{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MMCQCTE4QEEMQYYMG6WPQO5IIY","short_pith_number":"pith:MMCQCTE4","schema_version":"1.0","canonical_sha256":"6305014c9c8108c8630c37acf83ba8463b37b4decbf4fdbc7b716e0715e21a3d","source":{"kind":"arxiv","id":"1801.04459","version":1},"attestation_state":"computed","paper":{"title":"Graph Laplace and Markov operators on a measure space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OA"],"primary_cat":"math.FA","authors_text":"Palle E.T. Jorgensen, Sergey Bezuglyi","submitted_at":"2018-01-13T15:58:47Z","abstract_excerpt":"The main goal of this paper is to build a measurable analogue to the theory of weighted networks on infinite graphs. Our basic setting is an infinite $\\sigma$-finite measure space $(V, \\mathcal B, \\mu)$ and a symmetric measure $\\rho$ on $(V\\times V, \\mathcal B\\times \\mathcal B)$ supported by a measurable symmetric subset $E\\subset V\\times V$. This applies to such diverse areas as optimization, graphons (limits of finite graphs), symbolic dynamics, measurable equivalence relations, to determinantal processes, to jump-processes; and it extends earlier studies of infinite graphs $G = (V, E)$ whic"},"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":"1801.04459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-13T15:58:47Z","cross_cats_sorted":["math.DS","math.OA"],"title_canon_sha256":"ac550c3af66f95f8d70f7137d661812d030c7e5df10221fe2b8d7d5afd04ee60","abstract_canon_sha256":"ee73aebd16917946da59925c9fb11ea27270f2632553c3c1dcaa670a15abf58f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:06.429603Z","signature_b64":"azGwKqt/q1qKqPU7fdqO9DXu2bp1RUeqcoKjDjOgoU8OaOILuDKH/pKOhTb+RMT52KzAejxUsQXw9mQPm3+fCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6305014c9c8108c8630c37acf83ba8463b37b4decbf4fdbc7b716e0715e21a3d","last_reissued_at":"2026-05-18T00:26:06.429105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:06.429105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph Laplace and Markov operators on a measure space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OA"],"primary_cat":"math.FA","authors_text":"Palle E.T. Jorgensen, Sergey Bezuglyi","submitted_at":"2018-01-13T15:58:47Z","abstract_excerpt":"The main goal of this paper is to build a measurable analogue to the theory of weighted networks on infinite graphs. Our basic setting is an infinite $\\sigma$-finite measure space $(V, \\mathcal B, \\mu)$ and a symmetric measure $\\rho$ on $(V\\times V, \\mathcal B\\times \\mathcal B)$ supported by a measurable symmetric subset $E\\subset V\\times V$. This applies to such diverse areas as optimization, graphons (limits of finite graphs), symbolic dynamics, measurable equivalence relations, to determinantal processes, to jump-processes; and it extends earlier studies of infinite graphs $G = (V, E)$ whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04459","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":"1801.04459","created_at":"2026-05-18T00:26:06.429180+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04459v1","created_at":"2026-05-18T00:26:06.429180+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04459","created_at":"2026-05-18T00:26:06.429180+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMCQCTE4QEEM","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMCQCTE4QEEMQYYM","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMCQCTE4","created_at":"2026-05-18T12:32:37.024351+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/MMCQCTE4QEEMQYYMG6WPQO5IIY","json":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY.json","graph_json":"https://pith.science/api/pith-number/MMCQCTE4QEEMQYYMG6WPQO5IIY/graph.json","events_json":"https://pith.science/api/pith-number/MMCQCTE4QEEMQYYMG6WPQO5IIY/events.json","paper":"https://pith.science/paper/MMCQCTE4"},"agent_actions":{"view_html":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY","download_json":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY.json","view_paper":"https://pith.science/paper/MMCQCTE4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04459&json=true","fetch_graph":"https://pith.science/api/pith-number/MMCQCTE4QEEMQYYMG6WPQO5IIY/graph.json","fetch_events":"https://pith.science/api/pith-number/MMCQCTE4QEEMQYYMG6WPQO5IIY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY/action/storage_attestation","attest_author":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY/action/author_attestation","sign_citation":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY/action/citation_signature","submit_replication":"https://pith.science/pith/MMCQCTE4QEEMQYYMG6WPQO5IIY/action/replication_record"}},"created_at":"2026-05-18T00:26:06.429180+00:00","updated_at":"2026-05-18T00:26:06.429180+00:00"}