{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XXIMCWSPRFS4JECB27LA77W256","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":"6ed3c2c4bf23e37056e09b1134252b2b634e20f0a62dbc3e091e7e4f2c87e567","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T10:49:24Z","title_canon_sha256":"3a91c3cfa7031e7238a32931b2c349481ab7002ef1050573e5838488aea1a63c"},"schema_version":"1.0","source":{"id":"1512.02397","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02397","created_at":"2026-05-18T00:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02397v3","created_at":"2026-05-18T00:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02397","created_at":"2026-05-18T00:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"XXIMCWSPRFS4","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XXIMCWSPRFS4JECB","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XXIMCWSP","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:75fae3e4a4ff6f799727beccde017664d5c7743b946c6b7f8383f39e85b33d60","target":"graph","created_at":"2026-05-18T00:28:07Z","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":"We consider the activated random walk model on general vertex-transitive graphs. A central question in this model is whether the critical density $\\mu_c$ for sustained activity is strictly between 0 and 1. It was known that $\\mu_c>0$ on $\\mathbb{Z}^d$, $d\\geq 1$, and that $\\mu_c<1$ on $\\mathbb{Z}$ for small enough sleeping rate. We show that $\\mu_c\\to 0$ as $\\lambda\\to 0$ in all vertex-transitive transient graphs, implying that $\\mu_c<1$ for small enough sleeping rate. We also show that $\\mu_c<1$ for any sleeping rate in any vertex-transitive graph in which simple random walk has positive spee","authors_text":"Alexandre Stauffer, Lorenzo Taggi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T10:49:24Z","title":"Critical density of activated random walks on transitive graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02397","kind":"arxiv","version":3},"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":"sha256:8461a56e5ed8ce090a63f230245e7f27de7b31f4b938bb4680704b2a40b77f49","target":"record","created_at":"2026-05-18T00:28:07Z","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":"6ed3c2c4bf23e37056e09b1134252b2b634e20f0a62dbc3e091e7e4f2c87e567","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-08T10:49:24Z","title_canon_sha256":"3a91c3cfa7031e7238a32931b2c349481ab7002ef1050573e5838488aea1a63c"},"schema_version":"1.0","source":{"id":"1512.02397","kind":"arxiv","version":3}},"canonical_sha256":"bdd0c15a4f8965c49041d7d60ffedaefb6ef287c0f83821487217cb37faf7b37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdd0c15a4f8965c49041d7d60ffedaefb6ef287c0f83821487217cb37faf7b37","first_computed_at":"2026-05-18T00:28:07.413065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:07.413065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJ8ZGgv1yYfeCPHq3wGlbNT0gcCrbvYpYFfMFdq/i2gWeWdONwCgR05RZKq/ObX2uxasA/uUGLxwisI8fYfCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:07.413688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02397","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8461a56e5ed8ce090a63f230245e7f27de7b31f4b938bb4680704b2a40b77f49","sha256:75fae3e4a4ff6f799727beccde017664d5c7743b946c6b7f8383f39e85b33d60"],"state_sha256":"fe29be34e79da01ac97521ac2537c74d8e36c0eb275e8588926c249e2548ba10"}