{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7LKFFS3IVEKDNCFEXG3A7PILOF","short_pith_number":"pith:7LKFFS3I","canonical_record":{"source":{"id":"1503.06971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T10:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"6ab32eb91498da66c44a0180370c5f560bc1ed0cd542b27549b4862a5ce49043","abstract_canon_sha256":"74e1cf01dccfa7573002e3309305ec991e926d53f8c91d3e20c97fb72d1c51a9"},"schema_version":"1.0"},"canonical_sha256":"fad452cb68a9143688a4b9b60fbd0b715c6172e96bb78a792866d3f27e76a16b","source":{"kind":"arxiv","id":"1503.06971","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06971","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06971v1","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06971","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"7LKFFS3IVEKD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7LKFFS3IVEKDNCFE","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7LKFFS3I","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7LKFFS3IVEKDNCFEXG3A7PILOF","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T10:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"6ab32eb91498da66c44a0180370c5f560bc1ed0cd542b27549b4862a5ce49043","abstract_canon_sha256":"74e1cf01dccfa7573002e3309305ec991e926d53f8c91d3e20c97fb72d1c51a9"},"schema_version":"1.0"},"canonical_sha256":"fad452cb68a9143688a4b9b60fbd0b715c6172e96bb78a792866d3f27e76a16b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:29.653463Z","signature_b64":"rCNFrWD7kIeZckNlcJfZCGZ73LzT6me+pwpQYRqnt2lrjusU7A5yyQtvf1uvaGCvbqsDIsqoMMaQqpopFKbYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fad452cb68a9143688a4b9b60fbd0b715c6172e96bb78a792866d3f27e76a16b","last_reissued_at":"2026-05-18T02:20:29.652901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:29.652901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06971","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":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MllqFwp6+OrkcCGm6hjSuxSDzjh3uhAyOFuzbySRacTXqv9VDXxYbooQE9kZvkgf/3K2093jCJwENhdq8SfUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:09:02.925311Z"},"content_sha256":"80a6107524ad636343c3d08af0e87953471a41075cead9fb60955bfdd1c500da","schema_version":"1.0","event_id":"sha256:80a6107524ad636343c3d08af0e87953471a41075cead9fb60955bfdd1c500da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7LKFFS3IVEKDNCFEXG3A7PILOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Martin Rumpf, Paola Pozzi, Ricardo Perl","submitted_at":"2015-03-24T10:07:01Z","abstract_excerpt":"A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic, which in particular ensures that Wulff shapes are invariant up to scaling under the gradient flow. In each time step of the gradient flow a nested optimization problem has to be solved. Thereby, an outer variational problem reflects the time discretization of the actual Willmore flow and involves an approximate anisotropic $L^2$-distance between two consecutive "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06971","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":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MvQdBBewbiUR7U4zzsGX0u5C03vcUW9VMDFE40khKXT7G/LGHHrbv12JTH1OV9u+UdscYFYcJ2VsnKipggRgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:09:02.925942Z"},"content_sha256":"d8008931b93f60bc17b5ebf8ab3fb57d1340d7cc76f68d8657d97a66fe1a63d4","schema_version":"1.0","event_id":"sha256:d8008931b93f60bc17b5ebf8ab3fb57d1340d7cc76f68d8657d97a66fe1a63d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LKFFS3IVEKDNCFEXG3A7PILOF/bundle.json","state_url":"https://pith.science/pith/7LKFFS3IVEKDNCFEXG3A7PILOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LKFFS3IVEKDNCFEXG3A7PILOF/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":"2026-05-30T01:09:02Z","links":{"resolver":"https://pith.science/pith/7LKFFS3IVEKDNCFEXG3A7PILOF","bundle":"https://pith.science/pith/7LKFFS3IVEKDNCFEXG3A7PILOF/bundle.json","state":"https://pith.science/pith/7LKFFS3IVEKDNCFEXG3A7PILOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LKFFS3IVEKDNCFEXG3A7PILOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7LKFFS3IVEKDNCFEXG3A7PILOF","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":"74e1cf01dccfa7573002e3309305ec991e926d53f8c91d3e20c97fb72d1c51a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T10:07:01Z","title_canon_sha256":"6ab32eb91498da66c44a0180370c5f560bc1ed0cd542b27549b4862a5ce49043"},"schema_version":"1.0","source":{"id":"1503.06971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06971","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06971v1","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06971","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"7LKFFS3IVEKD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7LKFFS3IVEKDNCFE","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7LKFFS3I","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:d8008931b93f60bc17b5ebf8ab3fb57d1340d7cc76f68d8657d97a66fe1a63d4","target":"graph","created_at":"2026-05-18T02:20:29Z","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":"A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic, which in particular ensures that Wulff shapes are invariant up to scaling under the gradient flow. In each time step of the gradient flow a nested optimization problem has to be solved. Thereby, an outer variational problem reflects the time discretization of the actual Willmore flow and involves an approximate anisotropic $L^2$-distance between two consecutive ","authors_text":"Martin Rumpf, Paola Pozzi, Ricardo Perl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T10:07:01Z","title":"A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06971","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":"sha256:80a6107524ad636343c3d08af0e87953471a41075cead9fb60955bfdd1c500da","target":"record","created_at":"2026-05-18T02:20:29Z","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":"74e1cf01dccfa7573002e3309305ec991e926d53f8c91d3e20c97fb72d1c51a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T10:07:01Z","title_canon_sha256":"6ab32eb91498da66c44a0180370c5f560bc1ed0cd542b27549b4862a5ce49043"},"schema_version":"1.0","source":{"id":"1503.06971","kind":"arxiv","version":1}},"canonical_sha256":"fad452cb68a9143688a4b9b60fbd0b715c6172e96bb78a792866d3f27e76a16b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fad452cb68a9143688a4b9b60fbd0b715c6172e96bb78a792866d3f27e76a16b","first_computed_at":"2026-05-18T02:20:29.652901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:29.652901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rCNFrWD7kIeZckNlcJfZCGZ73LzT6me+pwpQYRqnt2lrjusU7A5yyQtvf1uvaGCvbqsDIsqoMMaQqpopFKbYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:29.653463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80a6107524ad636343c3d08af0e87953471a41075cead9fb60955bfdd1c500da","sha256:d8008931b93f60bc17b5ebf8ab3fb57d1340d7cc76f68d8657d97a66fe1a63d4"],"state_sha256":"617d7d94c03c1d7d66bbbb6f4aeafb6f7497406d143b45cb8ca07488219b8514"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XoeggJAOA3ak1HzF6w8JVKhmGz1q0stsWLXAIo2Wx8g7NViNi0TtV+fSzCmEBSgh7U6DQTP0hZ5jT+vIshgTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:09:02.928953Z","bundle_sha256":"e1049dbc2e9ca52912ef3dce8e0598e9eb068b19bce2ed3515b600ced80d0d04"}}