{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7ZAWE7OCJ3S5L6Z3JIJBUYTYSW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ddec791b86601a83f08e95881a417a9898c37c7c1a661a8ecb15b090884a948d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-24T15:49:10Z","title_canon_sha256":"50b4b7afd199d2bf4e716f32e6d6d89f7d4c5d0aceae00b0637b36119ae64222"},"schema_version":"1.0","source":{"id":"1805.09744","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09744","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09744v1","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09744","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"7ZAWE7OCJ3S5","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"7ZAWE7OCJ3S5L6Z3","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"7ZAWE7OC","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:376b5e9d8330fcbe8b798d3ffb96b863462e0bff96707d8744f61940a2ced334","target":"graph","created_at":"2026-05-18T00:15:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The purpose of these short notes is to provide a concise proof of a celebrated theorem by Dembo, Peres, Rosen and Zeitouni, which settles the leading order of cover times in the small-\\varepsilon regime.","authors_text":"Marius A. Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-24T15:49:10Z","title":"A Simple Proof of the DPRZ-Theorem for 2D Cover Times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09744","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa4773fefcd8253705ee9220ff873d3c21002a180ab84f3bfa5e0a4e6804d6b8","target":"record","created_at":"2026-05-18T00:15:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ddec791b86601a83f08e95881a417a9898c37c7c1a661a8ecb15b090884a948d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-24T15:49:10Z","title_canon_sha256":"50b4b7afd199d2bf4e716f32e6d6d89f7d4c5d0aceae00b0637b36119ae64222"},"schema_version":"1.0","source":{"id":"1805.09744","kind":"arxiv","version":1}},"canonical_sha256":"fe41627dc24ee5d5fb3b4a121a627895a6b17d376c0041c18cb194aaed814c2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe41627dc24ee5d5fb3b4a121a627895a6b17d376c0041c18cb194aaed814c2c","first_computed_at":"2026-05-18T00:15:02.943520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:02.943520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bT61E+KsmKLSNpo6JRsS+AhjNijwlRcdT8OAAkdCfntrJI2Hhr2GzhNpDKicQyT8y29hyw9X0tPy0nOkiADLAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:02.944262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09744","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa4773fefcd8253705ee9220ff873d3c21002a180ab84f3bfa5e0a4e6804d6b8","sha256:376b5e9d8330fcbe8b798d3ffb96b863462e0bff96707d8744f61940a2ced334"],"state_sha256":"1feda983c3db39a3412ae18ce925f6fd861caec9a9762839e42911e6d7ec98d8"}