https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test http://purl.org/dc/terms/description analysis.py (1) runs long division for 1/q, q = 1..20000, and for all p/q with q <= 300, in bases 2, 3 and 10 (64,850 expansions per base), recording preperiod and period from the first repeated remainder and counting violations of period <= q-1 or preperiod + period <= q; base-10 periods of 1/n are compared with the 10,000-term OEIS A007732 b-file. (2) It draws 20,000 random eventually periodic patterns (base in {2,3,10}, preperiod 0-20 digits, block 1-30 digits, all-(b-1) blocks rejected), reconstructs the exact rational with Python Fractions and re-expands it, counting patterns not reproduced digit for digit. (3) It downloads the first 10,000 decimal digits of sqrt(2), e and pi from OEIS and, for every p <= N/3, finds the smallest index after which the digit sequence agrees with its shift by p, flagging any p for which two full periods already agree. Run time about 9 s including downloads. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0 rational expansions violating period <= q-1 or preperiod + period <= q (out of 194,550) (n = 194550, exact). Interpretation: Wolfram's 'repetitive digit sequences' are eventually periodic positional expansions in an integer base; the clause 'period at most q - 1' in the claim text is the standard long-division bound (there are only q - 1 non-zero remainders). Terminating expansions are treated as eventually periodic with repeating 0, as the assessors note; period blocks consisting only of the digit b - 1 are excluded from the random patterns because they denote the alternative expansion of a terminating rational and would re-expand in the terminating form. The converse ('rationals are the only numbers with repetitive digit sequences') is tested constructively (every eventually periodic pattern reconstructs to a rational that reproduces it) and, as a sanity check only, on the published digits of three irrational constants; a finite digit string can never prove non-periodicity, so part (3) is a consistency check rather than a proof. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch04-14: supports, confidence 0.97 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-14/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: rational-expansions-bases-2-3-10-q-le-20000, oeis-a007732-bfile, random-eventually-periodic-patterns, oeis-a002193-bfile, oeis-a001113-bfile, oeis-a000796-bfile https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered: any rational whose expansion has minimal period > q - 1 or does not become periodic within q digits; any disagreement with A007732; any eventually periodic pattern whose reconstructed rational re-expands differently; or an irrational constant's published digits exhibiting at least two full agreeing periods for some p <= N/3. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/evidenceAgainst A finite digit string cannot establish that a number is not eventually periodic; part (3) only checks that 10,000 published digits of sqrt(2), e and pi show no two agreeing repeats for any period up to N/3 (the maximal agreement found was 1.33 periods, consistent with chance), which is a consistency check, not a proof of the 'only rationals' clause. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Both directions are classical theorems; the computation confirms the forward direction exhaustively for all denominators up to 20,000 in three bases (the bound period = q - 1 is attained, e.g. for full-reptend primes), agrees with OEIS A007732 on all 10,000 tabulated decimal periods, and confirms the converse constructively on 20,000 random eventually periodic patterns. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Terminating expansions are counted as eventually periodic with repeating 0 (period 1), following OEIS A007732; under the alternative convention (repeating b-1) they are still eventually periodic, so the verdict does not depend on this choice. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered: (1) for bases 2, 3 and 10 and all denominators q = 1..20000, the digit expansion of 1/q (and of p/q for all 1 <= p < q when q <= 300) has period <= q - 1 and preperiod + period <= q, with zero violations, and the base-10 periods of 1/q agree with OEIS A007732 for every n covered by its b-file; (2) 100% of 20000 random eventually periodic digit patterns (random preperiod of length 0..20, random non-trivial period block of length 1..30, bases 2, 3, 10) are reproduced exactly when the rational number reconstructed from them is re-expanded by long division; (3) none of the first 10000 decimal digits of sqrt(2), e and pi (OEIS b-files) is eventually periodic in the sense that, for some period p <= N/3, the last 2p digits already repeat with period p. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered: any rational whose expansion has minimal period > q - 1 or does not become periodic within q digits; any disagreement with A007732; any eventually periodic pattern whose reconstructed rational re-expands differently; or an irrational constant's published digits exhibiting at least two full agreeing periods for some p <= N/3. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.97 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/hypothesis In any integer base, every rational p/q has an eventually periodic digit expansion with period at most q - 1 (and preperiod + period at most q), every eventually periodic digit sequence is the expansion of a rational number, and the published digit expansions of irrational constants show no eventual periodicity. