{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QZM6BXSJ77VCFNBYOLJF5LZDWK","short_pith_number":"pith:QZM6BXSJ","canonical_record":{"source":{"id":"2506.01189","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2025-06-01T21:55:15Z","cross_cats_sorted":["cs.LG","math.DG","math.FA"],"title_canon_sha256":"da3408e5a23abfb38eca985114d2ea8dc2a82a48557ad19a74d5de4b8d99e1e9","abstract_canon_sha256":"973f362b5c68c8794b0da9bc9814232c3e61361b1033c0be41b64c97b3973dde"},"schema_version":"1.0"},"canonical_sha256":"8659e0de49ffea22b43872d25eaf23b29fe3fdcba2f09c018e70f84a00f92cf6","source":{"kind":"arxiv","id":"2506.01189","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01189","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01189v2","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01189","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"pith_short_12","alias_value":"QZM6BXSJ77VC","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"pith_short_16","alias_value":"QZM6BXSJ77VCFNBY","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"pith_short_8","alias_value":"QZM6BXSJ","created_at":"2026-07-05T11:51:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QZM6BXSJ77VCFNBYOLJF5LZDWK","target":"record","payload":{"canonical_record":{"source":{"id":"2506.01189","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2025-06-01T21:55:15Z","cross_cats_sorted":["cs.LG","math.DG","math.FA"],"title_canon_sha256":"da3408e5a23abfb38eca985114d2ea8dc2a82a48557ad19a74d5de4b8d99e1e9","abstract_canon_sha256":"973f362b5c68c8794b0da9bc9814232c3e61361b1033c0be41b64c97b3973dde"},"schema_version":"1.0"},"canonical_sha256":"8659e0de49ffea22b43872d25eaf23b29fe3fdcba2f09c018e70f84a00f92cf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:51:27.950310Z","signature_b64":"fCwlDQUWGKRCCGhY0OTg7l6Ng4O4/MFC3i4kafpEDNNUszI9dzRugWSI6vYsIQLqslDAveRL42BOPB9XVI7xCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8659e0de49ffea22b43872d25eaf23b29fe3fdcba2f09c018e70f84a00f92cf6","last_reissued_at":"2026-07-05T11:51:27.949809Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:51:27.949809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.01189","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":"2026-07-05T11:51:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJb3wzwt5kzHPWEMD6u0nW7xoWo5cx7jI2lA3wdLgz6tnF0ytdLfcBB3Z10CHKcGbjjOahIx3OlSHkF5CiKTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:59:30.157065Z"},"content_sha256":"1fc4a3c1ab4a14c5f51e927f94a2d1560e4c25d3277765c1b754696bf5e6a2d7","schema_version":"1.0","event_id":"sha256:1fc4a3c1ab4a14c5f51e927f94a2d1560e4c25d3277765c1b754696bf5e6a2d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QZM6BXSJ77VCFNBYOLJF5LZDWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.DG","math.FA"],"primary_cat":"cs.CV","authors_text":"Emmanuel Hartman, Nicolas Charon","submitted_at":"2025-06-01T21:55:15Z","abstract_excerpt":"Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the non-Euclidean nature of shape spaces, which are defined as equivalence classes under invariance groups. Building machine learning frameworks that incorporate such invariances, notably to shape parametrization, is often crucial to ensure generalizability of the trained models to new observations. This work proposes \\textit{SVarM} to exploit varifold representations of s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01189","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/2506.01189/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":"2026-07-05T11:51:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4wv01dql5Ivgc3FTU9vBpSiqsBooI5L6gsF1U17THFucFmvQwxH+1+4muWp1ztXc/CmfVhLyA30/NFtYvlpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:59:30.157580Z"},"content_sha256":"6e59ebe338f6b3b63bb28183885f1a1c958ffa046846381a3d8dda8a2a5bd7a8","schema_version":"1.0","event_id":"sha256:6e59ebe338f6b3b63bb28183885f1a1c958ffa046846381a3d8dda8a2a5bd7a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK/bundle.json