{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HMN4NBEYRGIPLPOUP7N7NTZ7RF","short_pith_number":"pith:HMN4NBEY","canonical_record":{"source":{"id":"1412.5346","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-12-17T11:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"6c90f780e87e12f2bd00b911de88772eb3134856d41e95110d122ff38e9192c3","abstract_canon_sha256":"acb191053a49e21beef13d337dd1bea5d320ff60cdd66ad3013d224b272a98de"},"schema_version":"1.0"},"canonical_sha256":"3b1bc684988990f5bdd47fdbf6cf3f896164a66494709dcf84b4aed6b9238b93","source":{"kind":"arxiv","id":"1412.5346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5346","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5346v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5346","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"HMN4NBEYRGIP","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMN4NBEYRGIPLPOU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMN4NBEY","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HMN4NBEYRGIPLPOUP7N7NTZ7RF","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5346","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-12-17T11:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"6c90f780e87e12f2bd00b911de88772eb3134856d41e95110d122ff38e9192c3","abstract_canon_sha256":"acb191053a49e21beef13d337dd1bea5d320ff60cdd66ad3013d224b272a98de"},"schema_version":"1.0"},"canonical_sha256":"3b1bc684988990f5bdd47fdbf6cf3f896164a66494709dcf84b4aed6b9238b93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:03.176596Z","signature_b64":"Ws0POgwz587ryQdibh9FhyGXGHHd9p9WmaRBCdTgCwiq2KcI0PZPIRjrMDpaE6kdwSGQwMbwtSQKurNqlVV9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b1bc684988990f5bdd47fdbf6cf3f896164a66494709dcf84b4aed6b9238b93","last_reissued_at":"2026-05-18T02:31:03.175917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:03.175917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5346","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":"2026-05-18T02:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w49Yj3VW9TAAZ+xwZz6QrZUBllPmkK/F98OEbpwvf5v1O5J6lzq96OhwOStNxRllfcSXwdH0zM5OK31wpg4eBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:26:56.330786Z"},"content_sha256":"7a113d748c636a327f54893fb3a21fc247213422fc693b80e13253ad0ffe17c5","schema_version":"1.0","event_id":"sha256:7a113d748c636a327f54893fb3a21fc247213422fc693b80e13253ad0ffe17c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HMN4NBEYRGIPLPOUP7N7NTZ7RF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sixth order averaged vector field method","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Haochen Li, Mengzhao Qin, Yushun Wang","submitted_at":"2014-12-17T11:31:19Z","abstract_excerpt":"In this paper, based on the theory of rooted trees and B-series, we propose the concrete formulas of the substitution law for the trees of order =5. With the help of the new substitution law, we derive a B-series integrator extending the averaged vector field (AVF) method to high order. The new integrator turns out to be of order six and exactly preserves energy for Hamiltonian systems. Numerical experiments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5346","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":"2026-05-18T02:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pMdgZXMqbQBj9NbKYMc/06hpkPK/7a7UKOKCBG17Cq7e4KZ8LlGE1+dJfnmFRki9IN6tPT9Orc6T3ZrFOu9yBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:26:56.331504Z"},"content_sha256":"baf072cff58c0b99f33d3047a84a28b6579dde1ef0c7f9207860acfc69039a6e","schema_version":"1.0","event_id":"sha256:baf072cff58c0b99f33d3047a84a28b6579dde1ef0c7f9207860acfc69039a6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF/bundle.json","state_url":"https://pith.science/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF/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":"2026-05-22T17:26:56Z","links":{"resolver":"https://pith.science/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF","bundle":"https://pith.science/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF/bundle.json","state":"https://pith.science/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMN4NBEYRGIPLPOUP7N7NTZ7RF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HMN4NBEYRGIPLPOUP7N7NTZ7RF","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":"acb191053a49e21beef13d337dd1bea5d320ff60cdd66ad3013d224b272a98de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-12-17T11:31:19Z","title_canon_sha256":"6c90f780e87e12f2bd00b911de88772eb3134856d41e95110d122ff38e9192c3"},"schema_version":"1.0","source":{"id":"1412.5346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5346","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5346v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5346","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"HMN4NBEYRGIP","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMN4NBEYRGIPLPOU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMN4NBEY","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:baf072cff58c0b99f33d3047a84a28b6579dde1ef0c7f9207860acfc69039a6e","target":"graph","created_at":"2026-05-18T02:31:03Z","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, based on the theory of rooted trees and B-series, we propose the concrete formulas of the substitution law for the trees of order =5. With the help of the new substitution law, we derive a B-series integrator extending the averaged vector field (AVF) method to high order. The new integrator turns out to be of order six and exactly preserves energy for Hamiltonian systems. Numerical experiments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method.","authors_text":"Haochen Li, Mengzhao Qin, Yushun Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-12-17T11:31:19Z","title":"A sixth order averaged vector field method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5346","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":"sha256:7a113d748c636a327f54893fb3a21fc247213422fc693b80e13253ad0ffe17c5","target":"record","created_at":"2026-05-18T02:31:03Z","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":"acb191053a49e21beef13d337dd1bea5d320ff60cdd66ad3013d224b272a98de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-12-17T11:31:19Z","title_canon_sha256":"6c90f780e87e12f2bd00b911de88772eb3134856d41e95110d122ff38e9192c3"},"schema_version":"1.0","source":{"id":"1412.5346","kind":"arxiv","version":1}},"canonical_sha256":"3b1bc684988990f5bdd47fdbf6cf3f896164a66494709dcf84b4aed6b9238b93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b1bc684988990f5bdd47fdbf6cf3f896164a66494709dcf84b4aed6b9238b93","first_computed_at":"2026-05-18T02:31:03.175917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:03.175917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ws0POgwz587ryQdibh9FhyGXGHHd9p9WmaRBCdTgCwiq2KcI0PZPIRjrMDpaE6kdwSGQwMbwtSQKurNqlVV9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:03.176596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a113d748c636a327f54893fb3a21fc247213422fc693b80e13253ad0ffe17c5","sha256:baf072cff58c0b99f33d3047a84a28b6579dde1ef0c7f9207860acfc69039a6e"],"state_sha256":"bd0e09e8de46d6b4cb75678f6cfc527c9d9bb59d03c69a96b86018aabd11119c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNOCBLCZ15lbboVr5hck5Fq5EgcCtFZZlgu1UpgR5Z1Cgj9IwudQ02y4REIEX27aRazOkAj7CeH7f392wj74AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T17:26:56.334863Z","bundle_sha256":"aa0e4a9ea0867fa0588f75c5dc48dd8ce288eff31edf238ed42927b567095d1d"}}