{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JOFA3VA3ITHVPIDJCZSAL2BU6A","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":"37f9ab6d777e03f763f6fc8c7d48ebd35da9dd90e51162f4b1636cc8d029ccf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-31T11:52:12Z","title_canon_sha256":"d02f7286b78e9816c80b08a5346cbc84209cad73b7030de9cfdd59651c27a419"},"schema_version":"1.0","source":{"id":"1701.08999","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08999","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08999v5","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08999","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"JOFA3VA3ITHV","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JOFA3VA3ITHVPIDJ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JOFA3VA3","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:57c4ab3ed120dd46145cef4f4e0446587c0536957610da608b651f19e31f29d1","target":"graph","created_at":"2026-05-18T00:05:56Z","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 common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional coordinates into the high-dimensional phase space, then the high-dimensional (microscopic) evolution is applied for some time, and finally a user-defined restriction operator maps down into a low-dimensional space again. We prove convergence of equation-free methods for finite time-scale separation with respect to a method parameter, the so-called healing time. Our","authors_text":"Christian Marschler, Jan Sieber, Jens Starke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-31T11:52:12Z","title":"Convergence of equation-free methods in the case of finite time scale separation with application to deterministic and stochastic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08999","kind":"arxiv","version":5},"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":"sha256:56d92290a8e9eab4f276dc9aee579d26af79d09929c290e5198a702e589eaf97","target":"record","created_at":"2026-05-18T00:05:56Z","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":"37f9ab6d777e03f763f6fc8c7d48ebd35da9dd90e51162f4b1636cc8d029ccf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-31T11:52:12Z","title_canon_sha256":"d02f7286b78e9816c80b08a5346cbc84209cad73b7030de9cfdd59651c27a419"},"schema_version":"1.0","source":{"id":"1701.08999","kind":"arxiv","version":5}},"canonical_sha256":"4b8a0dd41b44cf57a069166405e834f0175c4088ca904ee423a51ff91285343f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b8a0dd41b44cf57a069166405e834f0175c4088ca904ee423a51ff91285343f","first_computed_at":"2026-05-18T00:05:56.784758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:56.784758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/bdkWyeyzi+4KbhuIEGyKJNQCduoIrBGrgO6u44xzP2DcN0vzYhztYOyDXrkw5o5qgSNthrdhHXzDGm0cu6RCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:56.785137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08999","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56d92290a8e9eab4f276dc9aee579d26af79d09929c290e5198a702e589eaf97","sha256:57c4ab3ed120dd46145cef4f4e0446587c0536957610da608b651f19e31f29d1"],"state_sha256":"67a8b97a0c12ed021eadcf974a08c6fd149f4cd5b192a3b217a9616a823ef861"}