https://w3id.org/np/RAKykADcmyGU060bhxpza7oIrSvBkoq-tKQ_85ofdL9X8
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc: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.";
<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.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-28: supports, confidence 0.75";
<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>;
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<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: tm-2-2-enumeration-generator, nks-note-turing-machine-enumeration";
<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. 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/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.",
"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.",
"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.",
"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.",
"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/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/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/ontology/hasConfidence> "0.75"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-2>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<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/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/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.";
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<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-28--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-28--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the enumerated program family";
dc:license "CC0 (generated data)";
<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>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the count 560 of symmetry-distinct machines used as a consistency check";
dc:license "copyright Stephen Wolfram LLC";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: NKS note 'Turing machine enumeration' (p. 1120)";
prov:atLocation <https://www.wolframscience.com/nks/notes-11-12--turing-machine-enumeration/>;
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