{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:I6LCXQUSFAWSCKQ2EQRVBVMVCQ","short_pith_number":"pith:I6LCXQUS","schema_version":"1.0","canonical_sha256":"47962bc292282d212a1a242350d59514029106c0d5eb7375bce94ab10d214bc1","source":{"kind":"arxiv","id":"1808.05548","version":1},"attestation_state":"computed","paper":{"title":"Symmetric-adjoint and symplectic-adjoint methods and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NA","authors_text":"Geng Sun, Hongyu Liu, Siqing Gan, Zaijiu Shang","submitted_at":"2018-08-16T15:44:59Z","abstract_excerpt":"Symmetric method and symplectic method are classical notions in the theory of Runge-Kutta methods. They can generate numerical flows that respectively preserve the symmetry and symplecticity of the continuous flows in the phase space. Adjoint method is an important way of constructing a new Runge-Kutta method via the symmetrisation of another Runge-Kutta method. In this paper, we introduce a new notion, called symplectic-adjoint Runge-Kutta method. We prove some interesting properties of the symmetric-adjoint and symplectic-adjoint methods. These properties reveal some intrinsic connections am"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.05548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-16T15:44:59Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b932aa4b668bc09aa851b8a185a505ffbffa26fab2877873ae7898dd3562d2e2","abstract_canon_sha256":"4930baeeef15b80243faa4b1d055ba59701b204030dccd8dedff01bf98e63d8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:56.702906Z","signature_b64":"uLNRI4Ww1pgE12Rzxwf4UIkNGTgoqcgaMtJ0cspaEtU0ZdbLVpzhbKaxvufvTgKHdMtMuk29pbOhDQIbx+7nBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47962bc292282d212a1a242350d59514029106c0d5eb7375bce94ab10d214bc1","last_reissued_at":"2026-05-18T00:07:56.702197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:56.702197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric-adjoint and symplectic-adjoint methods and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NA","authors_text":"Geng Sun, Hongyu Liu, Siqing Gan, Zaijiu Shang","submitted_at":"2018-08-16T15:44:59Z","abstract_excerpt":"Symmetric method and symplectic method are classical notions in the theory of Runge-Kutta methods. They can generate numerical flows that respectively preserve the symmetry and symplecticity of the continuous flows in the phase space. Adjoint method is an important way of constructing a new Runge-Kutta method via the symmetrisation of another Runge-Kutta method. In this paper, we introduce a new notion, called symplectic-adjoint Runge-Kutta method. We prove some interesting properties of the symmetric-adjoint and symplectic-adjoint methods. These properties reveal some intrinsic connections am"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05548","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.05548","created_at":"2026-05-18T00:07:56.702332+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05548v1","created_at":"2026-05-18T00:07:56.702332+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05548","created_at":"2026-05-18T00:07:56.702332+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6LCXQUSFAWS","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6LCXQUSFAWSCKQ2","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6LCXQUS","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ","json":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ.json","graph_json":"https://pith.science/api/pith-number/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/graph.json","events_json":"https://pith.science/api/pith-number/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/events.json","paper":"https://pith.science/paper/I6LCXQUS"},"agent_actions":{"view_html":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ","download_json":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ.json","view_paper":"https://pith.science/paper/I6LCXQUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05548&json=true","fetch_graph":"https://pith.science/api/pith-number/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/action/storage_attestation","attest_author":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/action/author_attestation","sign_citation":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/action/citation_signature","submit_replication":"https://pith.science/pith/I6LCXQUSFAWSCKQ2EQRVBVMVCQ/action/replication_record"}},"created_at":"2026-05-18T00:07:56.702332+00:00","updated_at":"2026-05-18T00:07:56.702332+00:00"}