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'Localized structures' are persistent short runs of 1-bits in the binary picture, aligned at the least significant bit. 'No simple repetitive form' is the absence of a short period in the sequence of run lengths, not in the integers themselves (those strictly increase). The doubling map is the repetitive control: a single moving 1." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch04-07: supports, confidence 0.7" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-07/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "The orbit is generated by the locked reverse-and-add rule from 512 for 1000 steps. No external trajectory is loaded. This is not evidence about organisms." } ], "https://w3id.org/delphi/ontology/assessmentType": [ { "@value": "claim-test/0.1.0" } ], "https://w3id.org/delphi/ontology/dataKind": [ { "@value": "computational" } ], "https://w3id.org/delphi/ontology/disconfirmingObservation": [ { "@value": "Fewer than three persistent runs and a short-period signature, with the doubling control correctly flagged as repetitive." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "A match shows only that this computation behaves as claimed. It says nothing about organisms." }, { "@value": "Finite check: 1000 steps, final bit length 627, under the cap of 20000. A later period longer than 24 is not ruled out. The best short-period agreement on the last 400 signatures was 0.0." }, { "@value": "Runs longer than 32 bits are ignored by the tracker, and a structure that jumps more than 8 bits in one step is dropped." }, { "@value": "The count 408 is the number of greedy chains under an 8-bit pad, and the longest chain is 80 steps (18 chains last at least 50; none last 100). One visual structure can be split or re-linked, so 408 is not a particle census. The pre-registered bar was at least 3." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "At least three tracked runs last >= 20 steps, no period 1..24 reaches agreement 0.85 on the last 400 signatures, and the doubling control does reach that agreement." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. If the run finishes and the doubling control is repetitive, fewer than 3 persistent structures together with a simply repetitive signature refutes the claim on this bound. One of those two features without the other is mixed. Hitting the bit cap, finishing fewer than 1000 steps, or a control that is not flagged repetitive makes the verdict inconclusive. The check does not say the pattern never repeats at a longer period, and it says nothing about organisms." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.7", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-07--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "Base-2 reverse-and-add started at 512, run for 1000 steps, produces at least three localized structures and its run-length signature is not simply periodic, while the same tracker calls the doubling map repetitive." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "Greedy nearest-start tracking of runs of length 1..32 with an 8-bit pad, plus the maximum period-agreement of run-length signatures. Thresholds are the constants in analysis.py." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered. Rule: n -> n + int(bin(n)[2:][::-1], 2), dropping what would be leading zeros, start 512, 1000 iterations, stop if the bit length exceeds 20000. A localized run is a contiguous block of 1-bits of length 1..32, positions measured from the least significant bit. A run continues a chain if its interval lies within 8 bits of the previous run; chains are matched greedily by closest start. A structure is persistent if its chain lasts at least 20 steps. The pattern is simply repetitive if, on the last 400 run-length signatures, some period p in 1..24 agrees on at least 0.85 of the comparable steps. Supports if at least 3 persistent structures are found, the reverse-and-add signature is not simply repetitive, the run finishes all 1000 steps under the bit cap, and the control n -> 2n from 512 for 400 steps is simply repetitive. A moving-bit self-check (one chain of length 30) must pass or the script aborts." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-07--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "the orbit whose runs are tracked; the picture on the cited page is the same rule and start" } ], "http://purl.org/dc/terms/license": [ { "@value": "generated data" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Base-2 reverse-and-add orbit from 512" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://www.wolframscience.com/nks/p126--elementary-arithmetic/" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch04-07", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-07--claim-test" } ] } ] }, { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/Head", "@graph": [ { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.922Z", "@type": "http://www.w3.org/2001/XMLSchema#dateTime" } ], "http://purl.org/dc/terms/creator": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "http://purl.org/dc/terms/license": [ { "@id": "https://creativecommons.org/licenses/by/4.0/" } ], "http://purl.org/nanopub/x/hasNanopubType": [ { "@id": "https://w3id.org/delphi/ontology/Assessment" } ], "http://purl.org/nanopub/x/introduces": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-07--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch04-07: supports, confidence 0.7" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/sig", "http://purl.org/nanopub/x/hasAlgorithm": [ { "@value": "RSA" } ], "http://purl.org/nanopub/x/hasPublicKey": [ { "@value": "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } ], "http://purl.org/nanopub/x/hasSignature": [ { "@value": "QxYOLLXVdXo4CMWtIA18fwrRH7zCG1ciEYgY6jop/kRPmX0t/C4+Mhzk2soedFpiY+1wwYd+OYmPc2rC1RAFBht25YTuIMNVb4+vF0K5tYefBsn45EZDTftEYHeX6PNxJ5ntSEXjRzpyidh/GSG98fetKr3bny8EH8pwUlEPDCF3f/OAcqVvFNxT3w6h3YbFOyCohusid7HT49k3/SOzGobPANFlEGYAHAXsTKjUUYM76puJcGG6OCTX4Y5JeDusszrJsqk7tPNnRN5deWzcbIqO2mDe42sEsQvuDowBDpPIRCHxkKQgKpMUNasl6PErA2PygZF0YP8UoAx95sGuUQ==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] }, { "@id": "https://w3id.org/np/RAjiEqmoHsEln4az9dNosKmM4iuXl2hEdbLAzapoyFdl4/provenance", "@graph": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7", "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "delphisci claim tester (Grok 4.7; 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