","state_url":"https://pith.science/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK/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":"2026-08-08T09:59:30Z","links":{"resolver":"https://pith.science/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK","bundle":"https://pith.science/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK/bundle.json","state":"https://pith.science/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZM6BXSJ77VCFNBYOLJF5LZDWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QZM6BXSJ77VCFNBYOLJF5LZDWK","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":"973f362b5c68c8794b0da9bc9814232c3e61361b1033c0be41b64c97b3973dde","cross_cats_sorted":["cs.LG","math.DG","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2025-06-01T21:55:15Z","title_canon_sha256":"da3408e5a23abfb38eca985114d2ea8dc2a82a48557ad19a74d5de4b8d99e1e9"},"schema_version":"1.0","source":{"id":"2506.01189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01189","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01189v2","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01189","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"pith_short_12","alias_value":"QZM6BXSJ77VC","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"pith_short_16","alias_value":"QZM6BXSJ77VCFNBY","created_at":"2026-07-05T11:51:27Z"},{"alias_kind":"pith_short_8","alias_value":"QZM6BXSJ","created_at":"2026-07-05T11:51:27Z"}],"graph_snapshots":[{"event_id":"sha256:6e59ebe338f6b3b63bb28183885f1a1c958ffa046846381a3d8dda8a2a5bd7a8","target":"graph","created_at":"2026-07-05T11:51:27Z","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/2506.01189/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the non-Euclidean nature of shape spaces, which are defined as equivalence classes under invariance groups. Building machine learning frameworks that incorporate such invariances, notably to shape parametrization, is often crucial to ensure generalizability of the trained models to new observations. This work proposes \\textit{SVarM} to exploit varifold representations of s","authors_text":"Emmanuel Hartman, Nicolas Charon","cross_cats":["cs.LG","math.DG","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2025-06-01T21:55:15Z","title":"SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01189","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":"sha256:1fc4a3c1ab4a14c5f51e927f94a2d1560e4c25d3277765c1b754696bf5e6a2d7","target":"record","created_at":"2026-07-05T11:51:27Z","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":"973f362b5c68c8794b0da9bc9814232c3e61361b1033c0be41b64c97b3973dde","cross_cats_sorted":["cs.LG","math.DG","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2025-06-01T21:55:15Z","title_canon_sha256":"da3408e5a23abfb38eca985114d2ea8dc2a82a48557ad19a74d5de4b8d99e1e9"},"schema_version":"1.0","source":{"id":"2506.01189","kind":"arxiv","version":2}},"canonical_sha256":"8659e0de49ffea22b43872d25eaf23b29fe3fdcba2f09c018e70f84a00f92cf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8659e0de49ffea22b43872d25eaf23b29fe3fdcba2f09c018e70f84a00f92cf6","first_computed_at":"2026-07-05T11:51:27.949809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:51:27.949809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCwlDQUWGKRCCGhY0OTg7l6Ng4O4/MFC3i4kafpEDNNUszI9dzRugWSI6vYsIQLqslDAveRL42BOPB9XVI7xCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:51:27.950310Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fc4a3c1ab4a14c5f51e927f94a2d1560e4c25d3277765c1b754696bf5e6a2d7","sha256:6e59ebe338f6b3b63bb28183885f1a1c958ffa046846381a3d8dda8a2a5bd7a8"],"state_sha256":"722c78e5e12eb4c1332db2dd86a2105912ef499b203ef02f8684e0c334deda31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KO+6F+Ub9/2UF+4dxGfQMzjSLsVhsD+Snee51LfzW9oAvkRZT9n7Th5OXsZN1jW4tshKRf+Wls9NA8Y4Xsy0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:59:30.162934Z","bundle_sha256":"b60cef0f7fc1e511d11f4047873be459b63ecd5ef72ad49ba5533af65303ed2f"}}