{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BCUC7LLIS67GFTCKO73T3H7WYX","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":"9837baff3d820fb44d1b1d5b74d2873c87bbef6fafb534e3c63a55f5d01f3bc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-01T13:14:17Z","title_canon_sha256":"450e5b622df617bb4bb940d91d2a1a03c4f0c49338d0ff51d6507e25c0d1bc3c"},"schema_version":"1.0","source":{"id":"1203.0176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0176","created_at":"2026-05-18T04:01:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0176v1","created_at":"2026-05-18T04:01:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0176","created_at":"2026-05-18T04:01:02Z"},{"alias_kind":"pith_short_12","alias_value":"BCUC7LLIS67G","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BCUC7LLIS67GFTCK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BCUC7LLI","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:ec77fa8466854974df1df7f96725b22c89977681329668c9c6c35d6873e703af","target":"graph","created_at":"2026-05-18T04:01:02Z","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":"We consider \"bridges\" for the simple exclusion process on Z, either symmetric or asymmetric, in which particles jump to the right at rate p and to the left at rate 1-p. The initial state O has all negative sites occupied and all non-negative sites empty. We study the probability that the process is again in state O at time t, and the behaviour of the process on [0,t] conditioned on being in state O at time t. In the case p=1/2, we find that such a bridge typically goes a distance of order t (in the sense of graph distance) from the initial state. For the asymmetric systems, we note an interest","authors_text":"James B. Martin, Pablo A. Ferrari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-01T13:14:17Z","title":"How to squeeze the toothpaste back into the tube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0176","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":"sha256:900bf0fc2dac8cf32977e63146fa9584176dabbb223877c065243d27b25cb6fe","target":"record","created_at":"2026-05-18T04:01:02Z","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":"9837baff3d820fb44d1b1d5b74d2873c87bbef6fafb534e3c63a55f5d01f3bc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-01T13:14:17Z","title_canon_sha256":"450e5b622df617bb4bb940d91d2a1a03c4f0c49338d0ff51d6507e25c0d1bc3c"},"schema_version":"1.0","source":{"id":"1203.0176","kind":"arxiv","version":1}},"canonical_sha256":"08a82fad6897be62cc4a77f73d9ff6c5ca583c5f289d8e6ce2ad7faaf062d30f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08a82fad6897be62cc4a77f73d9ff6c5ca583c5f289d8e6ce2ad7faaf062d30f","first_computed_at":"2026-05-18T04:01:02.962171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:02.962171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+Qg+5H7KJ8amd5/vDFzdHfmVRNcHBhafnAJA5tbfn+gJJbP9B3cDhptwQqPiMojOxUssuebdFhXIIJvp2fmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:02.962862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:900bf0fc2dac8cf32977e63146fa9584176dabbb223877c065243d27b25cb6fe","sha256:ec77fa8466854974df1df7f96725b22c89977681329668c9c6c35d6873e703af"],"state_sha256":"a7c58c4bc86960b1c4cf9b1ff981ed406cf489f6ec92b062fe26dd134bd48e4c"}