{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OI47M24DCHAFJBFQJROZVSJ2D2","short_pith_number":"pith:OI47M24D","canonical_record":{"source":{"id":"1809.07268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-19T16:07:06Z","cross_cats_sorted":[],"title_canon_sha256":"e07265605c6d75f59f5d2cd2a4ce2795ddd37062d769dd5d4882763d6a9c4352","abstract_canon_sha256":"df927ed695b75580ac3d307136d2d8e85123444236767b4f95d1ab7fb153c0c5"},"schema_version":"1.0"},"canonical_sha256":"7239f66b8311c05484b04c5d9ac93a1e82b4d977861d64a06f782c47b730cbec","source":{"kind":"arxiv","id":"1809.07268","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07268","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07268v1","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07268","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"pith_short_12","alias_value":"OI47M24DCHAF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OI47M24DCHAFJBFQ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OI47M24D","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OI47M24DCHAFJBFQJROZVSJ2D2","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-19T16:07:06Z","cross_cats_sorted":[],"title_canon_sha256":"e07265605c6d75f59f5d2cd2a4ce2795ddd37062d769dd5d4882763d6a9c4352","abstract_canon_sha256":"df927ed695b75580ac3d307136d2d8e85123444236767b4f95d1ab7fb153c0c5"},"schema_version":"1.0"},"canonical_sha256":"7239f66b8311c05484b04c5d9ac93a1e82b4d977861d64a06f782c47b730cbec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:20.204024Z","signature_b64":"sM64v5zECHixu+XCZJvY4g0pMQr2PsUr9x7sQclUeTj+BgbBt7tdKpIR75ZrEMVIxPE227TOyQfTa7poi1BtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7239f66b8311c05484b04c5d9ac93a1e82b4d977861d64a06f782c47b730cbec","last_reissued_at":"2026-05-18T00:05:20.203455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:20.203455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07268","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":"2026-05-18T00:05:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SunK7IsGDcg+qgYExN65rS72sCoxFNoVCbSH70mjhkhwi4zwZEEmKe7V8cUqRyDfXrxbVfmLJC/xuD3rWY8qCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T07:00:26.236304Z"},"content_sha256":"e8d7c7d8cde7d9f051aaaf18de7dd066697fa9c28bb3fecedbbe33f04a0c9604","schema_version":"1.0","event_id":"sha256:e8d7c7d8cde7d9f051aaaf18de7dd066697fa9c28bb3fecedbbe33f04a0c9604"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OI47M24DCHAFJBFQJROZVSJ2D2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-term analysis of exponential integrators for highly oscillatory conservative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bin Wang, Jiyong Li, Yonglei Fang","submitted_at":"2018-09-19T16:07:06Z","abstract_excerpt":"In this paper, we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions. Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07268","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":"2026-05-18T00:05:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hT0CP9Um5C5SS4dyadzvLQqXYdyPrNFpKIwf2Ggttr2Dqtjp8cjQKz6M7d/Fp9l8KtSrzKvcZnDk0lKd+S5LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T07:00:26.236646Z"},"content_sha256":"f3859445f232b4f682f385f95e2f394339641889d6bb70352e9e07d73d1e3185","schema_version":"1.0","event_id":"sha256:f3859445f232b4f682f385f95e2f394339641889d6bb70352e9e07d73d1e3185"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OI47M24DCHAFJBFQJROZVSJ2D2/bundle.json","state_url":"https://pith.science/pith/OI47M24DCHAFJBFQJROZVSJ2D2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OI47M24DCHAFJBFQJROZVSJ2D2/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":"2026-08-22T07:00:26Z","links":{"resolver":"https://pith.science/pith/OI47M24DCHAFJBFQJROZVSJ2D2","bundle":"https://pith.science/pith/OI47M24DCHAFJBFQJROZVSJ2D2/bundle.json","state":"https://pith.science/pith/OI47M24DCHAFJBFQJROZVSJ2D2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OI47M24DCHAFJBFQJROZVSJ2D2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OI47M24DCHAFJBFQJROZVSJ2D2","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":"df927ed695b75580ac3d307136d2d8e85123444236767b4f95d1ab7fb153c0c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-19T16:07:06Z","title_canon_sha256":"e07265605c6d75f59f5d2cd2a4ce2795ddd37062d769dd5d4882763d6a9c4352"},"schema_version":"1.0","source":{"id":"1809.07268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07268","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07268v1","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07268","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"pith_short_12","alias_value":"OI47M24DCHAF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OI47M24DCHAFJBFQ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OI47M24D","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:f3859445f232b4f682f385f95e2f394339641889d6bb70352e9e07d73d1e3185","target":"graph","created_at":"2026-05-18T00:05:20Z","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":"In this paper, we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions. Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment.","authors_text":"Bin Wang, Jiyong Li, Yonglei Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-19T16:07:06Z","title":"Long-term analysis of exponential integrators for highly oscillatory conservative systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07268","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:e8d7c7d8cde7d9f051aaaf18de7dd066697fa9c28bb3fecedbbe33f04a0c9604","target":"record","created_at":"2026-05-18T00:05:20Z","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":"df927ed695b75580ac3d307136d2d8e85123444236767b4f95d1ab7fb153c0c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-19T16:07:06Z","title_canon_sha256":"e07265605c6d75f59f5d2cd2a4ce2795ddd37062d769dd5d4882763d6a9c4352"},"schema_version":"1.0","source":{"id":"1809.07268","kind":"arxiv","version":1}},"canonical_sha256":"7239f66b8311c05484b04c5d9ac93a1e82b4d977861d64a06f782c47b730cbec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7239f66b8311c05484b04c5d9ac93a1e82b4d977861d64a06f782c47b730cbec","first_computed_at":"2026-05-18T00:05:20.203455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:20.203455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sM64v5zECHixu+XCZJvY4g0pMQr2PsUr9x7sQclUeTj+BgbBt7tdKpIR75ZrEMVIxPE227TOyQfTa7poi1BtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:20.204024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8d7c7d8cde7d9f051aaaf18de7dd066697fa9c28bb3fecedbbe33f04a0c9604","sha256:f3859445f232b4f682f385f95e2f394339641889d6bb70352e9e07d73d1e3185"],"state_sha256":"cb436d72e41ffe6ee6adf3fc90e63295b92130c198b6d85fb7fa5fdd471a7365"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5lOnn3WZGN7EG/oIApXXORGMX1ckADLLOnAoS3EXNsMeHzI12FTMhxAph0MtN63VRQGRp4EiL7x3t1RT3n7+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T07:00:26.239179Z","bundle_sha256":"468cf9a692b812059e66b3b659789b1aa5f422fe71ef82045299e4c4bb12712d"}}