{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MPCVI6VJWG5W7L5F3GVHXSVMN7","short_pith_number":"pith:MPCVI6VJ","schema_version":"1.0","canonical_sha256":"63c5547aa9b1bb6fafa5d9aa7bcaac6fdfb8dbc74f52f6ee1a457614f3a3a86b","source":{"kind":"arxiv","id":"1507.06859","version":2},"attestation_state":"computed","paper":{"title":"Path lifting properties and embedding between RAAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eon-Kyung Lee, Sang-Jin Lee","submitted_at":"2015-07-24T14:32:02Z","abstract_excerpt":"For a finite simplicial graph $\\Gamma$, let $G(\\Gamma)$ denote the right-angled Artin group on the complement graph of $\\Gamma$. In this article, we introduce the notions of \"induced path lifting property\" and \"semi-induced path lifting property\" for immersions between graphs, and obtain graph theoretical criteria for the embedability between right-angled Artin groups. We recover the result of S.-h.{} Kim and T.{} Koberda that an arbitrary $G(\\Gamma)$ admits a quasi-isometric group embedding into $G(T)$ for some finite tree $T$. The upper bound on the number of vertices of $T$ is improved from"},"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":"1507.06859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-24T14:32:02Z","cross_cats_sorted":[],"title_canon_sha256":"ee4ee6d222f22fc446d1f9494ce67dfab31a5f19fff20013ad677b9e65fc2a84","abstract_canon_sha256":"df044dcdd93ad348f9c00c9cba20224f4f5a581e78d4a2475cc4794ed8642e1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:32.867471Z","signature_b64":"bsoy5ITROWKFTv8spSeFDd4EDrJu/0DyNvmvQ0en7ayoyuSYhCwczZBsctOgE+k5yWzq6o43NZqMv4eqhhlDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63c5547aa9b1bb6fafa5d9aa7bcaac6fdfb8dbc74f52f6ee1a457614f3a3a86b","last_reissued_at":"2026-05-18T01:24:32.867004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:32.867004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Path lifting properties and embedding between RAAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eon-Kyung Lee, Sang-Jin Lee","submitted_at":"2015-07-24T14:32:02Z","abstract_excerpt":"For a finite simplicial graph $\\Gamma$, let $G(\\Gamma)$ denote the right-angled Artin group on the complement graph of $\\Gamma$. In this article, we introduce the notions of \"induced path lifting property\" and \"semi-induced path lifting property\" for immersions between graphs, and obtain graph theoretical criteria for the embedability between right-angled Artin groups. We recover the result of S.-h.{} Kim and T.{} Koberda that an arbitrary $G(\\Gamma)$ admits a quasi-isometric group embedding into $G(T)$ for some finite tree $T$. The upper bound on the number of vertices of $T$ is improved from"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06859","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":"1507.06859","created_at":"2026-05-18T01:24:32.867072+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06859v2","created_at":"2026-05-18T01:24:32.867072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06859","created_at":"2026-05-18T01:24:32.867072+00:00"},{"alias_kind":"pith_short_12","alias_value":"MPCVI6VJWG5W","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MPCVI6VJWG5W7L5F","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MPCVI6VJ","created_at":"2026-05-18T12:29:32.376354+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/MPCVI6VJWG5W7L5F3GVHXSVMN7","json":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7.json","graph_json":"https://pith.science/api/pith-number/MPCVI6VJWG5W7L5F3GVHXSVMN7/graph.json","events_json":"https://pith.science/api/pith-number/MPCVI6VJWG5W7L5F3GVHXSVMN7/events.json","paper":"https://pith.science/paper/MPCVI6VJ"},"agent_actions":{"view_html":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7","download_json":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7.json","view_paper":"https://pith.science/paper/MPCVI6VJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06859&json=true","fetch_graph":"https://pith.science/api/pith-number/MPCVI6VJWG5W7L5F3GVHXSVMN7/graph.json","fetch_events":"https://pith.science/api/pith-number/MPCVI6VJWG5W7L5F3GVHXSVMN7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7/action/storage_attestation","attest_author":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7/action/author_attestation","sign_citation":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7/action/citation_signature","submit_replication":"https://pith.science/pith/MPCVI6VJWG5W7L5F3GVHXSVMN7/action/replication_record"}},"created_at":"2026-05-18T01:24:32.867072+00:00","updated_at":"2026-05-18T01:24:32.867072+00:00"}