{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:K32OL2WQ42TWARKY2R6YX5ETCQ","short_pith_number":"pith:K32OL2WQ","canonical_record":{"source":{"id":"2010.06540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-10-13T16:46:49Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"82e4b3ec8ca4f92dd93697d1b715a05d27df2927f18c1bb66664c57474bb4368","abstract_canon_sha256":"1567df7252a54d448d5b87cab2f8e0965d0230e3148222521a152aaf1eefb805"},"schema_version":"1.0"},"canonical_sha256":"56f4e5ead0e6a7604558d47d8bf493140f70e251da62a3c80489099b4384288b","source":{"kind":"arxiv","id":"2010.06540","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06540","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06540v2","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06540","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"K32OL2WQ42TW","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"K32OL2WQ42TWARKY","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"K32OL2WQ","created_at":"2026-07-05T02:12:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:K32OL2WQ42TWARKY2R6YX5ETCQ","target":"record","payload":{"canonical_record":{"source":{"id":"2010.06540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-10-13T16:46:49Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"82e4b3ec8ca4f92dd93697d1b715a05d27df2927f18c1bb66664c57474bb4368","abstract_canon_sha256":"1567df7252a54d448d5b87cab2f8e0965d0230e3148222521a152aaf1eefb805"},"schema_version":"1.0"},"canonical_sha256":"56f4e5ead0e6a7604558d47d8bf493140f70e251da62a3c80489099b4384288b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:12:53.384873Z","signature_b64":"79gLrQjaMsjoWoCXcoohQ442f6/UZIXrhhNbtoJzImBUCLwEblwUQQi+4T9QXUJDHdvBpdWPkmtfkZDQxvOJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56f4e5ead0e6a7604558d47d8bf493140f70e251da62a3c80489099b4384288b","last_reissued_at":"2026-07-05T02:12:53.384403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:12:53.384403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.06540","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6NIC1BNtfe9t1eBN0BkWG05bkYtKBwfMgDqD6Z/gGOFb+KT27djdwu8slVxDLzgz2tZgiYm7QLDU5M/B58X5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:38:50.828487Z"},"content_sha256":"214ddfd7bd07b234894749e3d58a3aeb5b4d3d7eded201e184a8a280cc53face","schema_version":"1.0","event_id":"sha256:214ddfd7bd07b234894749e3d58a3aeb5b4d3d7eded201e184a8a280cc53face"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:K32OL2WQ42TWARKY2R6YX5ETCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure-preserving algorithms with uniform error bound and long-time energy conservation for highly oscillatory Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bin Wang, Yaolin Jiang","submitted_at":"2020-10-13T16:46:49Z","abstract_excerpt":"Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly oscillatory solution, and the blended algorithms inherit and respect the advantage of each method. Two kinds of algorithms are presented to preserve the symplecticity and energy of the Hamiltonian systems, respectively. Moreover, the proposed algorithms are shown to have uniform error bound for the highly oscillatory structure. A numerical experiment is carr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06540","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.06540/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q1er9tqZAF+iWv9aVxBiYQDwk5SDZ4xd6UjWR7jkgJeBQDhRCIdI3FHOA3rEHPVlBhBQGxkvLPi80GMM/R1aDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:38:50.828876Z"},"content_sha256":"fb2923b4ee7e4a99a2d326ad868ff8fc750e308659b478925b3102d62a895391","schema_version":"1.0","event_id":"sha256:fb2923b4ee7e4a99a2d326ad868ff8fc750e308659b478925b3102d62a895391"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K32OL2WQ42TWARKY2R6YX5ETCQ/bundle.json","state_url":"https://pith.science/pith/K32OL2WQ42TWARKY2R6YX5ETCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K32OL2WQ42TWARKY2R6YX5ETCQ/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":"2026-08-03T20:38:50Z","links":{"resolver":"https://pith.science/pith/K32OL2WQ42TWARKY2R6YX5ETCQ","bundle":"https://pith.science/pith/K32OL2WQ42TWARKY2R6YX5ETCQ/bundle.json","state":"https://pith.science/pith/K32OL2WQ42TWARKY2R6YX5ETCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K32OL2WQ42TWARKY2R6YX5ETCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:K32OL2WQ42TWARKY2R6YX5ETCQ","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":"1567df7252a54d448d5b87cab2f8e0965d0230e3148222521a152aaf1eefb805","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-10-13T16:46:49Z","title_canon_sha256":"82e4b3ec8ca4f92dd93697d1b715a05d27df2927f18c1bb66664c57474bb4368"},"schema_version":"1.0","source":{"id":"2010.06540","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06540","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06540v2","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06540","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"K32OL2WQ42TW","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"K32OL2WQ42TWARKY","created_at":"2026-07-05T02:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"K32OL2WQ","created_at":"2026-07-05T02:12:53Z"}],"graph_snapshots":[{"event_id":"sha256:fb2923b4ee7e4a99a2d326ad868ff8fc750e308659b478925b3102d62a895391","target":"graph","created_at":"2026-07-05T02:12:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.06540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly oscillatory solution, and the blended algorithms inherit and respect the advantage of each method. Two kinds of algorithms are presented to preserve the symplecticity and energy of the Hamiltonian systems, respectively. Moreover, the proposed algorithms are shown to have uniform error bound for the highly oscillatory structure. A numerical experiment is carr","authors_text":"Bin Wang, Yaolin Jiang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-10-13T16:46:49Z","title":"Structure-preserving algorithms with uniform error bound and long-time energy conservation for highly oscillatory Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06540","kind":"arxiv","version":2},"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":"sha256:214ddfd7bd07b234894749e3d58a3aeb5b4d3d7eded201e184a8a280cc53face","target":"record","created_at":"2026-07-05T02:12:53Z","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":"1567df7252a54d448d5b87cab2f8e0965d0230e3148222521a152aaf1eefb805","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-10-13T16:46:49Z","title_canon_sha256":"82e4b3ec8ca4f92dd93697d1b715a05d27df2927f18c1bb66664c57474bb4368"},"schema_version":"1.0","source":{"id":"2010.06540","kind":"arxiv","version":2}},"canonical_sha256":"56f4e5ead0e6a7604558d47d8bf493140f70e251da62a3c80489099b4384288b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56f4e5ead0e6a7604558d47d8bf493140f70e251da62a3c80489099b4384288b","first_computed_at":"2026-07-05T02:12:53.384403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:12:53.384403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"79gLrQjaMsjoWoCXcoohQ442f6/UZIXrhhNbtoJzImBUCLwEblwUQQi+4T9QXUJDHdvBpdWPkmtfkZDQxvOJDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:12:53.384873Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.06540","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:214ddfd7bd07b234894749e3d58a3aeb5b4d3d7eded201e184a8a280cc53face","sha256:fb2923b4ee7e4a99a2d326ad868ff8fc750e308659b478925b3102d62a895391"],"state_sha256":"6bafb12a2e3028402a8dfde82dbcef7bbee559c2a52bbf159ac2a6687a2779a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7C69MIYg0URd1yr6roSjw3/Q5Xr91maY+JjXf4Dgvh1NhAlRv6gr9SXTdj7XIN3pNqwbGSwPbq//5wB1gxHxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:38:50.831292Z","bundle_sha256":"77befe920b193a25b8837b628a6b1040d2ac55bf1ba79f74547ca3a2b34e0299"}}