{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:X7AL72KNJWRNVSS2XZ276OPJZ4","short_pith_number":"pith:X7AL72KN","canonical_record":{"source":{"id":"math/0408372","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-08-26T13:59:59Z","cross_cats_sorted":[],"title_canon_sha256":"2218d1b50ff6c4caa8492405c30c6ae40d704d624862d05e13674be13995b9ea","abstract_canon_sha256":"c390c17eaa07512cf1644f700966933f4062e398220e9377d42a92294ac241f7"},"schema_version":"1.0"},"canonical_sha256":"bfc0bfe94d4da2daca5abe75ff39e9cf3ea7bb1897013b367b9579ab17983477","source":{"kind":"arxiv","id":"math/0408372","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408372","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408372v2","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408372","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"X7AL72KNJWRN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"X7AL72KNJWRNVSS2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"X7AL72KN","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:X7AL72KNJWRNVSS2XZ276OPJZ4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0408372","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-08-26T13:59:59Z","cross_cats_sorted":[],"title_canon_sha256":"2218d1b50ff6c4caa8492405c30c6ae40d704d624862d05e13674be13995b9ea","abstract_canon_sha256":"c390c17eaa07512cf1644f700966933f4062e398220e9377d42a92294ac241f7"},"schema_version":"1.0"},"canonical_sha256":"bfc0bfe94d4da2daca5abe75ff39e9cf3ea7bb1897013b367b9579ab17983477","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:23.992149Z","signature_b64":"IENM6viEfKw/B8sVdijNeWvYxkTd6ll9b5TZDSnV1Qm2ezciZ7HF6kVPYRoQ1sFNiXpuhwtfiHrSPOGvxST8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfc0bfe94d4da2daca5abe75ff39e9cf3ea7bb1897013b367b9579ab17983477","last_reissued_at":"2026-05-18T04:10:23.991679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:23.991679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0408372","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wznQTsRpVMc2XeUSbw5VTeLvyYIob4NGp/bsT5cP9VIe1EDc8c9TdoKi/0nOQCb3fLiGIBrNIt0x2+JL6fl/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:10:00.461966Z"},"content_sha256":"35898c190d9232ee5b0c7c9a8f1f1ecf051b8212b4e53fd797149ecff7d445a5","schema_version":"1.0","event_id":"sha256:35898c190d9232ee5b0c7c9a8f1f1ecf051b8212b4e53fd797149ecff7d445a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:X7AL72KNJWRNVSS2XZ276OPJZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic analysis of a particle system with mean-field interaction","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Manita, V. Shcherbakov","submitted_at":"2004-08-26T13:59:59Z","abstract_excerpt":"We study a system of $N$ interacting particles on $\\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs to the class of mean-field interactions and models a rollback synchronization in asynchronous networks of processors for a distributed simulation. First of all we study an empirical measure generated by the particle configuration on $\\bf{R}$. We prove that if space, time and a parameter of the interaction are appropriately scaled (hydrodynamical scale), the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408372","kind":"arxiv","version":2},"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":"2026-05-18T04:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESZ2d87ZeTT18DRn3v1gQelBM2hdY0bL1n/1KB0IjdbaQmTSksQ3UHN5sZAF1E5+x0lNT9n4CQy5aond7VysBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:10:00.462306Z"},"content_sha256":"672a3907404568d749ac6713c7f30644b24ad2bc9d398e681d354cd2071c210a","schema_version":"1.0","event_id":"sha256:672a3907404568d749ac6713c7f30644b24ad2bc9d398e681d354cd2071c210a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7AL72KNJWRNVSS2XZ276OPJZ4/bundle.json","state_url":"https://pith.science/pith/X7AL72KNJWRNVSS2XZ276OPJZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7AL72KNJWRNVSS2XZ276OPJZ4/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":"2026-06-21T23:10:00Z","links":{"resolver":"https://pith.science/pith/X7AL72KNJWRNVSS2XZ276OPJZ4","bundle":"https://pith.science/pith/X7AL72KNJWRNVSS2XZ276OPJZ4/bundle.json","state":"https://pith.science/pith/X7AL72KNJWRNVSS2XZ276OPJZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7AL72KNJWRNVSS2XZ276OPJZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:X7AL72KNJWRNVSS2XZ276OPJZ4","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":"c390c17eaa07512cf1644f700966933f4062e398220e9377d42a92294ac241f7","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-08-26T13:59:59Z","title_canon_sha256":"2218d1b50ff6c4caa8492405c30c6ae40d704d624862d05e13674be13995b9ea"},"schema_version":"1.0","source":{"id":"math/0408372","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408372","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408372v2","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408372","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"X7AL72KNJWRN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"X7AL72KNJWRNVSS2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"X7AL72KN","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:672a3907404568d749ac6713c7f30644b24ad2bc9d398e681d354cd2071c210a","target":"graph","created_at":"2026-05-18T04:10:23Z","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 a system of $N$ interacting particles on $\\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs to the class of mean-field interactions and models a rollback synchronization in asynchronous networks of processors for a distributed simulation. First of all we study an empirical measure generated by the particle configuration on $\\bf{R}$. We prove that if space, time and a parameter of the interaction are appropriately scaled (hydrodynamical scale), the","authors_text":"A. Manita, V. Shcherbakov","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2004-08-26T13:59:59Z","title":"Asymptotic analysis of a particle system with mean-field interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408372","kind":"arxiv","version":2},"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":"sha256:35898c190d9232ee5b0c7c9a8f1f1ecf051b8212b4e53fd797149ecff7d445a5","target":"record","created_at":"2026-05-18T04:10:23Z","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":"c390c17eaa07512cf1644f700966933f4062e398220e9377d42a92294ac241f7","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-08-26T13:59:59Z","title_canon_sha256":"2218d1b50ff6c4caa8492405c30c6ae40d704d624862d05e13674be13995b9ea"},"schema_version":"1.0","source":{"id":"math/0408372","kind":"arxiv","version":2}},"canonical_sha256":"bfc0bfe94d4da2daca5abe75ff39e9cf3ea7bb1897013b367b9579ab17983477","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfc0bfe94d4da2daca5abe75ff39e9cf3ea7bb1897013b367b9579ab17983477","first_computed_at":"2026-05-18T04:10:23.991679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:23.991679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IENM6viEfKw/B8sVdijNeWvYxkTd6ll9b5TZDSnV1Qm2ezciZ7HF6kVPYRoQ1sFNiXpuhwtfiHrSPOGvxST8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:23.992149Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408372","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35898c190d9232ee5b0c7c9a8f1f1ecf051b8212b4e53fd797149ecff7d445a5","sha256:672a3907404568d749ac6713c7f30644b24ad2bc9d398e681d354cd2071c210a"],"state_sha256":"8684c73890853d52c1c03b6e78d10f73c13561ad7481ffade53480bd483e473e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+PpOQ4mRFPUUn+3K1ukjCQ/RFMhlrva+7mXUIG9Pg0d3Att1hUkbqRznIS8JJYJ62ijBWrBnj8laSjzKKtwnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:10:00.464197Z","bundle_sha256":"685e1e0d6a207ba67ee29ff9c98515f32608c893176d8ed67260bf3af5a0f606"}}