{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.octal-game","code":"thing-q3177938","url":"https://ver.cy/models/thing/q3177938/","name":"octal game","alternateNames":[],"kind":"thing","status":"published","version":"0.2.0-wave.3","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.REL"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A class of impartial combinatorial games played with heaps of counters in which a move removes some counters from a heap and may split the remainder into at most two heaps, with the allowed moves encoded by a sequence of octal digits; Nim, Kayles and Dawson Kayles are octal games, and their outcomes are analysed with Sprague-Grundy values.","purpose":"Let an agent explain octal games and their code notation, analyse a given octal game with Sprague-Grundy theory, relay known periodicity results with attribution, and separate octal games from other take-and-break games.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Impartial heap game","Moves encoded in octal","Analysed by Sprague-Grundy values","Many have periodic Grundy sequences"],"structure":{"bundles":[{"id":"rules","name":"Rules","description":"Codes and rules.","layers":[{"id":"code","name":"Code","description":"Octal code.","findings":[{"id":"code-finding","name":"Code","description":"Code.","questions":[{"text":"How does an octal code encode which moves are allowed?","kind":"definition"},{"text":"Is the game an octal game or another take-and-break game?","kind":"boundary"}]}]},{"id":"examples","name":"Examples","description":"Classic games.","findings":[{"id":"examples-finding","name":"Examples","description":"Examples.","questions":[{"text":"Which classic games are octal games, and what are their codes?","kind":"provenance"},{"text":"Which entry fits Nim?","kind":"action"}]}]}]},{"id":"analyse","name":"Analyse","description":"Grundy values.","layers":[{"id":"grundy","name":"Grundy","description":"Sprague-Grundy analysis.","findings":[{"id":"grundy-finding","name":"Grundy","description":"Grundy.","questions":[{"text":"How are Grundy values computed for an octal game, and how do they decide the winner?","kind":"action"},{"text":"Which entry fits the Sprague-Grundy theorem?","kind":"action"}]}]},{"id":"periodicity","name":"Periodicity","description":"Periodicity.","findings":[{"id":"periodicity-finding","name":"Periodicity","description":"Periodicity.","questions":[{"text":"Which octal games have proven periodic Grundy sequences, and which remain open?","kind":"provenance"},{"text":"What is proven versus conjectured?","kind":"boundary"}]}]}]},{"id":"compute","name":"Compute","description":"Computation.","layers":[{"id":"algorithms","name":"Algorithms","description":"Algorithms.","findings":[{"id":"algorithms-finding","name":"Algorithms","description":"Algorithms.","questions":[{"text":"How are Grundy sequences computed efficiently, and what do the periodicity theorems allow?","kind":"action"},{"text":"What are the computational limits?","kind":"measurement"}]}]},{"id":"misere","name":"Misere","description":"Misere play.","findings":[{"id":"misere-finding","name":"Misere","description":"Misere.","questions":[{"text":"How does misere play change the analysis?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"context","name":"Context","description":"History and teaching.","layers":[{"id":"history","name":"History","description":"Origins.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Guy and Smith introduce the octal notation, and how did Winning Ways develop it?","kind":"provenance"},{"text":"Which entry fits combinatorial game theory?","kind":"action"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How are octal games used to teach game theory?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain octal games, their codes and how their Grundy values are computed.","Play, analyse or teach octal games."],"mustNot":["Claim the periodicity of an octal game is proven when only computed to some heap size.","Misread an octal code and analyse the wrong game.","Attribute results to researchers who did not obtain them."],"requiresHuman":["Correcting published tables of values."]},"ethics":{"considerations":["Many results rest on long computations whose limits should be stated.","Accurate attribution matters in research."],"affectedParties":["Students","Researchers"]},"owners":{"steward":"Nobody owns the concept; it belongs to mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q11371326","type":"parent","note":"registry parent class"},{"target":"impartial game","type":"related","note":"the game class"},{"target":"Kayles","type":"related","note":"a classic example"},{"target":"Sprague-Grundy theorem","type":"related","note":"the theory"},{"target":"subtraction game","type":"related","note":"a simpler class without splitting"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.octal-game","Wikidata: Q3177938 (https://www.wikidata.org/wiki/Q3177938)"]},"properties":{"applicability":"not-applicable","items":["Kayles code: 0.77 octal code","Dawson Kayles code: 0.07 octal code"]},"recognition":{"applicability":"optional","items":["Rules encoded by octal digits per number of counters removed","Impartial, normal play","Partizan games and games with other splitting rules are outside the class","Not visible; heaps of counters and a code such as 0.77."]},"capabilities":{"applicability":"required","items":["decode an octal code into rules","compute Grundy values for heap sizes","relay known periodicity results","identify classic games by their codes"]},"hazards":{"applicability":"required","items":["Misreading the octal code","Assuming periodicity that is not proven","Confusing normal and misere play"]},"interfaces":{"applicability":"required","items":["No regulation; conventions follow Winning Ways and the research literature"]},"context":{"applicability":"required","items":["Not for anything; a family of games studied in combinatorial game theory.","Nim as an octal game","Kayles and Dawson Kayles","games with finite codes","games with infinite codes","hexadecimal and other generalisations"]}},"sources":[{"title":"Wikidata item Q3177938: octal game","url":"https://www.wikidata.org/wiki/Q3177938","note":"identity and sense of the item"},{"title":"Wikipedia: Octal game","url":"https://en.wikipedia.org/wiki/Octal_game","note":"general description of the item"}],"openQuestions":["Should Kayles and Nim be separate entries?","How should Grundy value tables be linked?","Which games with unproven periodicity, such as Grundy game, should be recorded?"],"resources":{"spec":"/models/things/publications/thing-q3177938/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q3177938/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T20:13:51Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:58+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}