{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:P4ZE7M6DYSCGYWDZVIQNIKKK3Y","short_pith_number":"pith:P4ZE7M6D","schema_version":"1.0","canonical_sha256":"7f324fb3c3c4846c5879aa20d4294ade13481d775f3469de82db8afcb189856b","source":{"kind":"arxiv","id":"1601.05580","version":1},"attestation_state":"computed","paper":{"title":"Treeable Graphings Are Local Limits of Finite Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Hosseini, Patrice Ossona de Mendez","submitted_at":"2016-01-21T10:29:11Z","abstract_excerpt":"Let $\\mathbf G$ be a graphing, that is a Borel graph defined by $d$ measure preserving involutions. We prove that if $\\mathbf G$ is {\\em treeable} then it arises as the local limit of some sequence $(G_n)_{n\\in\\mathbb{N}}$ of graphs with maximum degree at most $d$. This extends a result by Elek [G. Elek, Note on limits of finite graphs, Combinatorica 27 (2007)] (for $\\mathbf G$ a treeing) and consequently extends the domain of the graphings for which Aldous-Lyons conjecture is known to be true."},"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":"1601.05580","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2016-01-21T10:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"3c7541d449f5f30a7f96187955a3f13d6b561b559482829cfb328757a67553da","abstract_canon_sha256":"44d4afbeb47b39a1673fe95141342ae6a6fb8124b9797c45a29599a95426140b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:13.458092Z","signature_b64":"0ek6++sCCJeATQJ+JnC/BXEFMso2yV1DCUar25E4I3b3VeP3l9qu4E3BxKb+hoWNMGVxtGDU1Jhw5Jw1x+VdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f324fb3c3c4846c5879aa20d4294ade13481d775f3469de82db8afcb189856b","last_reissued_at":"2026-05-18T01:22:13.457516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:13.457516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Treeable Graphings Are Local Limits of Finite Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Hosseini, Patrice Ossona de Mendez","submitted_at":"2016-01-21T10:29:11Z","abstract_excerpt":"Let $\\mathbf G$ be a graphing, that is a Borel graph defined by $d$ measure preserving involutions. We prove that if $\\mathbf G$ is {\\em treeable} then it arises as the local limit of some sequence $(G_n)_{n\\in\\mathbb{N}}$ of graphs with maximum degree at most $d$. This extends a result by Elek [G. Elek, Note on limits of finite graphs, Combinatorica 27 (2007)] (for $\\mathbf G$ a treeing) and consequently extends the domain of the graphings for which Aldous-Lyons conjecture is known to be true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05580","kind":"arxiv","version":1},"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":"1601.05580","created_at":"2026-05-18T01:22:13.457597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.05580v1","created_at":"2026-05-18T01:22:13.457597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05580","created_at":"2026-05-18T01:22:13.457597+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4ZE7M6DYSCG","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4ZE7M6DYSCGYWDZ","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4ZE7M6D","created_at":"2026-05-18T12:30:36.002864+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/P4ZE7M6DYSCGYWDZVIQNIKKK3Y","json":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y.json","graph_json":"https://pith.science/api/pith-number/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/graph.json","events_json":"https://pith.science/api/pith-number/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/events.json","paper":"https://pith.science/paper/P4ZE7M6D"},"agent_actions":{"view_html":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y","download_json":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y.json","view_paper":"https://pith.science/paper/P4ZE7M6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.05580&json=true","fetch_graph":"https://pith.science/api/pith-number/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/action/storage_attestation","attest_author":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/action/author_attestation","sign_citation":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/action/citation_signature","submit_replication":"https://pith.science/pith/P4ZE7M6DYSCGYWDZVIQNIKKK3Y/action/replication_record"}},"created_at":"2026-05-18T01:22:13.457597+00:00","updated_at":"2026-05-18T01:22:13.457597+00:00"}