https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8/Head https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8 http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8/assertion https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8 http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8/provenance https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8 http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8/pubinfo https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test http://purl.org/dc/terms/description analysis.py writes the random initial tapes, compiles tm22.c with gcc and runs it over all 4096 machines x 3176 initial conditions (13,008,896 runs, 10000-step limit). Each run is classified exactly as (A) eventually periodic modulo translation (the head-relative configuration recurs) or (B) escaping, with two exact escape tests: B1 as pre-registered (head beyond all non-zero cells moving outward with a repeated state) and B2 (two successive new-extreme head positions with identical state and identical non-zero tape, the head farther from the tape than the time between them, so the motion repeats verbatim on blank tape). Runs that are neither are put through three post-hoc heuristic classes added after the first full run showed 16% of runs growing their tape: (C) regular linear growth, where the last 16 events at which the head reaches a new extreme position (sampled with stride 1-3) have constant second time differences, constant state and tape contents S_{n+1} = P + S_n[:o] + B + S_n[o:] + Q with fixed P, B, Q, o; (D) the same with event gaps obeying g_{n+1} = a g_n + b, a >= 2 (binary-counter growth); (E) a counter certificate for runs whose tape never grows: at >= 8 returns of the head to one end of its range, in a fixed state, the tape read as a binary number changes by the same non-zero amount. C/D stop the run early once 16 events fit; as a check the program is also run without early stopping (full 10000 steps) on machines 256-319 and 2048-2111 and the class counts compared. Symmetry-distinct machines are counted under state relabelling, colour swap and reflection. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--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-ch11-28--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0.83358595533395 fraction of the 13,008,896 (machine, initial condition) runs classified exactly as eventually periodic (A) or escaping (B) within 10000 steps (pre-registered threshold 1.0) (n = 13008896, exact for A and B; C, D and E are heuristic pattern fits (see caveats)). Interpretation: 'Too simple to support universality' is operationalized as: every tested evolution is provably eventually periodic (with or without drift), established by exact recurrence detection rather than by visual inspection. This is necessary-condition evidence: universality requires some input with a non-eventually-periodic evolution, and the tested inputs cover all short tapes exhaustively plus random longer ones, but not all inputs; a proof for all inputs would need a per-machine argument. The convention follows NKS p. 78 and the note 'Turing machine enumeration' (p. 1120): machines never halt, and all 4096 = 8^4 rule tables are counted. The search program is in C (compiled by analysis.py with gcc) for speed; this tooling deviation is recorded. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch11-28: supports, confidence 0.75 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--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-ch11-28/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: tm-2-2-enumeration-generator, nks-note-turing-machine-enumeration https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. The test cannot establish universality, so 'refutes' is not reachable by this computation alone. 'Mixed' if any (machine, initial condition) pair is unclassified after 10000 steps (unbounded non-periodic behaviour within the tested inputs, which would be at least consistent with the complexity universality needs) or if periods above 1000 steps occur. 'Supports' otherwise. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Classes A and B are proofs of the individual run's future; classes C, D and E are pattern fits over a finite window (16 growth events, or 8 counter visits) and could in principle be fooled by behaviour that changes later. The no-early-stop check on 128 machines gives identical class counts, and the classes were designed after inspecting the actual mechanisms (sweepers, binary counters), but they are heuristics. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Implementation deviations from the pre-registration: the exhaustive set has 3076 initial conditions per machine, not 1284 (miscount in the pre-registration; the set itself is as described); the A test is applied for t <= 2000 and spans <= 128 only (for speed; no run escaped A because of this: the max transient to A or B is 3354 for B, and the max period is 24); an additional exact escape test B2 was added because many 'glider' runs carry a bounded pattern away from a fixed tape remnant and are neither periodic modulo translation nor caught by B1. The search is in C (gcc), a tooling deviation from the python/mjs rule, recorded in the pre-registration. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The computation is necessary-condition evidence only: it covers all tapes of length <= 7 and 100 random longer tapes per machine, not all inputs, and finding only repetitive and nested behaviour does not prove non-universality. The known proof is Pavlotskaya (1973), who showed every 2-state 2-colour machine has a decidable halting problem; that result is not checked here. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The pre-registered criterion fails: only 83.36% of runs are eventually periodic (A) or escaping (B); analysis.py reports preregistered_verdict = 'mixed'. The pre-registered hypothesis was too narrow, not the claim: the remaining runs are tapes that grow forever in a regular way (a head sweeping a growing block, 2,142,325 runs in 864 machines) or binary counters (22,536 runs in 11 machines belonging to just 2 symmetry classes, representatives 441 and 462), which Wolfram describes as the most complex 2,2 behaviour (NKS p. 79-80, 'nested'). Under the post-hoc classes C-E every run but 2 of 13,008,896 is accounted for, and both residual runs belong to counter machines (1372, 3654) whose other 3175 runs are classified; the verdict 'supports' rests on these post-hoc classes and is therefore given lower confidence. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The symmetry-reduced count of 560 distinct machines matches Wolfram's note (p. 1120), confirming the enumeration covers the same family. