{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DR7D4W6YVKURYM4B7OR4OJHAJJ","short_pith_number":"pith:DR7D4W6Y","schema_version":"1.0","canonical_sha256":"1c7e3e5bd8aaa91c3381fba3c724e04a78e5fcbf7ade747c610c82bd22722de6","source":{"kind":"arxiv","id":"1912.10695","version":2},"attestation_state":"computed","paper":{"title":"Constructing infinitely many half-arc-transitive covers of tetravalent graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Binzhou Xia, Pablo Spiga","submitted_at":"2019-12-23T09:15:39Z","abstract_excerpt":"We prove that, given a finite graph $\\Sigma$ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of $\\Sigma$. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order $2^8$ of finite connected tetravalent half-arc-transitive graphs. This sheds some new light on the longstanding problem of classifying the vertex stabilizers of finite tetravalent half-arc-transitive 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":"1912.10695","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-23T09:15:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"294ff9b11b95d3723d7c93da1d83c8ec524820078971de1bde9712146e4f83c7","abstract_canon_sha256":"19d7fa0c398d23c1c0c688f3202795c8b3a5551ddb0830369035f5ed99e3e740"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:53:47.686773Z","signature_b64":"M2mKDpEet43pLWrM6xYDnAamKSHBaO0LeFIbJxKfDf2XkPznjwBJ6Q8AHd38y9xvtcW5sdM58rFmI++ZbmxzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c7e3e5bd8aaa91c3381fba3c724e04a78e5fcbf7ade747c610c82bd22722de6","last_reissued_at":"2026-07-05T01:53:47.686329Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:53:47.686329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing infinitely many half-arc-transitive covers of tetravalent graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Binzhou Xia, Pablo Spiga","submitted_at":"2019-12-23T09:15:39Z","abstract_excerpt":"We prove that, given a finite graph $\\Sigma$ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of $\\Sigma$. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order $2^8$ of finite connected tetravalent half-arc-transitive graphs. This sheds some new light on the longstanding problem of classifying the vertex stabilizers of finite tetravalent half-arc-transitive graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.10695","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.10695/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1912.10695","created_at":"2026-07-05T01:53:47.686389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.10695v2","created_at":"2026-07-05T01:53:47.686389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.10695","created_at":"2026-07-05T01:53:47.686389+00:00"},{"alias_kind":"pith_short_12","alias_value":"DR7D4W6YVKUR","created_at":"2026-07-05T01:53:47.686389+00:00"},{"alias_kind":"pith_short_16","alias_value":"DR7D4W6YVKURYM4B","created_at":"2026-07-05T01:53:47.686389+00:00"},{"alias_kind":"pith_short_8","alias_value":"DR7D4W6Y","created_at":"2026-07-05T01:53:47.686389+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.09361","citing_title":"Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ","json":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ.json","graph_json":"https://pith.science/api/pith-number/DR7D4W6YVKURYM4B7OR4OJHAJJ/graph.json","events_json":"https://pith.science/api/pith-number/DR7D4W6YVKURYM4B7OR4OJHAJJ/events.json","paper":"https://pith.science/paper/DR7D4W6Y"},"agent_actions":{"view_html":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ","download_json":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ.json","view_paper":"https://pith.science/paper/DR7D4W6Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.10695&json=true","fetch_graph":"https://pith.science/api/pith-number/DR7D4W6YVKURYM4B7OR4OJHAJJ/graph.json","fetch_events":"https://pith.science/api/pith-number/DR7D4W6YVKURYM4B7OR4OJHAJJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ/action/storage_attestation","attest_author":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ/action/author_attestation","sign_citation":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ/action/citation_signature","submit_replication":"https://pith.science/pith/DR7D4W6YVKURYM4B7OR4OJHAJJ/action/replication_record"}},"created_at":"2026-07-05T01:53:47.686389+00:00","updated_at":"2026-07-05T01:53:47.686389+00:00"}