{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ALVHO6PDNMN64ZP6YP75EAK3CX","short_pith_number":"pith:ALVHO6PD","schema_version":"1.0","canonical_sha256":"02ea7779e36b1bee65fec3ffd2015b15ea3c00672e704226cd590a7f7c39d53a","source":{"kind":"arxiv","id":"1806.08196","version":2},"attestation_state":"computed","paper":{"title":"Revisiting Leighton's Theorem with the Haar Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Daniel J. Woodhouse","submitted_at":"2018-06-21T12:25:19Z","abstract_excerpt":"Leighton's graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton's theorem that allows generalizations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen-Macura and Hagen-Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups."},"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":"1806.08196","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-21T12:25:19Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"af083d76ced7a2338353f2e3a8a1ac7ff8f8395057643787cda89bf3869f6fa0","abstract_canon_sha256":"1dc4a2f405b35218a5f96e46727ffaf55cd1347fb48ae347e185b2ee9efa84ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:35.455981Z","signature_b64":"iTfbTJGfheN8BPrK+sRlgPPeobMY11je+x/2sACfxDjyCUnbKV6dmR/QUlrjQ5kXOkPhz5NResj0jsjYl+zdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ea7779e36b1bee65fec3ffd2015b15ea3c00672e704226cd590a7f7c39d53a","last_reissued_at":"2026-05-18T00:09:35.455277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:35.455277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting Leighton's Theorem with the Haar Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Daniel J. Woodhouse","submitted_at":"2018-06-21T12:25:19Z","abstract_excerpt":"Leighton's graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton's theorem that allows generalizations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen-Macura and Hagen-Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08196","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":""},"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":"1806.08196","created_at":"2026-05-18T00:09:35.455396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.08196v2","created_at":"2026-05-18T00:09:35.455396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08196","created_at":"2026-05-18T00:09:35.455396+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALVHO6PDNMN6","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALVHO6PDNMN64ZP6","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALVHO6PD","created_at":"2026-05-18T12:32:13.499390+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/ALVHO6PDNMN64ZP6YP75EAK3CX","json":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX.json","graph_json":"https://pith.science/api/pith-number/ALVHO6PDNMN64ZP6YP75EAK3CX/graph.json","events_json":"https://pith.science/api/pith-number/ALVHO6PDNMN64ZP6YP75EAK3CX/events.json","paper":"https://pith.science/paper/ALVHO6PD"},"agent_actions":{"view_html":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX","download_json":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX.json","view_paper":"https://pith.science/paper/ALVHO6PD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.08196&json=true","fetch_graph":"https://pith.science/api/pith-number/ALVHO6PDNMN64ZP6YP75EAK3CX/graph.json","fetch_events":"https://pith.science/api/pith-number/ALVHO6PDNMN64ZP6YP75EAK3CX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX/action/storage_attestation","attest_author":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX/action/author_attestation","sign_citation":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX/action/citation_signature","submit_replication":"https://pith.science/pith/ALVHO6PDNMN64ZP6YP75EAK3CX/action/replication_record"}},"created_at":"2026-05-18T00:09:35.455396+00:00","updated_at":"2026-05-18T00:09:35.455396+00:00"}