{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7IN7RLRVWZVD4JLVVPL5B5I32B","short_pith_number":"pith:7IN7RLRV","schema_version":"1.0","canonical_sha256":"fa1bf8ae35b66a3e2575abd7d0f51bd050f14fdbeba584c70806821a7683e7e5","source":{"kind":"arxiv","id":"1807.00547","version":3},"attestation_state":"computed","paper":{"title":"Realisation of groups as automorphism groups in categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Gareth A. Jones","submitted_at":"2018-07-02T09:09:22Z","abstract_excerpt":"It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, every countable group $A$ is isomorphic to the automorphism group of uncountably many non-isomorphic objects, infinitely many of them finite if $A$ is finite. In particular, this applies to dessins d'enfants, regarded as finite oriented hypermaps. The proof, involving maximal subgroups of various triangle groups, yields a simple construction of a regular map whose automorphism group contains an isomorphic copy of every finite group."},"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":"1807.00547","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-02T09:09:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"055d3cfc0664aed2071a3f1f9183cf31cd8df0ea6351bddd6784548acf4696fb","abstract_canon_sha256":"a80ff89b2ed42ad237d6e95668110ebb231f58aaa629f8b356b434654f725902"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.339361Z","signature_b64":"vbxSrhApreQSMNDddmLOTaishDjZrmIEB8BBLbA5CdeNnoiPX4HWLqe1p0TYIEHEX7hNn5zGL3PVsFYNa2lGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa1bf8ae35b66a3e2575abd7d0f51bd050f14fdbeba584c70806821a7683e7e5","last_reissued_at":"2026-05-18T00:03:24.338986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.338986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Realisation of groups as automorphism groups in categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Gareth A. Jones","submitted_at":"2018-07-02T09:09:22Z","abstract_excerpt":"It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, every countable group $A$ is isomorphic to the automorphism group of uncountably many non-isomorphic objects, infinitely many of them finite if $A$ is finite. In particular, this applies to dessins d'enfants, regarded as finite oriented hypermaps. The proof, involving maximal subgroups of various triangle groups, yields a simple construction of a regular map whose automorphism group contains an isomorphic copy of every finite group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00547","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":"1807.00547","created_at":"2026-05-18T00:03:24.339042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.00547v3","created_at":"2026-05-18T00:03:24.339042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00547","created_at":"2026-05-18T00:03:24.339042+00:00"},{"alias_kind":"pith_short_12","alias_value":"7IN7RLRVWZVD","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7IN7RLRVWZVD4JLV","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7IN7RLRV","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.06675","citing_title":"A short proof of Greenberg's Theorem","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B","json":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B.json","graph_json":"https://pith.science/api/pith-number/7IN7RLRVWZVD4JLVVPL5B5I32B/graph.json","events_json":"https://pith.science/api/pith-number/7IN7RLRVWZVD4JLVVPL5B5I32B/events.json","paper":"https://pith.science/paper/7IN7RLRV"},"agent_actions":{"view_html":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B","download_json":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B.json","view_paper":"https://pith.science/paper/7IN7RLRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.00547&json=true","fetch_graph":"https://pith.science/api/pith-number/7IN7RLRVWZVD4JLVVPL5B5I32B/graph.json","fetch_events":"https://pith.science/api/pith-number/7IN7RLRVWZVD4JLVVPL5B5I32B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B/action/storage_attestation","attest_author":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B/action/author_attestation","sign_citation":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B/action/citation_signature","submit_replication":"https://pith.science/pith/7IN7RLRVWZVD4JLVVPL5B5I32B/action/replication_record"}},"created_at":"2026-05-18T00:03:24.339042+00:00","updated_at":"2026-05-18T00:03:24.339042+00:00"}