{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BD2XTGB2TYW72C73XR7XNVQGCB","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":"67cd7c7c08d0f31a15600435c3ffd71717489860c5bcda10c729c61918d8f8bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-19T12:16:55Z","title_canon_sha256":"da7fd1dc83b1c3403eea9feee762290e74da3ccf85acea2974226cb4089b9cca"},"schema_version":"1.0","source":{"id":"1805.07578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07578","created_at":"2026-05-18T00:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07578v1","created_at":"2026-05-18T00:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07578","created_at":"2026-05-18T00:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"BD2XTGB2TYW7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BD2XTGB2TYW72C73","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BD2XTGB2","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:dc9109b5f19718d38c64dcc1d3d859fd1eed509c579023cdf82e40a8f6355022","target":"graph","created_at":"2026-05-18T00:15:33Z","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":"The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting schemes are intrinsic and do not depend on a particular choice of coordinates, nor on embedding of the manifold in a Euclidean space. Generalizations of well-known discrete gradient methods, such as the average vector field method and the Itoh--Abe method are obtained. It is shown how methods of higher order can be constructed via a collocation-like approach.","authors_text":"Brynjulf Owren, Elena Celledoni, S{\\o}lve Eidnes, Torbj{\\o}rn Ringholm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-19T12:16:55Z","title":"Energy preserving methods on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07578","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":"sha256:8c5572861957b6d5ac4aced3ff9b0b7d70c13c46d74689cb14ada39a90ced0e5","target":"record","created_at":"2026-05-18T00:15:33Z","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":"67cd7c7c08d0f31a15600435c3ffd71717489860c5bcda10c729c61918d8f8bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-19T12:16:55Z","title_canon_sha256":"da7fd1dc83b1c3403eea9feee762290e74da3ccf85acea2974226cb4089b9cca"},"schema_version":"1.0","source":{"id":"1805.07578","kind":"arxiv","version":1}},"canonical_sha256":"08f579983a9e2dfd0bfbbc7f76d606106283edcbee1806b255190f7e2e085149","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08f579983a9e2dfd0bfbbc7f76d606106283edcbee1806b255190f7e2e085149","first_computed_at":"2026-05-18T00:15:33.178081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:33.178081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bXtsO72aOKHQFnLKnM1N5f7qwaVVwAERs++mjBw8XiXMVWNvzZAZQ5rcTNiiRCg0Xeg/13NoQ8100Pe5cTNXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:33.178589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c5572861957b6d5ac4aced3ff9b0b7d70c13c46d74689cb14ada39a90ced0e5","sha256:dc9109b5f19718d38c64dcc1d3d859fd1eed509c579023cdf82e40a8f6355022"],"state_sha256":"f67169e5fce257fb2e718d9230723f6053d9120a40b6eb2175aa2603a3ae4769"}