{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BB62IP7NIHAS7SJQWCEZFYFBLZ","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":"2bd92103e16a2d827179a68eaa752e455d2de51ff51df6130aa30e0eb4760c4b","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-02T16:07:41Z","title_canon_sha256":"0dbcb2eca398b4bcd58a1a97431c9f6802132605abebb1fc294d7e54c5430515"},"schema_version":"1.0","source":{"id":"1210.0822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0822","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0822v1","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0822","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"BB62IP7NIHAS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BB62IP7NIHAS7SJQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BB62IP7N","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:85013ff4156256d510947bb54aa7ff56741c9bf195afa9546af7b1a48b37c4a4","target":"graph","created_at":"2026-05-18T03:44:14Z","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":"Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity measure is derived from a deformation energy whose Hessian reproduces the underlying Riemannian metric, and it is used to define length and energy of discrete paths in shape space. The notion of discrete geodesics defined as energy minimizing paths gives rise to a discrete logarithmic map, a variational definition of a discrete exponential map, and a time discrete","authors_text":"Benedikt Wirth, Martin Rumpf","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-02T16:07:41Z","title":"Discrete geodesic calculus in the space of viscous fluidic objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0822","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:b6cbca8eb8f64571974758985597c874919a4e5229b93d7ae3f16f239316e3c5","target":"record","created_at":"2026-05-18T03:44:14Z","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":"2bd92103e16a2d827179a68eaa752e455d2de51ff51df6130aa30e0eb4760c4b","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-02T16:07:41Z","title_canon_sha256":"0dbcb2eca398b4bcd58a1a97431c9f6802132605abebb1fc294d7e54c5430515"},"schema_version":"1.0","source":{"id":"1210.0822","kind":"arxiv","version":1}},"canonical_sha256":"087da43fed41c12fc930b08992e0a15e61160cf36a266ddac20fca1fb34ae035","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"087da43fed41c12fc930b08992e0a15e61160cf36a266ddac20fca1fb34ae035","first_computed_at":"2026-05-18T03:44:14.184919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:14.184919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+hoaibeAZyX+I6Nq+UqrqiLb1EQYS7ZT54NC+zk4nxJej7FF0BX3V2DlzjjOdA3HYWVgzPm52BNgDutk50m4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:14.185357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6cbca8eb8f64571974758985597c874919a4e5229b93d7ae3f16f239316e3c5","sha256:85013ff4156256d510947bb54aa7ff56741c9bf195afa9546af7b1a48b37c4a4"],"state_sha256":"c3713b0014bf78d3cfc4556d1e13cb85ae7eeca05243ade7829a191b94e5cf69"}