{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HPDLTZP6WTYJZ6RM3FI73TYNWY","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":"d76e6d866de56583323024ba2ccc67bd69842e3fd8c6a8a49c31e650398d940b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T13:49:32Z","title_canon_sha256":"8ee319d5edfd78160395c2eede011447cedfe883cc648c43466b6b59e1acc6e5"},"schema_version":"1.0","source":{"id":"1011.2909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2909","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2909v1","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2909","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"HPDLTZP6WTYJ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HPDLTZP6WTYJZ6RM","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HPDLTZP6","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:c68a6ca9dd7159cab2951cc1a1a418b254eb515aa3e0243966dbd120bfa48ae5","target":"graph","created_at":"2026-05-18T04:36:07Z","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":"A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.","authors_text":"Daomin Cao, Hongbo Fu, Jian Ren, Jinqiao Duan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T13:49:32Z","title":"Effective dynamicsof a coupled microscopic-macroscopic stochastic system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2909","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:f8a2160327bc4260a0911d9460444597044154f5fcb0a35619d184f0fc966c0a","target":"record","created_at":"2026-05-18T04:36:07Z","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":"d76e6d866de56583323024ba2ccc67bd69842e3fd8c6a8a49c31e650398d940b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T13:49:32Z","title_canon_sha256":"8ee319d5edfd78160395c2eede011447cedfe883cc648c43466b6b59e1acc6e5"},"schema_version":"1.0","source":{"id":"1011.2909","kind":"arxiv","version":1}},"canonical_sha256":"3bc6b9e5feb4f09cfa2cd951fdcf0db6131e4c3b0924be8b9e143b83a9460135","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bc6b9e5feb4f09cfa2cd951fdcf0db6131e4c3b0924be8b9e143b83a9460135","first_computed_at":"2026-05-18T04:36:07.880679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:07.880679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s1DFIKQiH3sI709koqavLBz32I4S+TD0pE20Ln+IvFFTCt1FlVYuLd4QzNz8WmDrxb2Snh8QJE3YvPPlE6+HBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:07.881350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a2160327bc4260a0911d9460444597044154f5fcb0a35619d184f0fc966c0a","sha256:c68a6ca9dd7159cab2951cc1a1a418b254eb515aa3e0243966dbd120bfa48ae5"],"state_sha256":"6caa447640b0605ba2029095882d7d44086a0b1b00d32c738490ca8c106f4a59"}