{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.embedding","code":"thing-q980509","url":"https://ver.cy/models/thing/q980509/","name":"embedding","alternateNames":["latent space","elementary embedding","fastText","graph embedding","knowledge graph embedding","Local flatness","RDF2Vec","book embedding","linkless embedding","planar embedding"],"kind":"thing","status":"published","version":"0.2.0-wave.4","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In mathematics, an embedding is a map that places one structure inside another so that the copy faithfully preserves the original structure; the term applies across geometry, topology and algebra. The registry aliases name several senses, including topological embeddings, elementary embeddings in logic, and, by extension, machine-learning embeddings such as word or graph embeddings that map items into a latent space of vectors. The precise meaning depends on the field, so the sense should be identified before answering.","purpose":"Let an agent explain the notion of embedding, relay its meaning across mathematics and its extension to machine learning from reference sources, distinguish the senses the aliases name, and steer a question to the right sense.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Structure-preserving","Field-dependent meaning","Extended to machine learning","Maps into a larger space"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What embedding means.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What does embedding mean in mathematics, and how does it differ from a general function or a projection?","kind":"definition"},{"text":"Which sense is meant, mathematical or machine-learning?","kind":"boundary"}]}]},{"id":"senses","name":"Senses","description":"The senses.","findings":[{"id":"senses-finding","name":"Senses","description":"Senses.","questions":[{"text":"What are topological, elementary and machine-learning embeddings?","kind":"definition"},{"text":"Which entry fits the intended sense?","kind":"action"}]}]}]},{"id":"math","name":"Math","description":"Mathematics.","layers":[{"id":"topology","name":"Topology","description":"Topological embedding.","findings":[{"id":"topology-finding","name":"Topology","description":"Topology.","questions":[{"text":"What is a topological embedding?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"logic","name":"Logic","description":"Elementary embedding.","findings":[{"id":"logic-finding","name":"Logic","description":"Logic.","questions":[{"text":"What is an elementary embedding in logic?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"ml","name":"ML","description":"Machine learning.","layers":[{"id":"latent","name":"Latent","description":"Latent space.","findings":[{"id":"latent-finding","name":"Latent","description":"Latent.","questions":[{"text":"What is a machine-learning embedding into a latent space?","kind":"provenance"},{"text":"Is the analogy to the mathematical sense loose?","kind":"boundary"}]}]},{"id":"kinds","name":"Kinds","description":"Embedding kinds.","findings":[{"id":"kinds-finding","name":"Kinds","description":"Kinds.","questions":[{"text":"What are word and graph embeddings?","kind":"provenance"},{"text":"Which entry fits the specific kind?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"Context.","layers":[{"id":"preservation","name":"Preservation","description":"What is preserved.","findings":[{"id":"preservation-finding","name":"Preservation","description":"Preservation.","questions":[{"text":"What structure does an embedding preserve in each field?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]},{"id":"use","name":"Use","description":"Use.","findings":[{"id":"use-finding","name":"Use","description":"Use.","questions":[{"text":"How are embeddings used in practice?","kind":"action"},{"text":"Is the sense correctly identified?","kind":"boundary"}]}]}]}]},"agentConduct":{"may":["Explain what an embedding is in the field the user is working in.","Check whether a given map is injective and structure-preserving.","Distinguish the mathematical sense from machine-learning vector embeddings."],"mustNot":["Mix senses of embedding from different fields in an argument.","Call a map an embedding when it does not preserve the structure.","Overstate what an embedding preserves.","Present a disputed proof involving embeddings as settled."],"requiresHuman":["Publishing a mathematical claim in someone else's name."]},"ethics":{"considerations":["Precise terms matter; confusing them can invalidate results.","Credit for mathematical work should be accurate."],"affectedParties":["Students","Researchers","Readers of mathematical work"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q11348","type":"parent","note":"registry parent class"},{"target":"function","type":"related","note":"in registry terms"},{"target":"projection","type":"related"},{"target":"machine learning","type":"related"},{"target":"representation","type":"related"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.embedding","Wikidata: Q980509 (https://www.wikidata.org/wiki/Q980509)"]},"properties":{"applicability":"not-applicable","items":["field: mathematics and its extensions note","key property: preserves structure note","registry parent: function note"]},"recognition":{"applicability":"optional","items":["A structure-preserving placement into a larger space","Topological embedding, elementary embedding, latent space, word and graph embeddings","A general function need not preserve structure; a projection may lose information","Not a visible object; a map or representation, sometimes pictured as points in a space."]},"capabilities":{"applicability":"required","items":["explain the mathematical notion","relay the machine-learning extension","distinguish the senses","steer to the right meaning"]},"hazards":{"applicability":"required","items":["Mixing the senses","Assuming one field s meaning everywhere","Overstating the analogy to latent spaces"]},"interfaces":{"applicability":"required","items":["Mathematical definitions per field"]},"context":{"applicability":"required","items":["Placing one structure faithfully inside another.","topological embedding","elementary embedding","word embedding","graph embedding"]}},"sources":[{"title":"Wikidata item Q980509: embedding","url":"https://www.wikidata.org/wiki/Q980509","note":"identity and sense of the item"},{"title":"Wikipedia: Embedding","url":"https://en.wikipedia.org/wiki/Embedding","note":"general description of the item"}],"openQuestions":["Should each sense be a separate entry?","How should the machine-learning sense be scoped?","How should the senses be signposted?"],"resources":{"spec":"/models/things/publications/thing-q980509/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q980509/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-14T03:25:52Z","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 2026-10-06T19:52:03+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}}