{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QDCUDSIGPH7OAANMAJMBRJ7EZO","short_pith_number":"pith:QDCUDSIG","schema_version":"1.0","canonical_sha256":"80c541c90679fee001ac025818a7e4cb9fc33a8bd36bf5ef30a7e2e4574bdc37","source":{"kind":"arxiv","id":"1508.02169","version":3},"attestation_state":"computed","paper":{"title":"A coalgebraic model of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.CO","authors_text":"Christian J\\\"akel","submitted_at":"2015-08-10T08:45:27Z","abstract_excerpt":"For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\\times Set$ and use the theory of coalgebras over arbitrary categories to conclude properties of the category of graphs."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.02169","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-10T08:45:27Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"28f30a1561c44514a6804606f64de82b3348b6327b5d690c98c085fbb4ca49a8","abstract_canon_sha256":"a7c29dc50b07bb2a59721d25fa5e700da597b5bb48b139823fdb52fd8a00465a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:48.220551Z","signature_b64":"Xdvkk/ZjnvC2P6PT++IWW0e+/tD90z17+Mm+n/MM+05sG11p/57qrMhufpQNkerxbWxUjzjs0E824eV4lipYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80c541c90679fee001ac025818a7e4cb9fc33a8bd36bf5ef30a7e2e4574bdc37","last_reissued_at":"2026-05-18T01:22:48.219998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:48.219998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A coalgebraic model of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.CO","authors_text":"Christian J\\\"akel","submitted_at":"2015-08-10T08:45:27Z","abstract_excerpt":"For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\\times Set$ and use the theory of coalgebras over arbitrary categories to conclude properties of the category of graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02169","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.02169","created_at":"2026-05-18T01:22:48.220078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.02169v3","created_at":"2026-05-18T01:22:48.220078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02169","created_at":"2026-05-18T01:22:48.220078+00:00"},{"alias_kind":"pith_short_12","alias_value":"QDCUDSIGPH7O","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QDCUDSIGPH7OAANM","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QDCUDSIG","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO","json":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO.json","graph_json":"https://pith.science/api/pith-number/QDCUDSIGPH7OAANMAJMBRJ7EZO/graph.json","events_json":"https://pith.science/api/pith-number/QDCUDSIGPH7OAANMAJMBRJ7EZO/events.json","paper":"https://pith.science/paper/QDCUDSIG"},"agent_actions":{"view_html":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO","download_json":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO.json","view_paper":"https://pith.science/paper/QDCUDSIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.02169&json=true","fetch_graph":"https://pith.science/api/pith-number/QDCUDSIGPH7OAANMAJMBRJ7EZO/graph.json","fetch_events":"https://pith.science/api/pith-number/QDCUDSIGPH7OAANMAJMBRJ7EZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO/action/storage_attestation","attest_author":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO/action/author_attestation","sign_citation":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO/action/citation_signature","submit_replication":"https://pith.science/pith/QDCUDSIGPH7OAANMAJMBRJ7EZO/action/replication_record"}},"created_at":"2026-05-18T01:22:48.220078+00:00","updated_at":"2026-05-18T01:22:48.220078+00:00"}