{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E4Y54UCVYMWCNVBF3L674XBN3N","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":"0da0d82e1373e2e06ad86c6fa3e2e69adacc15217525ff72136bbf6ebc742042","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-26T14:48:27Z","title_canon_sha256":"fc14e4a3aca4c36036e63eae912052ef6faacf54438aa3b5684a917d62169210"},"schema_version":"1.0","source":{"id":"1211.5974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5974","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5974v1","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5974","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"E4Y54UCVYMWC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E4Y54UCVYMWCNVBF","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E4Y54UCV","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:e971ff53b83d416e7c9ec044374e7d1a108f96873dd280cbcae314d98b800586","target":"graph","created_at":"2026-05-18T03:39:53Z","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":"On the rooted $k$-ary tree we consider a 0-1 kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are empty. For this process the following picture was conjectured to hold. As long as $p$ is below the percolation threshold $p_c=1/k$ the process is ergodic with a finite relaxation time while, for $p>p_c$, the process on the infinite tree is no longer ergodic and the relaxation time on a finite regular sub-tree becomes exponentially large in the depth of the tree. At the critical point $p=p_","authors_text":"Cristina Toninelli, Cyril Roberto, Fabio Martinelli, Nicoletta Cancrini","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-26T14:48:27Z","title":"Mixing time of a kinetically constrained spin model on trees: power law scaling at criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5974","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":"sha256:01460ee92b987a720e6ed9a6e29794aff53a994252f4da8d1abf7a83c6c65eb6","target":"record","created_at":"2026-05-18T03:39:53Z","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":"0da0d82e1373e2e06ad86c6fa3e2e69adacc15217525ff72136bbf6ebc742042","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-26T14:48:27Z","title_canon_sha256":"fc14e4a3aca4c36036e63eae912052ef6faacf54438aa3b5684a917d62169210"},"schema_version":"1.0","source":{"id":"1211.5974","kind":"arxiv","version":1}},"canonical_sha256":"2731de5055c32c26d425dafdfe5c2ddb56b750a4a1b46d1fe317bcdb0110b2c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2731de5055c32c26d425dafdfe5c2ddb56b750a4a1b46d1fe317bcdb0110b2c5","first_computed_at":"2026-05-18T03:39:53.700601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:53.700601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mfgdP0T9zteAtVDCduxCNbys7BQIl1GGBjvo6C6nlhSOboRoGkIolsEUVEsJaqKzUu5j1BR/jePUta8+yyTBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:53.701328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01460ee92b987a720e6ed9a6e29794aff53a994252f4da8d1abf7a83c6c65eb6","sha256:e971ff53b83d416e7c9ec044374e7d1a108f96873dd280cbcae314d98b800586"],"state_sha256":"b1966bebf2f539c23bf5fc7a67f240db820247d20d38b882c192df11bc30cb51"}