{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q7PGZ3EBTLANHRNPWAFL3JCDMM","short_pith_number":"pith:Q7PGZ3EB","canonical_record":{"source":{"id":"1405.0553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-03T04:20:07Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"91e0a429d6d6a7f274d36098fd3eb5ac4ae1bae0242f1c4d8a7424fc975ab2cb","abstract_canon_sha256":"f0a228248d2c16ed9847d3359d4ba7fd6c9f7984406232706fcf52e26e186dbf"},"schema_version":"1.0"},"canonical_sha256":"87de6cec819ac0d3c5afb00abda443633762329d2de1bc68c267851c8f84edf1","source":{"kind":"arxiv","id":"1405.0553","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0553","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0553v1","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0553","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q7PGZ3EBTLAN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q7PGZ3EBTLANHRNP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q7PGZ3EB","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q7PGZ3EBTLANHRNPWAFL3JCDMM","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-03T04:20:07Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"91e0a429d6d6a7f274d36098fd3eb5ac4ae1bae0242f1c4d8a7424fc975ab2cb","abstract_canon_sha256":"f0a228248d2c16ed9847d3359d4ba7fd6c9f7984406232706fcf52e26e186dbf"},"schema_version":"1.0"},"canonical_sha256":"87de6cec819ac0d3c5afb00abda443633762329d2de1bc68c267851c8f84edf1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:30.647278Z","signature_b64":"ZI5FwXzkJ6GIISP9lHJDyAGvjJkPLSty/3tQako/N5z0L+dmoUjL+jdroku5QLVH2sEkM8PrpIqntgNosDHYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87de6cec819ac0d3c5afb00abda443633762329d2de1bc68c267851c8f84edf1","last_reissued_at":"2026-05-18T02:46:30.646689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:30.646689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0553","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":"2026-05-18T02:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISv4RUBXUjHjyYZBUSop0kJzljhd76ovB7sHbkGxwZFb2NADzor9cf66M1ybujKW6hvHS40xAS7Ab3fH2O1YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:34:10.722577Z"},"content_sha256":"f72d17aa03444fd39164f41d6a4afcc2c5cbefde9e874782025ee8569c213b39","schema_version":"1.0","event_id":"sha256:f72d17aa03444fd39164f41d6a4afcc2c5cbefde9e874782025ee8569c213b39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q7PGZ3EBTLANHRNPWAFL3JCDMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slow Kinetics of Brownian Maxima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"E. Ben-Naim, P.L. Krapivsky","submitted_at":"2014-05-03T04:20:07Z","abstract_excerpt":"We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t, and find the algebraic decay P ~ t^(-beta) with exponent beta=1/4. When the two particles have diffusion constants D1 and D2, the exponent depends on the mobilities, beta=(1/pi)arctan[sqrt(D2/D1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0553","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":""},"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":"2026-05-18T02:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S10kcn1xJbUZ1KJIQHZWtkRRSEAm4nCf9D3kkiUJWfZmrgZq+QUYtRRCQe+ECOf5QcFJkPaTzoVoodQTNCI7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:34:10.722923Z"},"content_sha256":"7d44a88d18b9f6239d281747756d3d7fc75ee1ee30e0bea378de9736cb9fbaa4","schema_version":"1.0","event_id":"sha256:7d44a88d18b9f6239d281747756d3d7fc75ee1ee30e0bea378de9736cb9fbaa4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM/bundle.json","state_url":"https://pith.science/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM/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":"2026-06-26T04:34:10Z","links":{"resolver":"https://pith.science/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM","bundle":"https://pith.science/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM/bundle.json","state":"https://pith.science/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7PGZ3EBTLANHRNPWAFL3JCDMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q7PGZ3EBTLANHRNPWAFL3JCDMM","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":"f0a228248d2c16ed9847d3359d4ba7fd6c9f7984406232706fcf52e26e186dbf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-03T04:20:07Z","title_canon_sha256":"91e0a429d6d6a7f274d36098fd3eb5ac4ae1bae0242f1c4d8a7424fc975ab2cb"},"schema_version":"1.0","source":{"id":"1405.0553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0553","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0553v1","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0553","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q7PGZ3EBTLAN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q7PGZ3EBTLANHRNP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q7PGZ3EB","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:7d44a88d18b9f6239d281747756d3d7fc75ee1ee30e0bea378de9736cb9fbaa4","target":"graph","created_at":"2026-05-18T02:46:30Z","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 study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t, and find the algebraic decay P ~ t^(-beta) with exponent beta=1/4. When the two particles have diffusion constants D1 and D2, the exponent depends on the mobilities, beta=(1/pi)arctan[sqrt(D2/D1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest ex","authors_text":"E. Ben-Naim, P.L. Krapivsky","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-03T04:20:07Z","title":"Slow Kinetics of Brownian Maxima"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0553","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:f72d17aa03444fd39164f41d6a4afcc2c5cbefde9e874782025ee8569c213b39","target":"record","created_at":"2026-05-18T02:46:30Z","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":"f0a228248d2c16ed9847d3359d4ba7fd6c9f7984406232706fcf52e26e186dbf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-03T04:20:07Z","title_canon_sha256":"91e0a429d6d6a7f274d36098fd3eb5ac4ae1bae0242f1c4d8a7424fc975ab2cb"},"schema_version":"1.0","source":{"id":"1405.0553","kind":"arxiv","version":1}},"canonical_sha256":"87de6cec819ac0d3c5afb00abda443633762329d2de1bc68c267851c8f84edf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87de6cec819ac0d3c5afb00abda443633762329d2de1bc68c267851c8f84edf1","first_computed_at":"2026-05-18T02:46:30.646689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:30.646689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZI5FwXzkJ6GIISP9lHJDyAGvjJkPLSty/3tQako/N5z0L+dmoUjL+jdroku5QLVH2sEkM8PrpIqntgNosDHYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:30.647278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f72d17aa03444fd39164f41d6a4afcc2c5cbefde9e874782025ee8569c213b39","sha256:7d44a88d18b9f6239d281747756d3d7fc75ee1ee30e0bea378de9736cb9fbaa4"],"state_sha256":"beb53a7825628321ff2e2561f10613f9cfb606ec772ba917f6375a7c63bb8294"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvZqj1Ajrw5LydsTlzDKtoKErJAIxcuvp4rRCggCkC90JjKRj8lWr+RNd34ZKDXLPwt075kk/yOIK0v8IeReDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T04:34:10.724908Z","bundle_sha256":"a59fb58c50d19b01fc7f476b9b9d3308da84b283463809e5e921b42a9508b1ee"}}