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A program is strictly repetitive if, within 20000 steps, it halts, repeats a state, or shows a verified non-negative drift of period at most 2000. Lengths 1..4: 0 non-repetitive out of 10552. Length 5 non-repetitive programs: [['i[1]', 'd[2, 1]', 'i[2]', 'd[1, 3]', 'd[2, 1]'], ['i[2]', 'd[1, 1]', 'i[1]', 'd[2, 3]', 'd[1, 1]']]." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "Measured: 2 length-5 programs that are not strictly repetitive, out of 248832 (n = 248832, exact on the stated instruction set, within 20000 steps and drift period <= 2000). Interpretation: The page 99 sentence tested here is the finite census: among 10,552 programs of at most four instructions, none is more complicated than repetitive, and exactly two of the 248,832 five-instruction programs are not strictly repetitive (they differ by swapping the two registers, and the picture is nested). 'Strictly repetitive' is halt, an exact state cycle, or a proved linear drift of period at most 2000. Nesting is compressibility of the instruction stream in the absence of such a cycle. This does not test the claim's eight-instruction count, and it does not concern organisms." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch03-15: supports, confidence 0.9" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch03-15/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 complete finite instruction set stated in NKS note (a), page 896: two registers, i[r] and d[r, m], initial state {1,{0,0}}. No sampling and no other instruction set." } ], "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": "Any short program fails the repetitive test, or the length-5 non-repetitive count is not 2." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "A machine whose only repetitive drift has period above 2000, or whose transient exceeds 20000 steps, would be called non-repetitive. The notes' maximum halting time for length 5 is far below this bound; a long non-halting transient remains a caveat." }, { "@value": "Nesting is lzma compressibility of the program-counter sequence below 0.15, not a proof that the machine implements a substitution system. The run says nothing about organisms." }, { "@value": "The census is exhaustive for lengths 1..5 on the instruction set in the note. It does not enumerate lengths 6..8, and it does not check the stated count of 126 complex eight-instruction programs." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "Zero of 10,552 programs of length at most 4 fail the locked repetitive test, and exactly two of 248,832 length-5 programs fail it; both compress below the nesting threshold and are register swaps, including the program in the p. 896 note." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. Refutes if any length-1..4 program is not strictly repetitive, or if the number of non-repetitive length-5 programs is not 2. Mixed if that number is 2 but the two programs are not both nested, are not register-swaps, or do not include the note's program. The 11,019,960,576 eight-instruction programs and the lengths 6 and 7 are not enumerated." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.9", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-15--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "Under the two-register instruction set stated in NKS pp. 97-99 and note (a) on p. 896, every program of length 1..4 is strictly repetitive, and exactly two programs of length 5 are not; those two are nested, are register-swaps of each other, and one of them is the program printed in that note." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "Exhaustive enumeration. Classify each program by halt, exact cycle, or verified non-negative drift with p <= 2000 inside 20,000 steps. Classify the remainder by lzma ratio of the program-counter sequence against 0.15." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered. Instruction set, from the note: a program of length n is a list of n instructions, each either i[r] or d[r, m] with r in {1, 2} and m in {1, ..., n}. There are (2*(1+n))^n such programs. Semantics, from RMExecute in the note, initial state {1, {0, 0}}: i[r] adds one to register r and advances; d[r, m] jumps to m and subtracts one if register r is positive, otherwise advances without jumping; a program counter past n halts. Lengths 1..4 (10,552 programs) and length 5 (248,832 programs) are enumerated completely. A run is strictly repetitive within 20,000 steps if it halts, repeats an exact state (program counter, r1, r2), or exhibits a verified drift cycle of period p <= 2000: two visits to the same program counter separated by p steps, with non-negative register changes (c1, c2), such that every decrement in that window tested a register whose value v satisfies (v == 0 and c_r == 0) or (v > 0). A non-repetitive run is nested if the lzma-9 size of its 20,000 program-counter bytes is < 0.15 * 20000. 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