{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WYAZJWEHRAU5BUNBXIA27LD5JK","short_pith_number":"pith:WYAZJWEH","schema_version":"1.0","canonical_sha256":"b60194d8878829d0d1a1ba01afac7d4a816d794f97590416fbb4b565f0daeb34","source":{"kind":"arxiv","id":"2606.28890","version":1},"attestation_state":"computed","paper":{"title":"Logarithmic convergence of finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Ander Lamaison, Aranka Hru\\v{s}kov\\'a, M\\'arton Borb\\'enyi, Panna T\\'imea Fekete","submitted_at":"2026-06-27T12:34:35Z","abstract_excerpt":"In this paper, we study the so-called log-convergence of graphs defined by Bal\\'azs Szegedy (arXiv:1504.00858). We answer his Question 4 affirmatively: the sequence of incidence graphs of projective planes over finite fields log-converges, and the limit coincides with that of a particular random graph model."},"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":"2606.28890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-27T12:34:35Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"93d52ce039dd1e1ab6b88b508ffd94b24bf0be30f061dbb9c129dd485f55e521","abstract_canon_sha256":"19dcedc0affc71e634ae83a683a213dc9f27c2dc5102def1a7aa8d2474a442ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:43.909082Z","signature_b64":"0VvPR4kCGUYGus/gzAH/V7KTbSL06ao/ECGq3nqMwOa4jPH29WO0oY9OeKULT6s+o589yfcxwgh+Etjl8ixWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b60194d8878829d0d1a1ba01afac7d4a816d794f97590416fbb4b565f0daeb34","last_reissued_at":"2026-06-30T01:17:43.908336Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:43.908336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic convergence of finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Ander Lamaison, Aranka Hru\\v{s}kov\\'a, M\\'arton Borb\\'enyi, Panna T\\'imea Fekete","submitted_at":"2026-06-27T12:34:35Z","abstract_excerpt":"In this paper, we study the so-called log-convergence of graphs defined by Bal\\'azs Szegedy (arXiv:1504.00858). We answer his Question 4 affirmatively: the sequence of incidence graphs of projective planes over finite fields log-converges, and the limit coincides with that of a particular random graph model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28890","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28890/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":"2606.28890","created_at":"2026-06-30T01:17:43.908465+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.28890v1","created_at":"2026-06-30T01:17:43.908465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28890","created_at":"2026-06-30T01:17:43.908465+00:00"},{"alias_kind":"pith_short_12","alias_value":"WYAZJWEHRAU5","created_at":"2026-06-30T01:17:43.908465+00:00"},{"alias_kind":"pith_short_16","alias_value":"WYAZJWEHRAU5BUNB","created_at":"2026-06-30T01:17:43.908465+00:00"},{"alias_kind":"pith_short_8","alias_value":"WYAZJWEH","created_at":"2026-06-30T01:17:43.908465+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/WYAZJWEHRAU5BUNBXIA27LD5JK","json":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK.json","graph_json":"https://pith.science/api/pith-number/WYAZJWEHRAU5BUNBXIA27LD5JK/graph.json","events_json":"https://pith.science/api/pith-number/WYAZJWEHRAU5BUNBXIA27LD5JK/events.json","paper":"https://pith.science/paper/WYAZJWEH"},"agent_actions":{"view_html":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK","download_json":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK.json","view_paper":"https://pith.science/paper/WYAZJWEH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.28890&json=true","fetch_graph":"https://pith.science/api/pith-number/WYAZJWEHRAU5BUNBXIA27LD5JK/graph.json","fetch_events":"https://pith.science/api/pith-number/WYAZJWEHRAU5BUNBXIA27LD5JK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK/action/storage_attestation","attest_author":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK/action/author_attestation","sign_citation":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK/action/citation_signature","submit_replication":"https://pith.science/pith/WYAZJWEHRAU5BUNBXIA27LD5JK/action/replication_record"}},"created_at":"2026-06-30T01:17:43.908465+00:00","updated_at":"2026-06-30T01:17:43.908465+00:00"}