{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JZUSKTFSWTLXYUQL465IOQSHJC","short_pith_number":"pith:JZUSKTFS","canonical_record":{"source":{"id":"1012.3140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-14T19:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"e4c6ee9eb263dbd61a0a24d8f0b9fbb54209c10c1bb22ce39cf6ef151a2e1645","abstract_canon_sha256":"e7bc93df9f8cdbd28c1af72b536ad9ee78d619dd27d9ce64f17366b6dbc9230e"},"schema_version":"1.0"},"canonical_sha256":"4e69254cb2b4d77c520be7ba87424748bd7868cc8eeb93a0be764117df64a9be","source":{"kind":"arxiv","id":"1012.3140","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3140","created_at":"2026-05-18T04:33:18Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3140v1","created_at":"2026-05-18T04:33:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3140","created_at":"2026-05-18T04:33:18Z"},{"alias_kind":"pith_short_12","alias_value":"JZUSKTFSWTLX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JZUSKTFSWTLXYUQL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JZUSKTFS","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JZUSKTFSWTLXYUQL465IOQSHJC","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-14T19:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"e4c6ee9eb263dbd61a0a24d8f0b9fbb54209c10c1bb22ce39cf6ef151a2e1645","abstract_canon_sha256":"e7bc93df9f8cdbd28c1af72b536ad9ee78d619dd27d9ce64f17366b6dbc9230e"},"schema_version":"1.0"},"canonical_sha256":"4e69254cb2b4d77c520be7ba87424748bd7868cc8eeb93a0be764117df64a9be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:18.510432Z","signature_b64":"PGPdSmeTgYQRapzzgJHUfcF1feeFoRL3VOunDgDIYJkd5BXcyeLhY6lp7VrcMfMe5LMtp2EdvMYDz7UlKjejAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e69254cb2b4d77c520be7ba87424748bd7868cc8eeb93a0be764117df64a9be","last_reissued_at":"2026-05-18T04:33:18.509796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:18.509796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3140","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":"2026-05-18T04:33:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZKStWyzfSEEB4yhqOlKdeXczwHSe/Idta5ko1JqBtfaX6A3R5DH4eQFe6139b057wX2KJjyXODnlngr2ufSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:25:19.344063Z"},"content_sha256":"7847d484f32ca06739517d53f6cb6fe2f681355b6954f7981e6da0e7ceea11a6","schema_version":"1.0","event_id":"sha256:7847d484f32ca06739517d53f6cb6fe2f681355b6954f7981e6da0e7ceea11a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JZUSKTFSWTLXYUQL465IOQSHJC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time scales in large systems of Brownian particles with stochastic synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anatoly Manita","submitted_at":"2010-12-14T19:24:07Z","abstract_excerpt":"We consider a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$ Brownian particles with synchronizing interaction between them occurring at random time moments $\\{\\tau_{n}\\}_{n=1}^{\\infty}$. Under assumption that the free Brownian motions and the sequence $\\{\\tau_{n}\\}_{n=1}^{\\infty}$ are independent we study asymptotic properties of the system when both the dimension~$N$ and the time~$t$ go to infinity. We find three time scales $t=t(N)$ of qualitatively different behavior of the system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3140","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":"2026-05-18T04:33:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pI2KBybv0vlSCr52moSMHzmSqzJe97mMKZ4J7UaBpK2FDCF+8YsaOaZMlPANpVRKFQ3ZKAuNwaLYoYLnr0PiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:25:19.344423Z"},"content_sha256":"4bd958e94c3f08da517029de1e27752793bb63fc502298f124b47cb65f871c69","schema_version":"1.0","event_id":"sha256:4bd958e94c3f08da517029de1e27752793bb63fc502298f124b47cb65f871c69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZUSKTFSWTLXYUQL465IOQSHJC/bundle.json","state_url":"https://pith.science/pith/JZUSKTFSWTLXYUQL465IOQSHJC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZUSKTFSWTLXYUQL465IOQSHJC/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":"2026-06-25T12:25:19Z","links":{"resolver":"https://pith.science/pith/JZUSKTFSWTLXYUQL465IOQSHJC","bundle":"https://pith.science/pith/JZUSKTFSWTLXYUQL465IOQSHJC/bundle.json","state":"https://pith.science/pith/JZUSKTFSWTLXYUQL465IOQSHJC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZUSKTFSWTLXYUQL465IOQSHJC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JZUSKTFSWTLXYUQL465IOQSHJC","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":"e7bc93df9f8cdbd28c1af72b536ad9ee78d619dd27d9ce64f17366b6dbc9230e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-14T19:24:07Z","title_canon_sha256":"e4c6ee9eb263dbd61a0a24d8f0b9fbb54209c10c1bb22ce39cf6ef151a2e1645"},"schema_version":"1.0","source":{"id":"1012.3140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3140","created_at":"2026-05-18T04:33:18Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3140v1","created_at":"2026-05-18T04:33:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3140","created_at":"2026-05-18T04:33:18Z"},{"alias_kind":"pith_short_12","alias_value":"JZUSKTFSWTLX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JZUSKTFSWTLXYUQL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JZUSKTFS","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:4bd958e94c3f08da517029de1e27752793bb63fc502298f124b47cb65f871c69","target":"graph","created_at":"2026-05-18T04:33:18Z","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 a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$ Brownian particles with synchronizing interaction between them occurring at random time moments $\\{\\tau_{n}\\}_{n=1}^{\\infty}$. Under assumption that the free Brownian motions and the sequence $\\{\\tau_{n}\\}_{n=1}^{\\infty}$ are independent we study asymptotic properties of the system when both the dimension~$N$ and the time~$t$ go to infinity. We find three time scales $t=t(N)$ of qualitatively different behavior of the system.","authors_text":"Anatoly Manita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-14T19:24:07Z","title":"Time scales in large systems of Brownian particles with stochastic synchronization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3140","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":"sha256:7847d484f32ca06739517d53f6cb6fe2f681355b6954f7981e6da0e7ceea11a6","target":"record","created_at":"2026-05-18T04:33:18Z","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":"e7bc93df9f8cdbd28c1af72b536ad9ee78d619dd27d9ce64f17366b6dbc9230e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-14T19:24:07Z","title_canon_sha256":"e4c6ee9eb263dbd61a0a24d8f0b9fbb54209c10c1bb22ce39cf6ef151a2e1645"},"schema_version":"1.0","source":{"id":"1012.3140","kind":"arxiv","version":1}},"canonical_sha256":"4e69254cb2b4d77c520be7ba87424748bd7868cc8eeb93a0be764117df64a9be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e69254cb2b4d77c520be7ba87424748bd7868cc8eeb93a0be764117df64a9be","first_computed_at":"2026-05-18T04:33:18.509796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:18.509796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PGPdSmeTgYQRapzzgJHUfcF1feeFoRL3VOunDgDIYJkd5BXcyeLhY6lp7VrcMfMe5LMtp2EdvMYDz7UlKjejAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:18.510432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7847d484f32ca06739517d53f6cb6fe2f681355b6954f7981e6da0e7ceea11a6","sha256:4bd958e94c3f08da517029de1e27752793bb63fc502298f124b47cb65f871c69"],"state_sha256":"f08cd13164d7c5ab299651e0da2f580eb195154138397dadc7109dc2b3dad092"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OOqYozeAhILpYuNzxe2dBQPehMtmzryPz9UZF76ow+HJxnwUrJxMjco7Sf+g5T9xVPOQGvnnU3U31E6IB14fCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:25:19.346614Z","bundle_sha256":"3e8947237651e1b215ee756588221f46f9c979f8901b71f4ff09445559647a36"}}