{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BSXD7ITSMVHGVSITUTT4FJKLT3","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":"7652e6c787aa9509d6e8e1081d8a95fe003452e7c9fa934f3c2b41d98ea64936","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T11:07:42Z","title_canon_sha256":"d08d94b9452674dd608f3b4b7bd8c1c964bfbc4fc376bf7ef131c09cd3e3aec9"},"schema_version":"1.0","source":{"id":"1306.5917","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5917","created_at":"2026-05-18T01:32:57Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5917v4","created_at":"2026-05-18T01:32:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5917","created_at":"2026-05-18T01:32:57Z"},{"alias_kind":"pith_short_12","alias_value":"BSXD7ITSMVHG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BSXD7ITSMVHGVSIT","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BSXD7ITS","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:18c8f8d8904e2ce1a477afdac7c8143d2e5b07b4ab64529a8c0d048a0ad4a70b","target":"graph","created_at":"2026-05-18T01:32:57Z","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 first passage percolation with i.i.d. weights on edges of the d-dimensional cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the d-dimensional cubic lattice, and has moments bigger than 1, we investigate upper bounds on the so-called non-random fluctuations of the model. In addition, we give an application of our result to a lower bound for variance of the first passage percolation in the case where the limit shape has flat edges.","authors_text":"Naoki Kubota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T11:07:42Z","title":"Upper bounds on the non-random fluctuations in first passage percolation with low moment conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5917","kind":"arxiv","version":4},"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:cdd55b69f261ff592b6bd93b952e0151ed9300a56eef1f68da426a09fe25fdaa","target":"record","created_at":"2026-05-18T01:32:57Z","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":"7652e6c787aa9509d6e8e1081d8a95fe003452e7c9fa934f3c2b41d98ea64936","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T11:07:42Z","title_canon_sha256":"d08d94b9452674dd608f3b4b7bd8c1c964bfbc4fc376bf7ef131c09cd3e3aec9"},"schema_version":"1.0","source":{"id":"1306.5917","kind":"arxiv","version":4}},"canonical_sha256":"0cae3fa272654e6ac913a4e7c2a54b9ef471ff909ee237d48381f333a153da03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cae3fa272654e6ac913a4e7c2a54b9ef471ff909ee237d48381f333a153da03","first_computed_at":"2026-05-18T01:32:57.978270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:57.978270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NnK9IUaTewrYkggSdYSpEH9U0JLSb1DFoVp1M3DI4n06t6jOU5XTr9XRppTVOhWyUZ9z43jDCmvIrwJQ4IrqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:57.978994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5917","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd55b69f261ff592b6bd93b952e0151ed9300a56eef1f68da426a09fe25fdaa","sha256:18c8f8d8904e2ce1a477afdac7c8143d2e5b07b4ab64529a8c0d048a0ad4a70b"],"state_sha256":"7cbe54a21c40c7c481a8afdc882ac412141064c11186d41b3ac88ce88b492666"}