{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MO7WVKN4ASRONRVDV4HC2L36QF","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":"6bb56c0c6317834471ecb0c430d9d7c5a78817e77d979628a5c59551d68d2df3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-08-27T19:29:29Z","title_canon_sha256":"e5256ef742566d8db3bb39a45671dbbf253c96675aa26dfee77562b131cf9ac5"},"schema_version":"1.0","source":{"id":"1008.4790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4790","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4790v1","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4790","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"MO7WVKN4ASRO","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MO7WVKN4ASRONRVD","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MO7WVKN4","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:909b45734c80f078d3c42ec416bfdecb601b70271e6affed55ff33ec2aa25415","target":"graph","created_at":"2026-05-18T04:40:09Z","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":"Recently, a whole class of evergy-preserving integrators has been derived for the numerical solution of Hamiltonian problems. In the mainstream of this research, we have defined a new family of symplectic integrators depending on a real parameter. When it is zero, the corresponding method in the family becomes the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null value of the parameter, the corresponding method remains symplectic and has order 2s-2: hence it may be interpreted as a symplectic perturbation of the Gauss met","authors_text":"Donato Trigiante, Felice Iavernaro, Luigi Brugnano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-08-27T19:29:29Z","title":"Energy and quadratic invariants preserving integrators of Gaussian type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4790","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:ce6d398aad33b2f6474134844112a4bfbe59f86ae7b8cb10e95460ba220bf995","target":"record","created_at":"2026-05-18T04:40:09Z","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":"6bb56c0c6317834471ecb0c430d9d7c5a78817e77d979628a5c59551d68d2df3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-08-27T19:29:29Z","title_canon_sha256":"e5256ef742566d8db3bb39a45671dbbf253c96675aa26dfee77562b131cf9ac5"},"schema_version":"1.0","source":{"id":"1008.4790","kind":"arxiv","version":1}},"canonical_sha256":"63bf6aa9bc04a2e6c6a3af0e2d2f7e8167012c132e89abb7660064c977cc123a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63bf6aa9bc04a2e6c6a3af0e2d2f7e8167012c132e89abb7660064c977cc123a","first_computed_at":"2026-05-18T04:40:09.243101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.243101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IpHRxz9l8dHmvj7dtCjZIWxFj6SkefB3cLjjx8rRcc+6Nii5uJj9VmsQX6TrgIlLrjd44yHFFJgWn2Q0O14yCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.243592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce6d398aad33b2f6474134844112a4bfbe59f86ae7b8cb10e95460ba220bf995","sha256:909b45734c80f078d3c42ec416bfdecb601b70271e6affed55ff33ec2aa25415"],"state_sha256":"b16be68c547d64630c6e3e6b3878918bd71b767f9a9e5066b289f13c361991cb"}