{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.mathematical-proof","code":"thing-q11538","url":"https://ver.cy/models/thing/q11538/","name":"mathematical proof","alternateNames":["computer-assisted proof","strategy-stealing argument","proof by contrapositive","Proofs of Fermat's theorem on sums of two squares","indirect proof","proof of the pythagorean theorem","exponent combination laws","well-founded induction","non-constructive proof","proof by contradiction","non-surveyable proof","termination proof"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Information and virtual systems","entryKind":"thing","plane":"INF","domain":["INF.KNW"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A rigorous argument that establishes the truth of a mathematical statement from axioms, definitions and previously proved results by valid inference, in forms such as direct proof, proof by contradiction, proof by contrapositive, induction, construction, exhaustion, strategy-stealing arguments and computer-assisted proofs; proofs are the standard of certainty in mathematics, are written for human readers or checked by proof assistants, and famous examples include proofs of the Pythagorean theorem and of Fermat theorem on sums of two squares.","purpose":"Let an agent explain what a mathematical proof is and the main proof techniques, help construct, check and explain proofs, describe formal and computer-assisted proof, and support learning proof writing.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Deductive rigour","Techniques","Formalisable","Peer review"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What proofs are.","layers":[{"id":"concept","name":"Concept","description":"Concept and standards.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What makes an argument a mathematical proof, and how do axioms, definitions and inference rules function in it?","kind":"definition"},{"text":"Which entry fits logic?","kind":"action"}]}]},{"id":"techniques","name":"Techniques","description":"Techniques.","findings":[{"id":"techniques-finding","name":"Techniques","description":"Techniques.","questions":[{"text":"How do direct proof, contradiction, contrapositive, induction and construction work, and when is each used?","kind":"definition"},{"text":"Which entry fits a specific technique?","kind":"action"}]}]}]},{"id":"write","name":"Write","description":"Constructing and checking.","layers":[{"id":"construct","name":"Construct","description":"Constructing a proof.","findings":[{"id":"construct-finding","name":"Construct","description":"Constructing.","questions":[{"text":"How can this statement be proved, and which technique fits?","kind":"action"},{"text":"Is the statement precisely stated?","kind":"boundary"}]}]},{"id":"check","name":"Check","description":"Checking a proof.","findings":[{"id":"check-finding","name":"Check","description":"Checking.","questions":[{"text":"Is this proof valid, and where are its gaps or errors?","kind":"action"},{"text":"Which entry fits common proof errors?","kind":"action"}]}]}]},{"id":"formal","name":"Formal","description":"Formal and computer proof.","layers":[{"id":"assistants","name":"Assistants","description":"Proof assistants.","findings":[{"id":"assistants-finding","name":"Assistants","description":"Assistants.","questions":[{"text":"How do proof assistants and formal verification work, and which proofs have been formalised?","kind":"provenance"},{"text":"Which entry fits a specific proof assistant?","kind":"action"}]}]},{"id":"computer","name":"Computer","description":"Computer-assisted proofs.","findings":[{"id":"computer-finding","name":"Computer","description":"Computer.","questions":[{"text":"What are computer-assisted proofs, and what debates surround their acceptance, with positions attributed?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"learn","name":"Learn","description":"History and teaching.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the concept of proof develop from Euclid to modern foundations, and which proofs are famous?","kind":"provenance"},{"text":"Which entry fits a famous proof?","kind":"action"}]}]},{"id":"teach","name":"Teach","description":"Teaching proof.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can proof writing be taught to beginners?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Check the steps of a proof and point out gaps, circular reasoning or unproved assumptions.","Explain common proof techniques such as induction or contradiction with examples.","Help formalise a proof in a proof assistant when the user asks."],"mustNot":["Present a set of examples or a numerical check as a proof.","Claim a proof is correct when it has not been checked step by step.","Attribute a proof or theorem to a mathematician without evidence.","Submit proofs on a student's behalf in assessments where that is not allowed."],"requiresHuman":["Declaring a disputed proof of an open problem correct in a publication or award."]},"ethics":{"considerations":["Credit for proofs shapes careers; misattribution wrongs mathematicians.","Errors in proofs that others rely on, such as in safety or cryptography, can spread widely."],"affectedParties":["Mathematicians and students","Users of results built on the proof","Teachers and examiners"]},"owners":{"steward":"Nobody owns a proof's truth; authors answer for their published proofs and journals for review.","roles":[],"masterSystems":[]},"relations":[{"target":"Q122766417","type":"parent","note":"registry parent class"},{"target":"Q186619","type":"parent","note":"registry parent class"},{"target":"argument","type":"related","note":"category"},{"target":"mathematical reasoning","type":"related","note":"category"},{"target":"inequality","type":"related","note":"statements often proved"},{"target":"imaginary","type":"related","note":"objects proofs concern"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.mathematical-proof","Wikidata: Q11538 (https://www.wikidata.org/wiki/Q11538)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Deductive argument from axioms","Establishes a theorem","Evidence and heuristics are not proofs; a conjecture is unproved","Not physical; written arguments."]},"capabilities":{"applicability":"required","items":["explain proof and techniques","construct and check proofs","describe formal proof","support learning"]},"hazards":{"applicability":"required","items":["Circular reasoning and gaps","Confusing examples with proofs","Errors in long proofs"]},"interfaces":{"applicability":"required","items":["Conventions of mathematical writing","Peer review in journals","Proof assistant standards"]},"context":{"applicability":"required","items":["Rigorous arguments establishing mathematical truths.","direct proofs","proofs by contradiction and contrapositive","proofs by induction","constructive and existence proofs","computer-assisted and formal proofs"]}},"sources":[{"title":"Wikidata item Q11538: mathematical proof","url":"https://www.wikidata.org/wiki/Q11538","note":"identity and sense of the item"},{"title":"Wikipedia: Mathematical proof","url":"https://en.wikipedia.org/wiki/Mathematical_proof","note":"general description of the item"}],"openQuestions":["Should each technique be a separate entry?","How should proof assistants be linked?","How should famous proofs be linked?"],"resources":{"spec":"/models/things/publications/thing-q11538/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q11538/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T02:23:20Z","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 2026-10-06T19:51:53+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane INF: no invented physical properties."},"score":1.0}}