{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.degrees-of-freedom","code":"thing-q3253731","url":"https://ver.cy/models/thing/q3253731/","name":"degrees of freedom","alternateNames":[],"kind":"thing","status":"research-draft","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"The number of independent parameters that define the state or configuration of a system, in mechanics the number of independent movements a body or mechanism can make, such as six for a free rigid body, in statistics the number of values free to vary in a calculation, which governs the distributions used in tests, and in physics and chemistry the number of independent variables in phase rules and the modes of molecules; degrees of freedom are fundamental to modelling, robotics, statistics and thermodynamics.","purpose":"Let an agent explain degrees of freedom across mechanics, statistics, physics and chemistry, support counting and calculating them, describe their role in tests, mechanisms and models, and support learning.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Independence","Reduced by constraints","Field-specific meanings","Governs distributions and motion"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What degrees of freedom are.","layers":[{"id":"concept","name":"Concept","description":"Concept and senses.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What are degrees of freedom, and how do mechanical, statistical, thermodynamic and molecular senses differ?","kind":"definition"},{"text":"Which field is meant?","kind":"boundary"}]}]},{"id":"constraints","name":"Constraints","description":"Constraints.","findings":[{"id":"constraints-finding","name":"Constraints","description":"Constraints.","questions":[{"text":"How do constraints reduce degrees of freedom, and how are they counted for bodies and mechanisms?","kind":"definition"},{"text":"Which entry fits kinematics?","kind":"action"}]}]}]},{"id":"calculate","name":"Calculate","description":"Counting and calculation.","layers":[{"id":"mechanics","name":"Mechanics","description":"Mechanisms and robots.","findings":[{"id":"mechanics-finding","name":"Mechanics","description":"Mechanics.","questions":[{"text":"How many degrees of freedom does this mechanism or robot have, and how is this determined?","kind":"action"},{"text":"Which entry fits robot kinematics?","kind":"action"}]}]},{"id":"statistics","name":"Statistics","description":"Statistical tests.","findings":[{"id":"statistics-finding","name":"Statistics","description":"Statistics.","questions":[{"text":"How are degrees of freedom calculated for this statistical test, and why do they matter?","kind":"action"},{"text":"Which entry fits hypothesis testing?","kind":"action"}]}]}]},{"id":"science","name":"Science","description":"Physics and chemistry.","layers":[{"id":"thermodynamics","name":"Thermodynamics","description":"Phase rule and molecules.","findings":[{"id":"thermodynamics-finding","name":"Thermodynamics","description":"Thermodynamics.","questions":[{"text":"How do degrees of freedom appear in the phase rule, equipartition and molecular motion?","kind":"provenance"},{"text":"Which entry fits the phase rule?","kind":"action"}]}]},{"id":"models","name":"Models","description":"Modelling.","findings":[{"id":"models-finding","name":"Models","description":"Models.","questions":[{"text":"How do degrees of freedom shape model complexity and overfitting?","kind":"provenance"},{"text":"Which findings are contested?","kind":"boundary"}]}]}]},{"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 develop in mechanics and statistics?","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 degrees of freedom be taught across disciplines?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain degrees of freedom in mechanics, statistics, physics and chemistry with correct definitions.","Compute degrees of freedom for a model or test and show the working."],"mustNot":["Report statistical results with wrong degrees of freedom that make findings look stronger.","Confuse the mechanical and statistical senses in technical work.","Certify a robot's or mechanism's range of movement as safe without proper analysis."],"requiresHuman":["Accepting statistical conclusions used in medicine, policy or law."]},"ethics":{"considerations":["Statistical errors can mislead decisions about treatments and policies.","Robots with more degrees of freedom have larger, harder-to-predict hazard zones around people."],"affectedParties":["Readers of research","People working near robots"]},"owners":{"steward":"Nobody: a concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q614112","type":"parent","note":"registry parent class"},{"target":"number of entities","type":"related","note":"category"},{"target":"robotics","type":"related","note":"joints and degrees of freedom of robots"},{"target":"damping ratio","type":"related","note":"parameters of dynamic systems"},{"target":"relative species abundance","type":"related","note":"statistical analysis of ecological data"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.degrees-of-freedom","Wikidata: Q3253731 (https://www.wikidata.org/wiki/Q3253731)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Number of independent parameters","Mechanical, statistical, thermodynamic, molecular","Dimensions of a space are related but not identical; constraints reduce degrees of freedom","Not physical; a count."]},"capabilities":{"applicability":"required","items":["explain across fields","support counting","describe roles in tests and mechanisms","support learning"]},"hazards":{"applicability":"required","items":["Miscounting degrees of freedom in tests","Conflating senses across fields","Ignoring constraints"]},"interfaces":{"applicability":"required","items":["Statistical reporting conventions","Mechanism and robotics terminology","No regulation of the concept"]},"context":{"applicability":"required","items":["Independent parameters of a system.","degrees of freedom of rigid bodies and mechanisms","degrees of freedom in statistics","thermodynamic degrees of freedom and the phase rule","molecular degrees of freedom","degrees of freedom in robotics and control"]}},"sources":[{"title":"Wikidata item Q3253731: degrees of freedom","url":"https://www.wikidata.org/wiki/Q3253731","note":"identity and sense of the item"},{"title":"Wikipedia: Degrees of freedom (statistics)","url":"https://en.wikipedia.org/wiki/Degrees_of_freedom_%28statistics%29","note":"general description of the item"}],"openQuestions":["Should statistical degrees of freedom be a separate entry?","How should textbooks be linked?","How should robotics resources be linked?"],"resources":{"spec":"/models/things/publications/thing-q3253731/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q3253731/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T06:20:56Z","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":{"interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}