https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
@prefix this: <https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA> .
@prefix sub: <https://w3id.org/np/RAHoH2699Qk2gXT9TKw-nttCfxqgM5R4o5QEy6ZchQ2kA/> .
@prefix np: <http://www.nanopub.org/nschema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix prov: <http://www.w3.org/ns/prov#> .
@prefix npx: <http://purl.org/nanopub/x/> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
sub:Head {
this: a np:Nanopublication;
np:hasAssertion sub:assertion;
np:hasProvenance sub:provenance;
np:hasPublicationInfo sub:pubinfo .
}
sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc: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.";
<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.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch04-14: supports, confidence 0.97";
<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>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
<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/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<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/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.",
"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.",
"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/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/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/ontology/hasConfidence> "0.97"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-2>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-4>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<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/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/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/ontology/preregistered> "false"^^xsd:boolean .
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<https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-14--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "direction rational => eventually periodic with period <= q - 1";
dc:license "";
<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>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "independent tabulation of decimal periods for cross-checking";
dc:license "CC BY-SA 4.0 (OEIS)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: OEIS A007732: period of decimal representation of 1/n, b-file";
prov:atLocation <https://oeis.org/A007732/b007732.txt>;
prov:wasDerivedFrom <https://oeis.org/A007732>;
<https://w3id.org/delphi/ontology/hasChecksum> "sha256:eb0e8d499b46a8c12bdb8d9f747ca6d09f322a2de1ddd26971b95d4c89dca730" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-3>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "direction eventually periodic => rational (constructive)";
dc:license "";
<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>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "irrational sanity check";
dc:license "CC BY-SA 4.0 (OEIS)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: OEIS A002193: decimal expansion of sqrt(2), b-file";
prov:atLocation <https://oeis.org/A002193/b002193.txt>;
prov:wasDerivedFrom <https://oeis.org/A002193>;
<https://w3id.org/delphi/ontology/hasChecksum> "sha256:ca6c74f68ed066a0d703ce5bf2eb0f721fa07a7d233596ec9f86355d22a796e8" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-5>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "irrational sanity check";
dc:license "CC BY-SA 4.0 (OEIS)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: OEIS A001113: decimal expansion of e, b-file";
prov:atLocation <https://oeis.org/A001113/b001113.txt>;
prov:wasDerivedFrom <https://oeis.org/A001113>;
<https://w3id.org/delphi/ontology/hasChecksum> "sha256:9eef3a3fe766065b330d8f1f398efc62f19cd3af299af8ca252ef98818a3dc9d" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-14--claim-test--dataset-6>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "irrational sanity check";
dc:license "CC BY-SA 4.0 (OEIS)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: OEIS A000796: decimal expansion of pi, b-file";
prov:atLocation <https://oeis.org/A000796/b000796.txt>;
prov:wasDerivedFrom <https://oeis.org/A000796>;
<https://w3id.org/delphi/ontology/hasChecksum> "sha256:f8772370d624d403f056e3e3d4aadb15fec135d5075b5506053eb86460f4e20b" .
}
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prov:SoftwareAgent;
<http://www.w3.org/2000/01/rdf-schema#label> "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-0123)";
prov:actedOnBehalfOf <https://orcid.org/0009-0007-4948-9192>;
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<https://w3id.org/delphi/resource/model/claude-fable-5-1> a <https://w3id.org/delphi/ontology/LanguageModel>;
dc:identifier "claude-fable-5.1" .
sub:assertion prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
prov:wasDerivedFrom <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-14/result.json>;
prov:wasGeneratedBy sub:test .
sub:plan prov:hadPlan <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md> .
sub:test a prov:Activity;
prov:qualifiedAssociation sub:plan;
prov:wasAssociatedWith <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1> .
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this: dc:created "2026-11-08T16:24:31.923Z"^^xsd:dateTime;
dc:creator <https://orcid.org/0009-0007-4948-9192>;
dc:license <https://creativecommons.org/licenses/by/4.0/>;
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npx:introduces <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/ontology/domain> <https://w3id.org/delphi/resource/domain/wolfram-nks-2002> .
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