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. For each of the 4096 machines and each initial condition in the set I = {every binary tape string of length 1-7 with the head on each of its cells, in each of the 2 states} (1284 initial conditions per machine) plus 100 random tapes of length 16-32 per machine (seeded), simulate on an infinite blank (0) tape for up to 10000 steps and classify the evolution exactly as (A) eventually periodic modulo translation: the head-relative configuration (state, tape between the outermost non-zero cells, head offset) recurs exactly, which implies periodic evolution forever; or (B) escaping: the head is beyond all non-zero cells, moving outward over blank cells, and the same state occurs twice during that outward run, which implies it moves outward forever. 'Supports' if 100% of the (machine, initial condition) pairs are classified as (A) or (B) within 10000 steps, and the largest period found is at most 1000 steps. The symmetry-reduced count of distinct machines (state relabelling, colour swap, reflection) is also computed and compared with Wolfram's 560 as a consistency check on the enumeration. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. The test cannot establish universality, so 'refutes' is not reachable by this computation alone. 'Mixed' if any (machine, initial condition) pair is unclassified after 10000 steps (unbounded non-periodic behaviour within the tested inputs, which would be at least consistent with the complexity universality needs) or if periods above 1000 steps occur. 'Supports' otherwise. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.75 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/hypothesis Every one of the 4096 Turing machines with 2 states and 2 colours (Wolfram's convention: each (state, colour) maps to (new colour, new state, move left/right); no halt state) has behaviour that from every finite initial condition becomes eventually periodic, possibly with a drifting head (a 'glider'), after a short transient. Since a universal machine must have initial conditions whose evolution is not eventually periodic (otherwise every question about its evolution is decidable), such a classification is strong evidence that none is universal. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py writes the random initial tapes, compiles tm22.c with gcc and runs it over all 4096 machines x 3176 initial conditions (13,008,896 runs, 10000-step limit). Each run is classified exactly as (A) eventually periodic modulo translation (the head-relative configuration recurs) or (B) escaping, with two exact escape tests: B1 as pre-registered (head beyond all non-zero cells moving outward with a repeated state) and B2 (two successive new-extreme head positions with identical state and identical non-zero tape, the head farther from the tape than the time between them, so the motion repeats verbatim on blank tape). Runs that are neither are put through three post-hoc heuristic classes added after the first full run showed 16% of runs growing their tape: (C) regular linear growth, where the last 16 events at which the head reaches a new extreme position (sampled with stride 1-3) have constant second time differences, constant state and tape contents S_{n+1} = P + S_n[:o] + B + S_n[o:] + Q with fixed P, B, Q, o; (D) the same with event gaps obeying g_{n+1} = a g_n + b, a >= 2 (binary-counter growth); (E) a counter certificate for runs whose tape never grows: at >= 8 returns of the head to one end of its range, in a fixed state, the tape read as a binary number changes by the same non-zero amount. C/D stop the run early once 16 events fit; as a check the program is also run without early stopping (full 10000 steps) on machines 256-319 and 2048-2111 and the class counts compared. Symmetry-distinct machines are counted under state relabelling, colour swap and reflection. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. For each of the 4096 machines and each initial condition in the set I = {every binary tape string of length 1-7 with the head on each of its cells, in each of the 2 states} (1284 initial conditions per machine) plus 100 random tapes of length 16-32 per machine (seeded), simulate on an infinite blank (0) tape for up to 10000 steps and classify the evolution exactly as (A) eventually periodic modulo translation: the head-relative configuration (state, tape between the outermost non-zero cells, head offset) recurs exactly, which implies periodic evolution forever; or (B) escaping: the head is beyond all non-zero cells, moving outward over blank cells, and the same state occurs twice during that outward run, which implies it moves outward forever. 'Supports' if 100% of the (machine, initial condition) pairs are classified as (A) or (B) within 10000 steps, and the largest period found is at most 1000 steps. The symmetry-reduced count of distinct machines (state relabelling, colour swap, reflection) is also computed and compared with Wolfram's 560 as a consistency check on the enumeration. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch11-28 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-1 http://purl.org/dc/terms/description the enumerated program family https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-1 http://purl.org/dc/terms/license CC0 (generated data) https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--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-ch11-28--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: All 2-state 2-colour Turing machines (generated by analysis.py + tm22.c) https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2 http://purl.org/dc/terms/description the count 560 of symmetry-distinct machines used as a consistency check https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2 http://purl.org/dc/terms/license copyright Stephen Wolfram LLC https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--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-ch11-28--claim-test--dataset-2 http://www.w3.org/2000/01/rdf-schema#label Dataset: NKS note 'Turing machine enumeration' (p. 1120) https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2 http://www.w3.org/ns/prov#atLocation https://www.wolframscience.com/nks/notes-11-12--turing-machine-enumeration/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2 http://www.w3.org/ns/prov#wasDerivedFrom https://www.wolframscience.com/nks/notes-11-12--turing-machine-enumeration/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2 https://w3id.org/delphi/ontology/hasChecksum sha256:5f25641e45831bb01cdff9c5f595813e5ca4c8b0f7a734e091cb1b34b70bed66 https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent 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-cursor-cloud-agent http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (Claude Fable 5.1 (Cursor cloud agent); 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