{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.half-integer","code":"thing-q743139","url":"https://ver.cy/models/thing/q743139/","name":"half-integer","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.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A number of the form n plus one half, where n is an integer, such as one half, three halves and minus five halves; half-integers arise as spins of fermions in quantum mechanics, in rounding conventions, in the arguments of certain special functions and in lattice geometry, and are the odd multiples of one half.","purpose":"Let an agent define half-integers precisely, distinguish them from integers and general fractions, relay their roles in physics and mathematics, and support calculation and notation.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Form n plus one half","Closed under addition with integers","Fermion spins","Appear in Bessel functions and gamma function values"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What a half-integer is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a half-integer, and how does it relate to integers and dyadic rationals?","kind":"definition"},{"text":"Is the number a half-integer or another fraction?","kind":"boundary"}]}]},{"id":"properties","name":"Properties","description":"Properties.","findings":[{"id":"properties-finding","name":"Properties","description":"Properties.","questions":[{"text":"What arithmetic properties do half-integers have?","kind":"definition"},{"text":"Which entry fits rational numbers?","kind":"action"}]}]}]},{"id":"physics","name":"Physics","description":"Spin and quantum numbers.","layers":[{"id":"spin","name":"Spin","description":"Fermion spin.","findings":[{"id":"spin-finding","name":"Spin","description":"Spin.","questions":[{"text":"Why do fermions have half-integer spin, and what follows from it?","kind":"provenance"},{"text":"Which entry fits spin?","kind":"action"}]}]},{"id":"other","name":"Other","description":"Other physical uses.","findings":[{"id":"other-finding","name":"Other","description":"Other.","questions":[{"text":"Where else do half-integers appear in physics, such as angular momentum coupling and lattices?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"mathematics","name":"Mathematics","description":"Mathematical roles.","layers":[{"id":"functions","name":"Functions","description":"Special functions.","findings":[{"id":"functions-finding","name":"Functions","description":"Functions.","questions":[{"text":"What values do the gamma and Bessel functions take at half-integers?","kind":"provenance"},{"text":"Which entry fits the gamma function?","kind":"action"}]}]},{"id":"rounding","name":"Rounding","description":"Rounding.","findings":[{"id":"rounding-finding","name":"Rounding","description":"Rounding.","questions":[{"text":"How do rounding conventions treat half-integers?","kind":"action"},{"text":"Which convention applies in the context?","kind":"boundary"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching.","layers":[{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How are half-integers introduced in mathematics and physics teaching?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"notation","name":"Notation","description":"Notation.","findings":[{"id":"notation-finding","name":"Notation","description":"Notation.","questions":[{"text":"How are half-integers written and typeset?","kind":"provenance"},{"text":"Which entry fits mathematical notation?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Identify half-integers and explain where they arise.","State the rounding convention used when rounding half-integers."],"mustNot":["Call any fraction a half-integer.","Round half-integers without stating the convention used.","Confuse half-integer spin with other quantum numbers.","Silently change totals through inconsistent rounding."],"requiresHuman":["Choosing a rounding rule for financial or official figures."]},"ethics":{"considerations":["Rounding rules at half values can shift money or votes in aggregate."],"affectedParties":["Readers of figures","Learners"]},"owners":{"steward":"Nobody owns the concept; it belongs to the shared body of mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q2281400","type":"parent","note":"registry parent class"},{"target":"dyadic rational","type":"related","note":"a rational with denominator two"},{"target":"integer","type":"related","note":"the other residue class of halves"},{"target":"spin","type":"related","note":"fermion spin values"},{"target":"gamma function","type":"related","note":"values at half-integers"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.half-integer","Wikidata: Q743139 (https://www.wikidata.org/wiki/Q743139)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Odd multiple of one half","Not an integer, but twice it is an odd integer","Integers and other dyadic rationals are neighbouring classes","Not visible; numbers written as odd numerators over two."]},"capabilities":{"applicability":"required","items":["define and recognise half-integers","explain their role in spin and other physics","explain their appearance in mathematics","support notation and calculation"]},"hazards":{"applicability":"required","items":["Calling any fraction a half-integer","Rounding errors at half-integer boundaries","Confusing spin quantum numbers with measured values"]},"interfaces":{"applicability":"required","items":["No regulation; notation follows standard mathematics"]},"context":{"applicability":"required","items":["Not for anything in itself; a class of numbers with recurring roles.","positive and negative half-integers","half-integer spins","half-integer arguments of special functions","half-integer coordinates in lattices","half-integer weights in modular forms"]}},"sources":[{"title":"Wikidata item Q743139: half-integer","url":"https://www.wikidata.org/wiki/Q743139","note":"identity and sense of the item"},{"title":"Wikipedia: Half-integer","url":"https://en.wikipedia.org/wiki/Half-integer","note":"general description of the item"}],"openQuestions":["Should spin be the primary entry for the physics use?","How should special function references be linked?","How should rounding conventions be recorded?"],"resources":{"spec":"/models/things/publications/thing-q743139/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q743139/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T20:49:56Z","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}}