{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:2F4OMZXTJXXQDZMBFUMJL4CAXT","short_pith_number":"pith:2F4OMZXT","canonical_record":{"source":{"id":"0804.1165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-04-08T01:02:21Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"c5dbcf07264409b7b10ddacbe5861f07575db1bba63d590b7fbb325e71c9505a","abstract_canon_sha256":"8411978f48be52c4a53b924a2ae82b8f5c0fd491ce6d261878fd2a8dbfb670cf"},"schema_version":"1.0"},"canonical_sha256":"d178e666f34def01e5812d1895f040bcf288ee3e8d1be7ce2918003604a2a7cc","source":{"kind":"arxiv","id":"0804.1165","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.1165","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"0804.1165v1","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.1165","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"2F4OMZXTJXXQ","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"pith_short_16","alias_value":"2F4OMZXTJXXQDZMB","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"pith_short_8","alias_value":"2F4OMZXT","created_at":"2026-07-04T15:11:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:2F4OMZXTJXXQDZMBFUMJL4CAXT","target":"record","payload":{"canonical_record":{"source":{"id":"0804.1165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-04-08T01:02:21Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"c5dbcf07264409b7b10ddacbe5861f07575db1bba63d590b7fbb325e71c9505a","abstract_canon_sha256":"8411978f48be52c4a53b924a2ae82b8f5c0fd491ce6d261878fd2a8dbfb670cf"},"schema_version":"1.0"},"canonical_sha256":"d178e666f34def01e5812d1895f040bcf288ee3e8d1be7ce2918003604a2a7cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:11:35.419017Z","signature_b64":"YM026eOlq//tGbmZab0wcMG7WT+YbPxINnjFNHs9S9QBljgYYeIbCCVT5xhIsupsAa+MJZMNi+LnMdRO5bE7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d178e666f34def01e5812d1895f040bcf288ee3e8d1be7ce2918003604a2a7cc","last_reissued_at":"2026-07-04T15:11:35.418618Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:11:35.418618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0804.1165","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:11:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jPbO98pX7s/ul9Rmz4OHN3QtBekGeU/HxgzTQMegOGaZQcfyeGegBXpH790Qoe4hjTvbbTGiQhAaUi1Qrs3CBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:17:25.465614Z"},"content_sha256":"32b0e601d2eabddf96c83348589275bfc8364c847ee553517d552815f6fcb3b4","schema_version":"1.0","event_id":"sha256:32b0e601d2eabddf96c83348589275bfc8364c847ee553517d552815f6fcb3b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:2F4OMZXTJXXQDZMBFUMJL4CAXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How rare are diffusive rare events?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"David P. Sanders, Hern\\'an Larralde (Instituto de Ciencias F\\'isicas, Universidad Nacional Aut\\'onoma de M\\'exico)","submitted_at":"2008-04-08T01:02:21Z","abstract_excerpt":"We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers can jump anywhere in the system, we obtain a simple asymptotic form for the mean first-passage time to have a given number k of particles at a distinguished site. We show numerically, and argue heuristically, that for large enough k, the mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1165","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0804.1165/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:11:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsIE0ezImszwu0wePQBXB4m/Uk2BM3Q2fOqzNeveiTDQWB0uxPkF8R1Ak1w2DfR81xiB5At92Zt1Qvvs985eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:17:25.466188Z"},"content_sha256":"e0cbced06abd71627023e401bacb169f1d6950fc2252508097a42c20b52ff193","schema_version":"1.0","event_id":"sha256:e0cbced06abd71627023e401bacb169f1d6950fc2252508097a42c20b52ff193"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT/bundle.json","state_url":"https://pith.science/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T00:17:25Z","links":{"resolver":"https://pith.science/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT","bundle":"https://pith.science/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT/bundle.json","state":"https://pith.science/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2F4OMZXTJXXQDZMBFUMJL4CAXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2F4OMZXTJXXQDZMBFUMJL4CAXT","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":"8411978f48be52c4a53b924a2ae82b8f5c0fd491ce6d261878fd2a8dbfb670cf","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-04-08T01:02:21Z","title_canon_sha256":"c5dbcf07264409b7b10ddacbe5861f07575db1bba63d590b7fbb325e71c9505a"},"schema_version":"1.0","source":{"id":"0804.1165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.1165","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"0804.1165v1","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.1165","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"2F4OMZXTJXXQ","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"pith_short_16","alias_value":"2F4OMZXTJXXQDZMB","created_at":"2026-07-04T15:11:35Z"},{"alias_kind":"pith_short_8","alias_value":"2F4OMZXT","created_at":"2026-07-04T15:11:35Z"}],"graph_snapshots":[{"event_id":"sha256:e0cbced06abd71627023e401bacb169f1d6950fc2252508097a42c20b52ff193","target":"graph","created_at":"2026-07-04T15:11:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0804.1165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers can jump anywhere in the system, we obtain a simple asymptotic form for the mean first-passage time to have a given number k of particles at a distinguished site. We show numerically, and argue heuristically, that for large enough k, the mea","authors_text":"David P. Sanders, Hern\\'an Larralde (Instituto de Ciencias F\\'isicas, Universidad Nacional Aut\\'onoma de M\\'exico)","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-04-08T01:02:21Z","title":"How rare are diffusive rare events?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1165","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":"sha256:32b0e601d2eabddf96c83348589275bfc8364c847ee553517d552815f6fcb3b4","target":"record","created_at":"2026-07-04T15:11:35Z","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":"8411978f48be52c4a53b924a2ae82b8f5c0fd491ce6d261878fd2a8dbfb670cf","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-04-08T01:02:21Z","title_canon_sha256":"c5dbcf07264409b7b10ddacbe5861f07575db1bba63d590b7fbb325e71c9505a"},"schema_version":"1.0","source":{"id":"0804.1165","kind":"arxiv","version":1}},"canonical_sha256":"d178e666f34def01e5812d1895f040bcf288ee3e8d1be7ce2918003604a2a7cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d178e666f34def01e5812d1895f040bcf288ee3e8d1be7ce2918003604a2a7cc","first_computed_at":"2026-07-04T15:11:35.418618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:11:35.418618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YM026eOlq//tGbmZab0wcMG7WT+YbPxINnjFNHs9S9QBljgYYeIbCCVT5xhIsupsAa+MJZMNi+LnMdRO5bE7Cg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:11:35.419017Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.1165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32b0e601d2eabddf96c83348589275bfc8364c847ee553517d552815f6fcb3b4","sha256:e0cbced06abd71627023e401bacb169f1d6950fc2252508097a42c20b52ff193"],"state_sha256":"056e960bf1b09d3d9fe5f4893d74ef4f6da110f2233bb023102e454ef7b073f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nn9KGDLItY0OKugBgVPG6XU7RGHStAF4Qhwhz80o06r4vvWNhOOM8RGJaSDq3tI2GR2/5q8gBF3fHNzeAC7YAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T00:17:25.468390Z","bundle_sha256":"f986bf5c45b903050475a50af25401074bed767f18f6dcc8b1dba630839ce2f6"}}