{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.multiplier","code":"thing-multiplier","url":"https://ver.cy/models/thing/multiplier/","name":"multiplier","alternateNames":["multiplier factor","scale factor","time-scale factor"],"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 by which a multiplicand is multiplied to give a product, and by extension any factor that scales a quantity, such as a scale factor in geometry and maps, a time-scale factor in simulation, a multiplier in economics that relates a change in output to an initial change in spending and can be less than one, and multipliers in games and scoring; the multiplier is a basic concept of arithmetic that recurs wherever quantities are scaled.","purpose":"Let an agent explain the multiplier in arithmetic and its extended uses as scale factor and economic multiplier, support calculations and interpretation, distinguish senses across fields, and support learning.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Scaling role","Commutative with multiplicand","Field-specific senses","Dimensionless in scaling"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a multiplier is.","layers":[{"id":"concept","name":"Concept","description":"Arithmetic concept.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What is the multiplier in multiplication, and how do multiplier, multiplicand and product relate?","kind":"definition"},{"text":"Which sense of multiplier is meant?","kind":"boundary"}]}]},{"id":"scale","name":"Scale","description":"Scale factors.","findings":[{"id":"scale-finding","name":"Scale","description":"Scale.","questions":[{"text":"How do scale factors work in geometry, maps and simulation time scaling?","kind":"definition"},{"text":"Which entry fits scale?","kind":"action"}]}]}]},{"id":"apply","name":"Apply","description":"Calculation and use.","layers":[{"id":"calculate","name":"Calculate","description":"Calculating.","findings":[{"id":"calculate-finding","name":"Calculate","description":"Calculation.","questions":[{"text":"How can a quantity be scaled by this multiplier, and how are scale factors combined?","kind":"action"},{"text":"Which entry fits proportion?","kind":"action"}]}]},{"id":"games","name":"Games","description":"Games and scoring.","findings":[{"id":"games-finding","name":"Games","description":"Games.","questions":[{"text":"How are multipliers used in scoring systems and games?","kind":"provenance"},{"text":"Which entry fits game design?","kind":"action"}]}]}]},{"id":"economics","name":"Economics","description":"Economic multiplier.","layers":[{"id":"concept","name":"Concept","description":"The economic multiplier.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What is the economic multiplier, and how is it estimated, with positions attributed?","kind":"provenance"},{"text":"Which findings are contested?","kind":"boundary"}]}]},{"id":"policy","name":"Policy","description":"Policy use.","findings":[{"id":"policy-finding","name":"Policy","description":"Policy.","questions":[{"text":"How are multipliers used in fiscal policy debates, with positions attributed?","kind":"provenance"},{"text":"Is the presentation neutral?","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 can multiplication and scaling be taught?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the terminology of multiplication develop?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain the multiplier in arithmetic and as scale factor or economic multiplier, naming the sense.","Support calculations, stating units.","Present economic multiplier estimates with sources and ranges."],"mustNot":["Confuse multiplier and multiplicand where it matters.","Present a single economic multiplier estimate as certain.","Use multiplier claims to mislead the public about policy.","Confuse senses across fields."],"requiresHuman":["Using a multiplier estimate in a budget or policy decision."]},"ethics":{"considerations":["Overstated multipliers justify wasteful spending.","Help with learning should build understanding."],"affectedParties":["Taxpayers","Students","Policy makers"]},"owners":{"steward":"Nobody: a concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"oewn-13603216-n","type":"parent","note":"registry parent class"},{"target":"number","type":"related","note":"category"},{"target":"remainder","type":"related","note":"another arithmetic concept"},{"target":"trillion","type":"related","note":"large numbers as multipliers of units"},{"target":"economist","type":"related","note":"analysts of economic multipliers"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.multiplier","Open English WordNet: oewn-13755958-n"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Number multiplying a multiplicand","Scale factors, economic multipliers, game multipliers","The multiplicand is what is multiplied; the product is the result; a divisor divides","Not physical; a number."]},"capabilities":{"applicability":"required","items":["explain the arithmetic concept","describe extended uses","support calculations","support learning"]},"hazards":{"applicability":"required","items":["Confusing multiplier and multiplicand","Confusing senses across fields","Overstating economic multiplier estimates"]},"interfaces":{"applicability":"required","items":["Mathematical notation conventions","Curriculum standards for arithmetic","No regulation of the concept"]},"context":{"applicability":"required","items":["The factor that scales a quantity.","multiplier in arithmetic","scale factors in geometry and maps","time-scale factors in simulation","economic multipliers","multipliers in games and scoring"]}},"sources":[{"title":"Open English WordNet 2024, synset oewn-13755958-n","url":"https://en-word.net/id/oewn-13755958-n","note":"sense and gloss of the concept"},{"title":"Wiktionary: multiplier","url":"https://en.wiktionary.org/wiki/multiplier","note":"word senses and usage"}],"openQuestions":["Should the economic multiplier be a separate entry?","How should textbooks be linked?","How should economic estimates be attributed?"],"resources":{"spec":"/models/things/publications/thing-multiplier/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-multiplier/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T06:00:47Z","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 2026-10-08T18:54:35+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}}