{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UTPK3JJCLC3YQN4F7B5SVWMV4G","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":"6210aa7c53f31003ee74ead2b82f05f18f2c91120d6c55e034c7138eb17c028c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-09T05:33:17Z","title_canon_sha256":"22141e5b27b0ba0f8fafad71538f7f1cb4d2fc2e0b4241021e3ebc01b3b1ed06"},"schema_version":"1.0","source":{"id":"1711.03258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03258","created_at":"2026-05-18T00:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03258v1","created_at":"2026-05-18T00:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03258","created_at":"2026-05-18T00:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"UTPK3JJCLC3Y","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UTPK3JJCLC3YQN4F","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UTPK3JJC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:58efdd564984d6a9b53b75cd6c505a78c1c1a4131d94aa4a1c6aae29a2f474d7","target":"graph","created_at":"2026-05-18T00:30:56Z","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":"We give a theoretical framework of stochastic non-canonical Hamiltonian systems as well as their modified symplectic structure which is named stochastic K-symplectic structure. The framework can be applied to the study of the Lotka--Volterra model perturbed by external noises. In terms of internal properties of the stochastic Lotka--Volterra model, we propose different kinds of stochastic K-symplectic integrators which could inherit the positivity of the solution. The K-symplectic conditions are also obtained to ensure that the proposed schemes admit the same geometric structure as the origina","authors_text":"Jialin Hong, Jingjing Zhang, Lihai Ji, Xu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-09T05:33:17Z","title":"Stochastic K-symplectic integrators for stochastic non-canonical Hamiltonian systems and applications to the Lotka--Volterra model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03258","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":"sha256:90981126003879f86025495b4501e74781cfc5bb867fc7d4599dfe9a30aedf50","target":"record","created_at":"2026-05-18T00:30:56Z","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":"6210aa7c53f31003ee74ead2b82f05f18f2c91120d6c55e034c7138eb17c028c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-09T05:33:17Z","title_canon_sha256":"22141e5b27b0ba0f8fafad71538f7f1cb4d2fc2e0b4241021e3ebc01b3b1ed06"},"schema_version":"1.0","source":{"id":"1711.03258","kind":"arxiv","version":1}},"canonical_sha256":"a4deada52258b7883785f87b2ad995e1808cfde18eef424f662ee2511ec2aa29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4deada52258b7883785f87b2ad995e1808cfde18eef424f662ee2511ec2aa29","first_computed_at":"2026-05-18T00:30:56.771230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:56.771230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S9J9XAP5/ctOak2sANGpQWRS7Lk+ygL30+xooGhk+GChePl9yXqt+IZKD7s2G9wP8wpdJ/XboPawRi50egFBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:56.771660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90981126003879f86025495b4501e74781cfc5bb867fc7d4599dfe9a30aedf50","sha256:58efdd564984d6a9b53b75cd6c505a78c1c1a4131d94aa4a1c6aae29a2f474d7"],"state_sha256":"343c3df0e95accaf6472afaccb5b7378fe8373523a48e14c6ce58e8a3de170c7"}