{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WTNL4XH7A7HBVWSNPLBT5RBJSW","short_pith_number":"pith:WTNL4XH7","canonical_record":{"source":{"id":"2506.21278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-06-26T14:01:51Z","cross_cats_sorted":["cs.AI","cs.LG","math.ST","stat.TH"],"title_canon_sha256":"6293278884621d74c4ddd86042dab960137c3cd8fe8da631336f14b5abff9be4","abstract_canon_sha256":"cbf74c949ce46b006dddf63f4f8061b61d8cb938f568b0c24788aa82677e81d9"},"schema_version":"1.0"},"canonical_sha256":"b4dabe5cff07ce1ada4d7ac33ec4299582744b5df41cff68eb7433bab158a612","source":{"kind":"arxiv","id":"2506.21278","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21278","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21278v3","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21278","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"WTNL4XH7A7HB","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_16","alias_value":"WTNL4XH7A7HBVWSN","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_8","alias_value":"WTNL4XH7","created_at":"2026-06-02T01:03:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WTNL4XH7A7HBVWSNPLBT5RBJSW","target":"record","payload":{"canonical_record":{"source":{"id":"2506.21278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-06-26T14:01:51Z","cross_cats_sorted":["cs.AI","cs.LG","math.ST","stat.TH"],"title_canon_sha256":"6293278884621d74c4ddd86042dab960137c3cd8fe8da631336f14b5abff9be4","abstract_canon_sha256":"cbf74c949ce46b006dddf63f4f8061b61d8cb938f568b0c24788aa82677e81d9"},"schema_version":"1.0"},"canonical_sha256":"b4dabe5cff07ce1ada4d7ac33ec4299582744b5df41cff68eb7433bab158a612","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:32.411414Z","signature_b64":"NElV5KHbpwHRQJdcagmyevY+IhjUjPWrM2mAnSiqZLO59EmJH5EK6UC2nBsWSq+m5owoSFx9v8xPzL1oOcw4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4dabe5cff07ce1ada4d7ac33ec4299582744b5df41cff68eb7433bab158a612","last_reissued_at":"2026-06-02T01:03:32.410898Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:32.410898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.21278","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T01:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LHbTj6jYHSPheRQze2ord43aojorHmlQedH1wDuMDeto20ml73f6Ll6G+OY2tC+262ZU6OtljkVJcEa5wH5XDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:05:01.588335Z"},"content_sha256":"076d6b356e402d7c5700d3efba88e0c148df63e4773989794318b34af36febe0","schema_version":"1.0","event_id":"sha256:076d6b356e402d7c5700d3efba88e0c148df63e4773989794318b34af36febe0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WTNL4XH7A7HBVWSNPLBT5RBJSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Kurt Hornik, Lukas Sablica","submitted_at":"2025-06-26T14:01:51Z","abstract_excerpt":"We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces. The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\\\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution under an explicit concentration parameter mapping, while avoiding the high-order Bessel-function evaluations required by vMF implementations. For training, the Ku"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21278","kind":"arxiv","version":3},"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/2506.21278/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":"2026-06-02T01:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IaQeUcJ8f9p88GSpFhK+eNEi0jI1z4jEofoXiRq6YfrtdUhM6NiMOgTN0qKDoO5vnUgRcSRofewz2JNP5iCcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:05:01.588749Z"},"content_sha256":"23d36c957fef153d521155485ff149d5c7ab80f1dad0ef7f7be587a1320b76f9","schema_version":"1.0","event_id":"sha256:23d36c957fef153d521155485ff149d5c7ab80f1dad0ef7f7be587a1320b76f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW/bundle.json","state_url":"https://pith.science/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW/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":"2026-06-21T18:05:01Z","links":{"resolver":"https://pith.science/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW","bundle":"https://pith.science/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW/bundle.json","state":"https://pith.science/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTNL4XH7A7HBVWSNPLBT5RBJSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WTNL4XH7A7HBVWSNPLBT5RBJSW","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":"cbf74c949ce46b006dddf63f4f8061b61d8cb938f568b0c24788aa82677e81d9","cross_cats_sorted":["cs.AI","cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-06-26T14:01:51Z","title_canon_sha256":"6293278884621d74c4ddd86042dab960137c3cd8fe8da631336f14b5abff9be4"},"schema_version":"1.0","source":{"id":"2506.21278","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21278","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21278v3","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21278","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"WTNL4XH7A7HB","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_16","alias_value":"WTNL4XH7A7HBVWSN","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_8","alias_value":"WTNL4XH7","created_at":"2026-06-02T01:03:32Z"}],"graph_snapshots":[{"event_id":"sha256:23d36c957fef153d521155485ff149d5c7ab80f1dad0ef7f7be587a1320b76f9","target":"graph","created_at":"2026-06-02T01:03:32Z","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/2506.21278/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces. The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\\\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution under an explicit concentration parameter mapping, while avoiding the high-order Bessel-function evaluations required by vMF implementations. For training, the Ku","authors_text":"Kurt Hornik, Lukas Sablica","cross_cats":["cs.AI","cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-06-26T14:01:51Z","title":"Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21278","kind":"arxiv","version":3},"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":"sha256:076d6b356e402d7c5700d3efba88e0c148df63e4773989794318b34af36febe0","target":"record","created_at":"2026-06-02T01:03:32Z","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":"cbf74c949ce46b006dddf63f4f8061b61d8cb938f568b0c24788aa82677e81d9","cross_cats_sorted":["cs.AI","cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-06-26T14:01:51Z","title_canon_sha256":"6293278884621d74c4ddd86042dab960137c3cd8fe8da631336f14b5abff9be4"},"schema_version":"1.0","source":{"id":"2506.21278","kind":"arxiv","version":3}},"canonical_sha256":"b4dabe5cff07ce1ada4d7ac33ec4299582744b5df41cff68eb7433bab158a612","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4dabe5cff07ce1ada4d7ac33ec4299582744b5df41cff68eb7433bab158a612","first_computed_at":"2026-06-02T01:03:32.410898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:32.410898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NElV5KHbpwHRQJdcagmyevY+IhjUjPWrM2mAnSiqZLO59EmJH5EK6UC2nBsWSq+m5owoSFx9v8xPzL1oOcw4DA==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:32.411414Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.21278","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:076d6b356e402d7c5700d3efba88e0c148df63e4773989794318b34af36febe0","sha256:23d36c957fef153d521155485ff149d5c7ab80f1dad0ef7f7be587a1320b76f9"],"state_sha256":"62626d0917b471a6e7e7dee062e0ec2d5d42a4831f3541f890f1757aee644680"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXZICpKbmScoPUYDBCTHfiylnczy7MAhyntu4QV+JkyElRTZosmJ2JQS7owwWK0buoArDGqKjNTjwClN9l/RBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T18:05:01.590959Z","bundle_sha256":"459e9658079ff54c0199256321dfb4fd4cc9cdbec62047ec22eb5246a70a0769"}}