{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FVIZQ7K3VGS7Y6A2FVXRIGUJBG","short_pith_number":"pith:FVIZQ7K3","canonical_record":{"source":{"id":"2504.03309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-04T09:36:11Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"ab21e4ef60756288f2606a90ad68ef4212d40d39e838930f591bac39b09e38bb","abstract_canon_sha256":"fcb02197f980c51a9f70f328c369c80625e684e5490a5bba005bfd63bf5b0332"},"schema_version":"1.0"},"canonical_sha256":"2d51987d5ba9a5fc781a2d6f141a8909aa407b8482f2db2c7bc59f4ed9e31502","source":{"kind":"arxiv","id":"2504.03309","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.03309","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"2504.03309v2","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.03309","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"FVIZQ7K3VGS7","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"pith_short_16","alias_value":"FVIZQ7K3VGS7Y6A2","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"pith_short_8","alias_value":"FVIZQ7K3","created_at":"2026-07-05T11:31:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FVIZQ7K3VGS7Y6A2FVXRIGUJBG","target":"record","payload":{"canonical_record":{"source":{"id":"2504.03309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-04T09:36:11Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"ab21e4ef60756288f2606a90ad68ef4212d40d39e838930f591bac39b09e38bb","abstract_canon_sha256":"fcb02197f980c51a9f70f328c369c80625e684e5490a5bba005bfd63bf5b0332"},"schema_version":"1.0"},"canonical_sha256":"2d51987d5ba9a5fc781a2d6f141a8909aa407b8482f2db2c7bc59f4ed9e31502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:06.121284Z","signature_b64":"1ZEOUCHO5WXnQlyPiaBr2uTME0h9aW3oGtBw4e5yJchmRcn21TUek9ypIljKZSKBsenOpY2oRX7YssZFob7jAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d51987d5ba9a5fc781a2d6f141a8909aa407b8482f2db2c7bc59f4ed9e31502","last_reissued_at":"2026-07-05T11:31:06.120776Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:06.120776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.03309","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5biM1RbgC1giLxnjWY4jPiyS+Uv7Iy+GzgIMPI5V8xWKF+XYqXIxSYNvFRaX5N0w8rtJOV3Cj2wuDz8gmidHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:44:49.965477Z"},"content_sha256":"cd1060c9739e6713d78cc211759405de886014681bb97a82d93563d1a447e7eb","schema_version":"1.0","event_id":"sha256:cd1060c9739e6713d78cc211759405de886014681bb97a82d93563d1a447e7eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FVIZQ7K3VGS7Y6A2FVXRIGUJBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Roto-Translation Invariant Metrics on Position-Orientation Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.DG","authors_text":"Bart M. N. Smets, Gijs Bellaard","submitted_at":"2025-04-04T09:36:11Z","abstract_excerpt":"Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image analysis tasks like enhancement, denoising, and segmentation. These metrics enable roto-translation equivariant algorithms, with the associated Riemannian distance often used in implementation.\n  However, computing the Riemannian distance is costly, which makes it unsuitable in situations where constant recomputation is needed. We propose the mav (minimal angular velocity) distance, defined as the Riemannian length of a geometrically meaningful curve, as a practica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.03309","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.03309/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppHSslp46aAAb3Mo0K/KghS6apEmt3RNffRbVF38PwgK01hQ1wBHRedOs3ADOx1HU0cr4UzYhVcmEQAq4iqpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:44:49.966005Z"},"content_sha256":"e7de1e463ed19929b8a6f45e124b12292175c7571c284c015c66f8a7ef09cfe8","schema_version":"1.0","event_id":"sha256:e7de1e463ed19929b8a6f45e124b12292175c7571c284c015c66f8a7ef09cfe8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG/bundle.json","state_url":"https://pith.science/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG/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":"2026-08-20T05:44:49Z","links":{"resolver":"https://pith.science/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG","bundle":"https://pith.science/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG/bundle.json","state":"https://pith.science/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVIZQ7K3VGS7Y6A2FVXRIGUJBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FVIZQ7K3VGS7Y6A2FVXRIGUJBG","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":"fcb02197f980c51a9f70f328c369c80625e684e5490a5bba005bfd63bf5b0332","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-04T09:36:11Z","title_canon_sha256":"ab21e4ef60756288f2606a90ad68ef4212d40d39e838930f591bac39b09e38bb"},"schema_version":"1.0","source":{"id":"2504.03309","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.03309","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"2504.03309v2","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.03309","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"FVIZQ7K3VGS7","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"pith_short_16","alias_value":"FVIZQ7K3VGS7Y6A2","created_at":"2026-07-05T11:31:06Z"},{"alias_kind":"pith_short_8","alias_value":"FVIZQ7K3","created_at":"2026-07-05T11:31:06Z"}],"graph_snapshots":[{"event_id":"sha256:e7de1e463ed19929b8a6f45e124b12292175c7571c284c015c66f8a7ef09cfe8","target":"graph","created_at":"2026-07-05T11:31:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.03309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image analysis tasks like enhancement, denoising, and segmentation. These metrics enable roto-translation equivariant algorithms, with the associated Riemannian distance often used in implementation.\n  However, computing the Riemannian distance is costly, which makes it unsuitable in situations where constant recomputation is needed. We propose the mav (minimal angular velocity) distance, defined as the Riemannian length of a geometrically meaningful curve, as a practica","authors_text":"Bart M. N. Smets, Gijs Bellaard","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-04T09:36:11Z","title":"Roto-Translation Invariant Metrics on Position-Orientation Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.03309","kind":"arxiv","version":2},"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:cd1060c9739e6713d78cc211759405de886014681bb97a82d93563d1a447e7eb","target":"record","created_at":"2026-07-05T11:31:06Z","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":"fcb02197f980c51a9f70f328c369c80625e684e5490a5bba005bfd63bf5b0332","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-04T09:36:11Z","title_canon_sha256":"ab21e4ef60756288f2606a90ad68ef4212d40d39e838930f591bac39b09e38bb"},"schema_version":"1.0","source":{"id":"2504.03309","kind":"arxiv","version":2}},"canonical_sha256":"2d51987d5ba9a5fc781a2d6f141a8909aa407b8482f2db2c7bc59f4ed9e31502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d51987d5ba9a5fc781a2d6f141a8909aa407b8482f2db2c7bc59f4ed9e31502","first_computed_at":"2026-07-05T11:31:06.120776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:06.120776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ZEOUCHO5WXnQlyPiaBr2uTME0h9aW3oGtBw4e5yJchmRcn21TUek9ypIljKZSKBsenOpY2oRX7YssZFob7jAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:06.121284Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.03309","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd1060c9739e6713d78cc211759405de886014681bb97a82d93563d1a447e7eb","sha256:e7de1e463ed19929b8a6f45e124b12292175c7571c284c015c66f8a7ef09cfe8"],"state_sha256":"d0076acfe58a10c477c822f3e45617352426b1d50d1f6e309e49ca1a74064b3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9T97r6DX1f9eacNfWPzIkgobaX9aV4zw5X7VEYVZUvHUqs0BH19Xl/+Lj//LWa+so54MQRk9WhxKJYi/l7pAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T05:44:49.971782Z","bundle_sha256":"9ab6d787b3d99958b0e94467a3bb7d6cbf3b74e7bd3bc8d878be6e57657e02a0"}}