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py (1) runs long division for 1/q, q = 1..20000, and for all p/q with q <= 300, in bases 2, 3 and 10 (64,850 expansions per base), recording preperiod and period from the first repeated remainder and counting violations of period <= q-1 or preperiod + period <= q; base-10 periods of 1/n are compared with the 10,000-term OEIS A007732 b-file. (2) It draws 20,000 random eventually periodic patterns (base in {2,3,10}, preperiod 0-20 digits, block 1-30 digits, all-(b-1) blocks rejected), reconstructs the exact rational with Python Fractions and re-expands it, counting patterns not reproduced digit for digit. (3) It downloads the first 10,000 decimal digits of sqrt(2), e and pi from OEIS and, for every p <= N/3, finds the smallest index after which the digit sequence agrees with its shift by p, flagging any p for which two full periods already agree. Run time about 9 s including downloads. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered: (1) for bases 2, 3 and 10 and all denominators q = 1..20000, the digit expansion of 1/q (and of p/q for all 1 <= p < q when q <= 300) has period <= q - 1 and preperiod + period <= q, with zero violations, and the base-10 periods of 1/q agree with OEIS A007732 for every n covered by its b-file; (2) 100% of 20000 random eventually periodic digit patterns (random preperiod of length 0..20, random non-trivial period block of length 1..30, bases 2, 3, 10) are reproduced exactly when the rational number reconstructed from them is re-expanded by long division; (3) none of the first 10000 decimal digits of sqrt(2), e and pi (OEIS b-files) is eventually periodic in the sense that, for some period p <= N/3, the last 2p digits already repeat with period p. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch04-14 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1 http://purl.org/dc/terms/description direction rational => eventually periodic with period <= q - 1 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: Preperiod and period of 1/q (q <= 20000) and p/q (q <= 300) in bases 2, 3, 10 by long division (generated by analysis.py) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 http://purl.org/dc/terms/description independent tabulation of decimal periods for cross-checking https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 http://purl.org/dc/terms/license CC BY-SA 4.0 (OEIS) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 http://www.w3.org/2000/01/rdf-schema#label Dataset: OEIS A007732: period of decimal representation of 1/n, b-file https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 http://www.w3.org/ns/prov#atLocation https://oeis.org/A007732/b007732.txt https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 http://www.w3.org/ns/prov#wasDerivedFrom https://oeis.org/A007732 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2 https://w3id.org/delphi/ontology/hasChecksum sha256:eb0e8d499b46a8c12bdb8d9f747ca6d09f322a2de1ddd26971b95d4c89dca730 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3 http://purl.org/dc/terms/description direction eventually periodic => rational (constructive) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3 http://www.w3.org/2000/01/rdf-schema#label Dataset: 20000 random eventually periodic digit patterns (numpy default_rng seed 20261031; generated by analysis.py) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 http://purl.org/dc/terms/description irrational sanity check https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 http://purl.org/dc/terms/license CC BY-SA 4.0 (OEIS) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 http://www.w3.org/2000/01/rdf-schema#label Dataset: OEIS A002193: decimal expansion of sqrt(2), b-file https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 http://www.w3.org/ns/prov#atLocation https://oeis.org/A002193/b002193.txt https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 http://www.w3.org/ns/prov#wasDerivedFrom https://oeis.org/A002193 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4 https://w3id.org/delphi/ontology/hasChecksum sha256:ca6c74f68ed066a0d703ce5bf2eb0f721fa07a7d233596ec9f86355d22a796e8 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 http://purl.org/dc/terms/description irrational sanity check https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 http://purl.org/dc/terms/license CC BY-SA 4.0 (OEIS) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 http://www.w3.org/2000/01/rdf-schema#label Dataset: OEIS A001113: decimal expansion of e, b-file https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 http://www.w3.org/ns/prov#atLocation https://oeis.org/A001113/b001113.txt https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 http://www.w3.org/ns/prov#wasDerivedFrom https://oeis.org/A001113 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5 https://w3id.org/delphi/ontology/hasChecksum sha256:9eef3a3fe766065b330d8f1f398efc62f19cd3af299af8ca252ef98818a3dc9d https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 http://purl.org/dc/terms/description irrational sanity check https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 http://purl.org/dc/terms/license CC BY-SA 4.0 (OEIS) https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 http://www.w3.org/2000/01/rdf-schema#label Dataset: OEIS A000796: decimal expansion of pi, b-file https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 http://www.w3.org/ns/prov#atLocation https://oeis.org/A000796/b000796.txt https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 http://www.w3.org/ns/prov#wasDerivedFrom https://oeis.org/A000796 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6 https://w3id.org/delphi/ontology/hasChecksum sha256:f8772370d624d403f056e3e3d4aadb15fec135d5075b5506053eb86460f4e20b https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (claude-fable-5.1; 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