{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.remainder-2","code":"thing-remainder-2","url":"https://ver.cy/models/thing/remainder-2/","name":"remainder","alternateNames":["difference","denivelation","solvency margin"],"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":"The number left after subtracting one number from another, that is the difference that when added to the subtrahend gives the minuend, and in related uses the amount remaining after a deduction, such as a height difference in surveying or a solvency margin in finance; this sense of remainder in subtraction is distinct from the remainder left after division, though both express what is left over.","purpose":"Let an agent explain the remainder as the result of subtraction, distinguish it from the division remainder, compute differences and margins, and support arithmetic learning.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Subtraction result","Difference","Applied margins","Elementary arithmetic"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What the remainder is.","layers":[{"id":"definition","name":"Definition","description":"Definition and terms.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What are the minuend, subtrahend and remainder in subtraction, and how does the remainder check the subtraction?","kind":"definition"},{"text":"Is the subtraction remainder or the division remainder meant?","kind":"boundary"}]}]},{"id":"properties","name":"Properties","description":"Properties.","findings":[{"id":"properties-finding","name":"Properties","description":"Properties.","questions":[{"text":"How does the remainder behave with negative numbers, and how does subtraction relate to addition?","kind":"definition"},{"text":"Which entry fits subtraction generally?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Computing remainders.","layers":[{"id":"calculate","name":"Calculate","description":"Calculation.","findings":[{"id":"calculate-finding","name":"Calculate","description":"Calculation.","questions":[{"text":"What is the remainder when this number is subtracted from that, and how can it be checked?","kind":"action"},{"text":"Which mental methods help?","kind":"action"}]}]},{"id":"applied","name":"Applied","description":"Applied remainders.","findings":[{"id":"applied-finding","name":"Applied","description":"Applied.","questions":[{"text":"How are height differences in surveying and margins such as solvency margins computed as remainders?","kind":"definition"},{"text":"Which entry fits solvency regulation?","kind":"action"}]}]}]},{"id":"teach","name":"Teach","description":"Teaching subtraction.","layers":[{"id":"methods","name":"Methods","description":"Teaching methods.","findings":[{"id":"methods-finding","name":"Methods","description":"Methods.","questions":[{"text":"How is subtraction taught, including borrowing and complementary methods?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"language","name":"Language","description":"Terminology.","findings":[{"id":"language-finding","name":"Language","description":"Terminology.","questions":[{"text":"How do the terms remainder and difference differ in usage across curricula and languages?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"learn","name":"Learn","description":"History.","layers":[{"id":"history","name":"History","description":"History of subtraction.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did subtraction methods and terminology develop historically?","kind":"provenance"},{"text":"Which entry fits history of arithmetic?","kind":"action"}]}]},{"id":"computing","name":"Computing","description":"Subtraction in computing.","findings":[{"id":"computing-finding","name":"Computing","description":"Computing.","questions":[{"text":"How is subtraction performed in computers, and what are overflow and underflow?","kind":"definition"},{"text":"Which entry fits computer arithmetic?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Compute differences, labelling minuend and subtrahend.","Distinguish the subtraction remainder from the division remainder."],"mustNot":["Confuse the division remainder with the difference.","Report a difference with the sign reversed.","Mark a learner wrong over a terminology difference."],"requiresHuman":["Using computed differences in survey or financial records."]},"ethics":{"considerations":["Small arithmetic errors in records can cost people money."],"affectedParties":["Learners","Surveyors"]},"owners":{"steward":"Nobody owns the concept; it is held in common by mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"oewn-13603216-n","type":"parent","note":"registry parent class"},{"target":"number","type":"related","note":"category"},{"target":"difference","type":"related","note":"the general relation"},{"target":"output","type":"related","note":"quantities compared by difference"},{"target":"unit cost","type":"related","note":"margins over cost"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.remainder-2","Open English WordNet: oewn-13751346-n"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Minuend minus subtrahend","What is left after taking away","The division remainder is what is left after dividing","Not physical; a number."]},"capabilities":{"applicability":"required","items":["explain the concept","distinguish from division remainder","compute differences and margins","support learning"]},"hazards":{"applicability":"required","items":["Confusing subtraction and division remainders","Sign errors","Confusing minuend and subtrahend"]},"interfaces":{"applicability":"required","items":["Arithmetic conventions and terminology","Financial regulation defining solvency margins"]},"context":{"applicability":"required","items":["The result of subtraction.","arithmetic difference","height differences and denivelations","margins such as solvency margin","remaining amounts after deductions"]}},"sources":[{"title":"Open English WordNet 2024, synset oewn-13751346-n","url":"https://en-word.net/id/oewn-13751346-n","note":"sense and gloss of the concept"},{"title":"Wiktionary: remainder","url":"https://en.wiktionary.org/wiki/remainder","note":"word senses and usage"}],"openQuestions":["Should the division remainder be linked?","How should surveying uses be linked?","How should financial margins be linked?"],"resources":{"spec":"/models/things/publications/thing-remainder-2/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-remainder-2/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T00:36:46Z","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}}