{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GAO3OS4XJBBVSUGTBGXEMADEPZ","short_pith_number":"pith:GAO3OS4X","canonical_record":{"source":{"id":"1106.0598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-03T09:52:36Z","cross_cats_sorted":[],"title_canon_sha256":"8e26541856f9401db7099d1de24e584e9ec8ad3bca65c2bd25293ed9265ac88d","abstract_canon_sha256":"e556a1947f6a7668b27da7f514f5111c70a434eb281c45b0b7706aae6bdf614f"},"schema_version":"1.0"},"canonical_sha256":"301db74b9748435950d309ae4600647e5fe274af062a61838679931743dfd325","source":{"kind":"arxiv","id":"1106.0598","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0598","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0598v1","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0598","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"GAO3OS4XJBBV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GAO3OS4XJBBVSUGT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GAO3OS4X","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GAO3OS4XJBBVSUGTBGXEMADEPZ","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-03T09:52:36Z","cross_cats_sorted":[],"title_canon_sha256":"8e26541856f9401db7099d1de24e584e9ec8ad3bca65c2bd25293ed9265ac88d","abstract_canon_sha256":"e556a1947f6a7668b27da7f514f5111c70a434eb281c45b0b7706aae6bdf614f"},"schema_version":"1.0"},"canonical_sha256":"301db74b9748435950d309ae4600647e5fe274af062a61838679931743dfd325","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:06.174640Z","signature_b64":"24p9U14H4v4LXnfsfUBc6iDeTl1pgnS2L3LPZUlA/gkj1IIjNLLntYmoQg9VoMpPesqCgSqRHdkQ3HntjFKyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"301db74b9748435950d309ae4600647e5fe274af062a61838679931743dfd325","last_reissued_at":"2026-05-18T03:54:06.173803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:06.173803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0598","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7//i5C4jNSrOAYTLP1zVR8o4NR0+P7+QRMUVXaEhMFS3SXDoQs6dR4yh++TTkloWrjsSMT7qChXWIxNgU8JwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:29:41.569358Z"},"content_sha256":"99abf3bcda4172bc675f9eacb4fb78ce9aaa47778347d139a755717f02beccf2","schema_version":"1.0","event_id":"sha256:99abf3bcda4172bc675f9eacb4fb78ce9aaa47778347d139a755717f02beccf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GAO3OS4XJBBVSUGTBGXEMADEPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Two Step, Fourth Order, Nearly-Linear Method with Energy Preserving Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Donato Trigiante, Felice Iavernaro, Luigi Brugnano","submitted_at":"2011-06-03T09:52:36Z","abstract_excerpt":"We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction term is O(h^5) (h is the stepsize of integration). The key tools the new methods are based upon are the line integral associated with a conservative vector field (such as the one defined by a Hamiltonian dynamical system) and its discretization obtained by the aid of a quadrature formula. Energy conservation is equivalent to the requirement that the quadratu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0598","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NR984sArLBznlF1jDm2jxEVnvBcID3tN31ydfsy7HnFNJlYaRlxlDodPzvAFJN/Cg/VxZaO4ZQqbHp7MAAaJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:29:41.569708Z"},"content_sha256":"30daec03bdf3c371f0a63f0e79bceea8044c89d6871b39ad2d82b3fff603de13","schema_version":"1.0","event_id":"sha256:30daec03bdf3c371f0a63f0e79bceea8044c89d6871b39ad2d82b3fff603de13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ/bundle.json","state_url":"https://pith.science/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T19:29:41Z","links":{"resolver":"https://pith.science/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ","bundle":"https://pith.science/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ/bundle.json","state":"https://pith.science/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAO3OS4XJBBVSUGTBGXEMADEPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GAO3OS4XJBBVSUGTBGXEMADEPZ","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":"e556a1947f6a7668b27da7f514f5111c70a434eb281c45b0b7706aae6bdf614f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-03T09:52:36Z","title_canon_sha256":"8e26541856f9401db7099d1de24e584e9ec8ad3bca65c2bd25293ed9265ac88d"},"schema_version":"1.0","source":{"id":"1106.0598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0598","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0598v1","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0598","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"GAO3OS4XJBBV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GAO3OS4XJBBVSUGT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GAO3OS4X","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:30daec03bdf3c371f0a63f0e79bceea8044c89d6871b39ad2d82b3fff603de13","target":"graph","created_at":"2026-05-18T03:54:06Z","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 introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction term is O(h^5) (h is the stepsize of integration). The key tools the new methods are based upon are the line integral associated with a conservative vector field (such as the one defined by a Hamiltonian dynamical system) and its discretization obtained by the aid of a quadrature formula. Energy conservation is equivalent to the requirement that the quadratu","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":"2011-06-03T09:52:36Z","title":"A Two Step, Fourth Order, Nearly-Linear Method with Energy Preserving Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0598","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":"sha256:99abf3bcda4172bc675f9eacb4fb78ce9aaa47778347d139a755717f02beccf2","target":"record","created_at":"2026-05-18T03:54:06Z","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":"e556a1947f6a7668b27da7f514f5111c70a434eb281c45b0b7706aae6bdf614f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-03T09:52:36Z","title_canon_sha256":"8e26541856f9401db7099d1de24e584e9ec8ad3bca65c2bd25293ed9265ac88d"},"schema_version":"1.0","source":{"id":"1106.0598","kind":"arxiv","version":1}},"canonical_sha256":"301db74b9748435950d309ae4600647e5fe274af062a61838679931743dfd325","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"301db74b9748435950d309ae4600647e5fe274af062a61838679931743dfd325","first_computed_at":"2026-05-18T03:54:06.173803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:06.173803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"24p9U14H4v4LXnfsfUBc6iDeTl1pgnS2L3LPZUlA/gkj1IIjNLLntYmoQg9VoMpPesqCgSqRHdkQ3HntjFKyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:06.174640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99abf3bcda4172bc675f9eacb4fb78ce9aaa47778347d139a755717f02beccf2","sha256:30daec03bdf3c371f0a63f0e79bceea8044c89d6871b39ad2d82b3fff603de13"],"state_sha256":"2d337d12dea30b95795bf6dea535350b08bd12804c6d306d5f2ecb321c1b1d18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3Yo0L0m8hwMrKeNlyhaNhL3C+1nDlgZ+QSr+ccm/kTLIF4gOOOR8G1o73uHdQvfzjRK1FO3fyQeb0q+ct/1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T19:29:41.571711Z","bundle_sha256":"280e19ed80a7092c517f0932df75d1292c0a5af1c23bfd89433d0a9bc9bc9130"}}