{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.root-quantity","code":"thing-root-quantity","url":"https://ver.cy/models/thing/root-quantity/","name":"root","alternateNames":["square root","cube root"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"noun.quantity","plane":"XCT","domain":["XCT.QTY"],"industry":[],"navPath":"","tags":[],"facets":{"substance":"abstract","origin":"conceptual","agency":"inert","mobility":"not-applicable","scale":"not-applicable","affordances":["observable"]}},"whatItIs":"A number that, when multiplied by itself a given number of times, equals a given number, as the square root, which multiplied by itself gives the number, the cube root and higher roots, denoted by the radical sign and expressible as fractional powers, with positive and negative real roots, irrational roots such as the square root of two, and complex roots; roots are fundamental in algebra, geometry and computation and are also the solutions of equations.","purpose":"Let an agent explain roots of numbers and their notation and properties, support computing and simplifying roots, describe irrational and complex roots, and support learning in mathematics.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Inverse of powers","Radical notation","Multiple roots","Irrational values"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a root is.","layers":[{"id":"concept","name":"Concept","description":"Concept and notation.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What are square, cube and nth roots, and how are they written with radicals and fractional exponents?","kind":"definition"},{"text":"Is the numerical or another sense of root meant?","kind":"boundary"}]}]},{"id":"properties","name":"Properties","description":"Properties.","findings":[{"id":"properties-finding","name":"Properties","description":"Properties.","questions":[{"text":"What rules govern roots of products, quotients and powers, and when are there several roots?","kind":"definition"},{"text":"Which entry fits exponents?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Computation.","layers":[{"id":"calculate","name":"Calculate","description":"Calculating roots.","findings":[{"id":"calculate-finding","name":"Calculate","description":"Calculation.","questions":[{"text":"How can this root be calculated by hand, by algorithm or with a calculator, and how accurately?","kind":"action"},{"text":"Which entry fits numerical methods?","kind":"action"}]}]},{"id":"simplify","name":"Simplify","description":"Simplifying radicals.","findings":[{"id":"simplify-finding","name":"Simplify","description":"Simplification.","questions":[{"text":"How can this radical expression be simplified or rationalised?","kind":"action"},{"text":"Which entry fits algebraic manipulation?","kind":"action"}]}]}]},{"id":"theory","name":"Theory","description":"Irrational and complex roots.","layers":[{"id":"irrational","name":"Irrational","description":"Irrational roots.","findings":[{"id":"irrational-finding","name":"Irrational","description":"Irrational.","questions":[{"text":"Why are most roots irrational, and how is this proved?","kind":"provenance"},{"text":"Which entry fits irrational numbers?","kind":"action"}]}]},{"id":"complex","name":"Complex","description":"Complex roots.","findings":[{"id":"complex-finding","name":"Complex","description":"Complex.","questions":[{"text":"What are complex roots and roots of unity?","kind":"provenance"},{"text":"Which entry fits complex numbers?","kind":"action"}]}]}]},{"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 were roots computed historically, from Babylonian methods to modern algorithms?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can roots be taught?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain square, cube and higher roots and their notation.","Compute and simplify roots, stating whether negative or complex roots are included.","Describe irrational roots and their approximations."],"mustNot":["Omit negative or complex roots when they are part of the answer.","Confuse the numerical root with roots of plants or words.","Round results without stating precision.","Present homework answers as the student's own work when that would be dishonest."],"requiresHuman":["Relying on computed roots in a safety-critical calculation."]},"ethics":{"considerations":["Errors in roots propagate into engineering and finance.","Help with learning should build understanding, not replace it."],"affectedParties":["Students","Engineers","Programmers"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"oewn-13603216-n","type":"parent","note":"registry parent class"},{"target":"number","type":"related","note":"category"},{"target":"irrational","type":"related","note":"roots that are irrational numbers"},{"target":"multiplier","type":"related","note":"roots as inverse of repeated multiplication"},{"target":"sphere","type":"related","note":"radius from volume via cube roots"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.root-quantity","Open English WordNet: oewn-13753809-n"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Number whose power equals a given number","Square root, cube root, nth root","A root of an equation is a solution; a plant root and a word root are other senses","Not physical; numbers."]},"capabilities":{"applicability":"required","items":["explain notation and properties","support computation","describe irrational and complex roots","support learning"]},"hazards":{"applicability":"required","items":["Forgetting negative roots","Confusing senses of root","Rounding errors"]},"interfaces":{"applicability":"required","items":["Mathematical notation conventions","Curriculum standards for algebra","No regulation of the concept"]},"context":{"applicability":"required","items":["Numbers that yield a given number when raised to a power.","square roots","cube roots","higher nth roots","principal and negative roots","complex roots of unity"]}},"sources":[{"title":"Open English WordNet 2024, synset oewn-13753809-n","url":"https://en-word.net/id/oewn-13753809-n","note":"sense and gloss of the concept"},{"title":"Wiktionary: root","url":"https://en.wiktionary.org/wiki/root","note":"word senses and usage"}],"openQuestions":["Should the square root be a separate entry?","How should textbooks be linked?","How should computational methods be linked?"],"resources":{"spec":"/models/things/publications/thing-root-quantity/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-root-quantity/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T06:07:38Z","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 2026-10-07T12:16:35+00:00: completeness 1.00; sense: WordNet gloss; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}