{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OO3XA2TY6R2I7OYNFKYVYOUWGL","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":"5f5b50ad9d2eca706e2df6eee4d8dea327ce47bf693aa045620d532ebd9e92cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-20T18:11:26Z","title_canon_sha256":"bb6891e6702384847603f0d0d0f7bf40644e76e4b9e0b9a9ba88330fb6da53bd"},"schema_version":"1.0","source":{"id":"1510.05995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05995","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05995v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05995","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"OO3XA2TY6R2I","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OO3XA2TY6R2I7OYN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OO3XA2TY","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:c6bba1e224af1fedffbe8b1a9e2b24daa927edae31443f18a883935c9af2baba","target":"graph","created_at":"2026-05-18T01:29:39Z","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 frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumor spreading model. We given an alternate and elementary proof that the wake-up time, i.e. the expected time for every particle to be activated, is Theta(log n). Additionally, we give an explicit distributional equation for the wakeup time as a weighted sum of geometric random variables. This project was part of the University of Washington Research Experience for Undergraduates program.","authors_text":"Andrew You, Austin Stromme, Brittany Dygert, Collin Litterell, Matthew Junge, Nikki Cartern, Stephen Lacina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-20T18:11:26Z","title":"Frog model wakeup time on the complete graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05995","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":"sha256:4c98a6b6f7beb0e238b088bac59ac2c24090984b2c2cc38d7bf0ba2c6e8196eb","target":"record","created_at":"2026-05-18T01:29:39Z","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":"5f5b50ad9d2eca706e2df6eee4d8dea327ce47bf693aa045620d532ebd9e92cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-20T18:11:26Z","title_canon_sha256":"bb6891e6702384847603f0d0d0f7bf40644e76e4b9e0b9a9ba88330fb6da53bd"},"schema_version":"1.0","source":{"id":"1510.05995","kind":"arxiv","version":1}},"canonical_sha256":"73b7706a78f4748fbb0d2ab15c3a9632e52e519009020044aed1975891d9c336","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73b7706a78f4748fbb0d2ab15c3a9632e52e519009020044aed1975891d9c336","first_computed_at":"2026-05-18T01:29:39.174016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:39.174016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UxHfxxcYU+xUveHEYiWs1xu9j0HEF8G+knfMsBQaaXDqNIlxaS8l9ZNzoUmgwx45K7iv5fmGd965rHwEz1ZjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:39.174648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c98a6b6f7beb0e238b088bac59ac2c24090984b2c2cc38d7bf0ba2c6e8196eb","sha256:c6bba1e224af1fedffbe8b1a9e2b24daa927edae31443f18a883935c9af2baba"],"state_sha256":"9ae567c44f37f22f22d7cc0c325088c562248cc1c3610642e39a0649cf8113d4"}