{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AY6K5TJHHPEALY6EBNREIBURVW","short_pith_number":"pith:AY6K5TJH","canonical_record":{"source":{"id":"2503.05540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-07T16:08:53Z","cross_cats_sorted":["cs.RO"],"title_canon_sha256":"aac8a2e434459024eaa8a6f3ac38b2be9c09eae1154f0882080e65f9382474e7","abstract_canon_sha256":"b9efb5a0e34314b016e06f50993f38b12070e8d9afb1c19e32c46238c72b4623"},"schema_version":"1.0"},"canonical_sha256":"063caecd273bc805e3c40b62440691ad81f97c8fddc4984c9bbf0fada2b1225b","source":{"kind":"arxiv","id":"2503.05540","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05540","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05540v1","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05540","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"AY6K5TJHHPEA","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"AY6K5TJHHPEALY6E","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"AY6K5TJH","created_at":"2026-07-05T10:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AY6K5TJHHPEALY6EBNREIBURVW","target":"record","payload":{"canonical_record":{"source":{"id":"2503.05540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-07T16:08:53Z","cross_cats_sorted":["cs.RO"],"title_canon_sha256":"aac8a2e434459024eaa8a6f3ac38b2be9c09eae1154f0882080e65f9382474e7","abstract_canon_sha256":"b9efb5a0e34314b016e06f50993f38b12070e8d9afb1c19e32c46238c72b4623"},"schema_version":"1.0"},"canonical_sha256":"063caecd273bc805e3c40b62440691ad81f97c8fddc4984c9bbf0fada2b1225b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:30.289652Z","signature_b64":"NTAyYog0YbwzgCOPwqKDDan6XtxjN2kkeEs6zxW2iFIEiODjVKSsStI9GRergniMJWYg8kHc01Llu5fVi/etDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"063caecd273bc805e3c40b62440691ad81f97c8fddc4984c9bbf0fada2b1225b","last_reissued_at":"2026-07-05T10:26:30.289106Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:30.289106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.05540","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":"2026-07-05T10:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wA/dRrulBpIYpVDCfFdpLmDk8FCIB0oSPNSThrYFLU3MK5GAVCQzMGAovMcNC7KzJ++80lL5oDmypuztm/C7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:58:14.937457Z"},"content_sha256":"08e59c76a94e24022acf71126cd4153f2046955f4b25d1ba1acb572f8511e4d6","schema_version":"1.0","event_id":"sha256:08e59c76a94e24022acf71126cd4153f2046955f4b25d1ba1acb572f8511e4d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AY6K5TJHHPEALY6EBNREIBURVW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemann$^2$: Learning Riemannian Submanifolds from Riemannian Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.RO"],"primary_cat":"cs.LG","authors_text":"Leonel Rozo, Miguel Gonz\\'alez-Duque, No\\'emie Jaquier, S{\\o}ren Hauberg","submitted_at":"2025-03-07T16:08:53Z","abstract_excerpt":"Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches ignore the underlying geometric constraints or fail to provide meaningful metrics in the latent space. To address these limitations, we propose to learn Riemannian latent representations of such geometric data. To do so, we estimate the pullback metric induced by a Wrapped Gaussian Process Latent Variable Model, which explicitly accounts for the data geometr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05540","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.05540/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":"2026-07-05T10:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ljlv1zT3FQfyAYhI28bVgKZc/ztDTeqQiBmWjaIRG6QA8hpAtffyoGAyRaqCS6whYqzFLbRp+nrOp2ZeYdXfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:58:14.938397Z"},"content_sha256":"73d6297ca0d69e30e3658b1da658294e32af4965956edf330e9315074f421500","schema_version":"1.0","event_id":"sha256:73d6297ca0d69e30e3658b1da658294e32af4965956edf330e9315074f421500"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AY6K5TJHHPEALY6EBNREIBURVW/bundle.json","state_url":"https://pith.science/pith/AY6K5TJHHPEALY6EBNREIBURVW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AY6K5TJHHPEALY6EBNREIBURVW/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":"2026-08-14T19:58:14Z","links":{"resolver":"https://pith.science/pith/AY6K5TJHHPEALY6EBNREIBURVW","bundle":"https://pith.science/pith/AY6K5TJHHPEALY6EBNREIBURVW/bundle.json","state":"https://pith.science/pith/AY6K5TJHHPEALY6EBNREIBURVW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AY6K5TJHHPEALY6EBNREIBURVW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AY6K5TJHHPEALY6EBNREIBURVW","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":"b9efb5a0e34314b016e06f50993f38b12070e8d9afb1c19e32c46238c72b4623","cross_cats_sorted":["cs.RO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-07T16:08:53Z","title_canon_sha256":"aac8a2e434459024eaa8a6f3ac38b2be9c09eae1154f0882080e65f9382474e7"},"schema_version":"1.0","source":{"id":"2503.05540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05540","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05540v1","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05540","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"AY6K5TJHHPEA","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"AY6K5TJHHPEALY6E","created_at":"2026-07-05T10:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"AY6K5TJH","created_at":"2026-07-05T10:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:73d6297ca0d69e30e3658b1da658294e32af4965956edf330e9315074f421500","target":"graph","created_at":"2026-07-05T10:26:30Z","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/2503.05540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches ignore the underlying geometric constraints or fail to provide meaningful metrics in the latent space. To address these limitations, we propose to learn Riemannian latent representations of such geometric data. To do so, we estimate the pullback metric induced by a Wrapped Gaussian Process Latent Variable Model, which explicitly accounts for the data geometr","authors_text":"Leonel Rozo, Miguel Gonz\\'alez-Duque, No\\'emie Jaquier, S{\\o}ren Hauberg","cross_cats":["cs.RO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-07T16:08:53Z","title":"Riemann$^2$: Learning Riemannian Submanifolds from Riemannian Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05540","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":"sha256:08e59c76a94e24022acf71126cd4153f2046955f4b25d1ba1acb572f8511e4d6","target":"record","created_at":"2026-07-05T10:26:30Z","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":"b9efb5a0e34314b016e06f50993f38b12070e8d9afb1c19e32c46238c72b4623","cross_cats_sorted":["cs.RO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-07T16:08:53Z","title_canon_sha256":"aac8a2e434459024eaa8a6f3ac38b2be9c09eae1154f0882080e65f9382474e7"},"schema_version":"1.0","source":{"id":"2503.05540","kind":"arxiv","version":1}},"canonical_sha256":"063caecd273bc805e3c40b62440691ad81f97c8fddc4984c9bbf0fada2b1225b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"063caecd273bc805e3c40b62440691ad81f97c8fddc4984c9bbf0fada2b1225b","first_computed_at":"2026-07-05T10:26:30.289106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:26:30.289106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NTAyYog0YbwzgCOPwqKDDan6XtxjN2kkeEs6zxW2iFIEiODjVKSsStI9GRergniMJWYg8kHc01Llu5fVi/etDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:26:30.289652Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.05540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08e59c76a94e24022acf71126cd4153f2046955f4b25d1ba1acb572f8511e4d6","sha256:73d6297ca0d69e30e3658b1da658294e32af4965956edf330e9315074f421500"],"state_sha256":"673d99cc2c7e2662275d6b9baed341fa236896cf6960730e249c7d1fcbd7583a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zlptI6aOxRDfW6Y0xcjZ3G3N/+63TOp0Hz9eQ7ylkPskimK/tvJxyLEc2FneBLJZLU7BgmThxtoabJo/5kRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:58:14.945755Z","bundle_sha256":"d574f29cd9b9af26287d7fc697bc842d47f5e82b97af6e7a3e7ba0755e06c475"}}