{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.poset-game","code":"thing-q7233029","url":"https://ver.cy/models/thing/q7233029/","name":"poset 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 two-player impartial game played on a partially ordered set in which players alternately choose an element and remove it together with every element greater than it, the player unable to move losing under normal play; poset games include Nim, Chomp and Hackendot, and deciding the winner is hard in general although special cases are solved.","purpose":"Let an agent explain poset games and their rules, identify classic examples, relay known results on winning strategies and complexity with attribution, and separate poset games from other combinatorial games.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Played on a partial order","Upward removal rule","Impartial and finite","Includes Nim and Chomp"],"structure":{"bundles":[{"id":"rules","name":"Rules","description":"How poset games work.","layers":[{"id":"play","name":"Play","description":"Rules.","findings":[{"id":"play-finding","name":"Play","description":"Play.","questions":[{"text":"What are the rules of a poset game, and who wins?","kind":"definition"},{"text":"Is the game a poset game or another impartial game?","kind":"boundary"}]}]},{"id":"examples","name":"Examples","description":"Classic examples.","findings":[{"id":"examples-finding","name":"Examples","description":"Examples.","questions":[{"text":"How are Nim, Chomp and Hackendot poset games?","kind":"definition"},{"text":"Which entry fits Chomp?","kind":"action"}]}]}]},{"id":"results","name":"Results","description":"Known results.","layers":[{"id":"strategy","name":"Strategy","description":"Strategy stealing.","findings":[{"id":"strategy-finding","name":"Strategy","description":"Strategy.","questions":[{"text":"Why does the first player win on posets with a greatest element, and what does strategy stealing show?","kind":"provenance"},{"text":"What is proven versus constructive?","kind":"boundary"}]}]},{"id":"solved","name":"Solved","description":"Solved cases.","findings":[{"id":"solved-finding","name":"Solved","description":"Solved.","questions":[{"text":"Which poset games are fully solved, and how?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"complexity","name":"Complexity","description":"Computational complexity.","layers":[{"id":"hardness","name":"Hardness","description":"Hardness results.","findings":[{"id":"hardness-finding","name":"Hardness","description":"Hardness.","questions":[{"text":"What is known about the complexity of deciding poset games?","kind":"provenance"},{"text":"Which entry fits computational complexity?","kind":"action"}]}]},{"id":"algorithms","name":"Algorithms","description":"Computing outcomes.","findings":[{"id":"algorithms-finding","name":"Algorithms","description":"Algorithms.","questions":[{"text":"How are outcomes computed for small posets?","kind":"action"},{"text":"What are the limits?","kind":"measurement"}]}]}]},{"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 poset games develop from Nim and Chomp to the general theory?","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 poset games used in teaching?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain the rules of poset games and examples such as Chomp and Nim.","Compute winning positions for small games and show the reasoning."],"mustNot":["Claim an explicit winning strategy where only its existence is proven.","Confuse normal play with misere play.","Overstate what is known about the complexity of general poset games.","Present a computed result for small cases as a general theorem."],"requiresHuman":["Publishing a claimed new result as proven."]},"ethics":{"considerations":["Honest statements about what is proven protect students and the research record."],"affectedParties":["Students of combinatorics","Researchers"]},"owners":{"steward":"Nobody owns the concept; it belongs to the shared body of mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q11371326","type":"parent","note":"registry parent class"},{"target":"finite two-player zero-sum game","type":"related","note":"game classification"},{"target":"Chomp","type":"related","note":"a classic example"},{"target":"Nim","type":"related","note":"a special case"},{"target":"combinatorial game theory","type":"related","note":"the field"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.poset-game","Wikidata: Q7233029 (https://www.wikidata.org/wiki/Q7233029)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Remove an element and everything above it","Normal play convention","Games with other removal rules are outside the family","Not visible; a game on a diagram of an ordered set."]},"capabilities":{"applicability":"required","items":["explain the rules and examples","relay known results and strategy-stealing arguments","relay complexity results","distinguish from other game families"]},"hazards":{"applicability":"required","items":["Assuming a known strategy where only existence is proven","Confusing misere and normal play","Overstating solved cases"]},"interfaces":{"applicability":"required","items":["No regulation; definitions follow the research literature"]},"context":{"applicability":"required","items":["Not for anything; a family of games studied in combinatorial game theory.","Nim as a poset game on disjoint chains","Chomp on a grid","Hackendot on trees","divisor games and subset games","poset games on general orders"]}},"sources":[{"title":"Wikidata item Q7233029: poset game","url":"https://www.wikidata.org/wiki/Q7233029","note":"identity and sense of the item"},{"title":"Wikipedia: Poset game","url":"https://en.wikipedia.org/wiki/Poset_game","note":"general description of the item"}],"openQuestions":["Should Chomp and Nim be separate entries?","How should complexity results be linked?","Which open problems, such as explicit Chomp strategies, should be recorded?"],"resources":{"spec":"/models/things/publications/thing-q7233029/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q7233029/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T20:49:57Z","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 2026-10-06T19:52:01+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}}