{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BI7ORE5GMAHG6QTNYR4JSX36UF","short_pith_number":"pith:BI7ORE5G","canonical_record":{"source":{"id":"1012.5936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-12-29T13:33:01Z","cross_cats_sorted":[],"title_canon_sha256":"8eba2abc017903c07c02a48a645de6496b58c3be45627121c41be605f93ab535","abstract_canon_sha256":"ca53e870ba462aab08ddc075d50ddc973e81fdd34df7a7049c4ae36349c6d3c2"},"schema_version":"1.0"},"canonical_sha256":"0a3ee893a6600e6f426dc478995f7ea17448f3c4e1bf7a0f3feed1d0021b4e7f","source":{"kind":"arxiv","id":"1012.5936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5936","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5936v1","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5936","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"BI7ORE5GMAHG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BI7ORE5GMAHG6QTN","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BI7ORE5G","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BI7ORE5GMAHG6QTNYR4JSX36UF","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-12-29T13:33:01Z","cross_cats_sorted":[],"title_canon_sha256":"8eba2abc017903c07c02a48a645de6496b58c3be45627121c41be605f93ab535","abstract_canon_sha256":"ca53e870ba462aab08ddc075d50ddc973e81fdd34df7a7049c4ae36349c6d3c2"},"schema_version":"1.0"},"canonical_sha256":"0a3ee893a6600e6f426dc478995f7ea17448f3c4e1bf7a0f3feed1d0021b4e7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:21.021050Z","signature_b64":"G/l7Ou+Nsd04PpuaZLrVd3c769rNHKD+ouC4g2tQqiVTpPacATU0H3YbBQWZyWOn860WnJCx1zuJaqxwm3i8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a3ee893a6600e6f426dc478995f7ea17448f3c4e1bf7a0f3feed1d0021b4e7f","last_reissued_at":"2026-05-18T04:32:21.020230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:21.020230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5936","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":"2026-05-18T04:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKSs5nrQOgjzeWQPmAEHhzpk1zfxlJjK2tXu/8YqDbDSu1W+ZJ3mMapBT63kdFCD3hxZW+hfW4lvymO7ZwXtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:02:43.483203Z"},"content_sha256":"f3df73f8e29c59713d9776dc12b2757840abc35543331a9f90a5eb44b85082bc","schema_version":"1.0","event_id":"sha256:f3df73f8e29c59713d9776dc12b2757840abc35543331a9f90a5eb44b85082bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BI7ORE5GMAHG6QTNYR4JSX36UF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Affine-invariant geodesic geometry of deformable 3D shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Alexander M. Bronstein, Dan Raviv, Michael M. Bronstein, Nir Sochen, Ron Kimmel","submitted_at":"2010-12-29T13:33:01Z","abstract_excerpt":"Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing non-rigid shape analysis tools. In fact, we show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method techn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5936","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":"2026-05-18T04:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttiNT4CiFeSl2CAjPOv7AVRV+C9HqXj+OPFSVocwk4AHkEoLTcbZMny6GIV270U8EkL92j7RkPVv8YTXk4U5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:02:43.483931Z"},"content_sha256":"e4ccfbd70db7048328c7a23c365ffaaabf90e8c2bcea92007326d2f78e12a9ec","schema_version":"1.0","event_id":"sha256:e4ccfbd70db7048328c7a23c365ffaaabf90e8c2bcea92007326d2f78e12a9ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BI7ORE5GMAHG6QTNYR4JSX36UF/bundle.json","state_url":"https://pith.science/pith/BI7ORE5GMAHG6QTNYR4JSX36UF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BI7ORE5GMAHG6QTNYR4JSX36UF/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":"2026-05-26T03:02:43Z","links":{"resolver":"https://pith.science/pith/BI7ORE5GMAHG6QTNYR4JSX36UF","bundle":"https://pith.science/pith/BI7ORE5GMAHG6QTNYR4JSX36UF/bundle.json","state":"https://pith.science/pith/BI7ORE5GMAHG6QTNYR4JSX36UF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BI7ORE5GMAHG6QTNYR4JSX36UF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BI7ORE5GMAHG6QTNYR4JSX36UF","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":"ca53e870ba462aab08ddc075d50ddc973e81fdd34df7a7049c4ae36349c6d3c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-12-29T13:33:01Z","title_canon_sha256":"8eba2abc017903c07c02a48a645de6496b58c3be45627121c41be605f93ab535"},"schema_version":"1.0","source":{"id":"1012.5936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5936","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5936v1","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5936","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"BI7ORE5GMAHG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BI7ORE5GMAHG6QTN","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BI7ORE5G","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e4ccfbd70db7048328c7a23c365ffaaabf90e8c2bcea92007326d2f78e12a9ec","target":"graph","created_at":"2026-05-18T04:32:21Z","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":"Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing non-rigid shape analysis tools. In fact, we show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method techn","authors_text":"Alexander M. Bronstein, Dan Raviv, Michael M. Bronstein, Nir Sochen, Ron Kimmel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-12-29T13:33:01Z","title":"Affine-invariant geodesic geometry of deformable 3D shapes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5936","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:f3df73f8e29c59713d9776dc12b2757840abc35543331a9f90a5eb44b85082bc","target":"record","created_at":"2026-05-18T04:32:21Z","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":"ca53e870ba462aab08ddc075d50ddc973e81fdd34df7a7049c4ae36349c6d3c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-12-29T13:33:01Z","title_canon_sha256":"8eba2abc017903c07c02a48a645de6496b58c3be45627121c41be605f93ab535"},"schema_version":"1.0","source":{"id":"1012.5936","kind":"arxiv","version":1}},"canonical_sha256":"0a3ee893a6600e6f426dc478995f7ea17448f3c4e1bf7a0f3feed1d0021b4e7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a3ee893a6600e6f426dc478995f7ea17448f3c4e1bf7a0f3feed1d0021b4e7f","first_computed_at":"2026-05-18T04:32:21.020230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:21.020230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G/l7Ou+Nsd04PpuaZLrVd3c769rNHKD+ouC4g2tQqiVTpPacATU0H3YbBQWZyWOn860WnJCx1zuJaqxwm3i8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:21.021050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3df73f8e29c59713d9776dc12b2757840abc35543331a9f90a5eb44b85082bc","sha256:e4ccfbd70db7048328c7a23c365ffaaabf90e8c2bcea92007326d2f78e12a9ec"],"state_sha256":"dab5faf0fd877df2e1f2df272765c06e5f9339bede860d24dc1aa82be7c33aec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnECVqfyjwcwQ9lquihGCW+dX2QhAQPQD2jfG/8jTDintmyUsOuTI9ibXB+75S2c7HOT79HAugqDz2b48HisDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:02:43.487774Z","bundle_sha256":"0001aa75d43705bdcde234cc39d71ea497ddbfbc496eaa59b119a169756172bc"}}