{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:Z7JAZOCUISE5ZH7BBF5OK64Q7Q","short_pith_number":"pith:Z7JAZOCU","canonical_record":{"source":{"id":"2412.19212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-26T13:23:37Z","cross_cats_sorted":[],"title_canon_sha256":"e389a74ed128451b46a06b42735c1ebd75d2e18abca83382106b6d9a656232d2","abstract_canon_sha256":"c37aeb41b79eb76da74738a2d95a8913175277f4125f97901fcdbfbc8fff4884"},"schema_version":"1.0"},"canonical_sha256":"cfd20cb8544489dc9fe1097ae57b90fc161bbaa103ac25684f671e1cefef7aaf","source":{"kind":"arxiv","id":"2412.19212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19212","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19212v1","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19212","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"Z7JAZOCUISE5","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"pith_short_16","alias_value":"Z7JAZOCUISE5ZH7B","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"pith_short_8","alias_value":"Z7JAZOCU","created_at":"2026-07-05T09:54:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:Z7JAZOCUISE5ZH7BBF5OK64Q7Q","target":"record","payload":{"canonical_record":{"source":{"id":"2412.19212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-26T13:23:37Z","cross_cats_sorted":[],"title_canon_sha256":"e389a74ed128451b46a06b42735c1ebd75d2e18abca83382106b6d9a656232d2","abstract_canon_sha256":"c37aeb41b79eb76da74738a2d95a8913175277f4125f97901fcdbfbc8fff4884"},"schema_version":"1.0"},"canonical_sha256":"cfd20cb8544489dc9fe1097ae57b90fc161bbaa103ac25684f671e1cefef7aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:32.474944Z","signature_b64":"qpVYEbKQxQfS4w3VHv6B+VjOBsjUP4ii4F/3Q/WkezIHD6PzTgNVUtyy0Y/xKdUqQzx/ko2YIc2kQgKpjh0gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfd20cb8544489dc9fe1097ae57b90fc161bbaa103ac25684f671e1cefef7aaf","last_reissued_at":"2026-07-05T09:54:32.474590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:32.474590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.19212","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":"2026-07-05T09:54:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QiwytY2IJEkYSyVchhx8eXcUIJDR4ujNlCBy+hyQ2/kT90GElRZJhRcqyybZKeyY/UrvAIeNDkrybp83KASeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:32:43.749428Z"},"content_sha256":"81ce3fcdfb39aaadd6724b960953f5d268b33c20fb4cd5340a98277f1cb0c642","schema_version":"1.0","event_id":"sha256:81ce3fcdfb39aaadd6724b960953f5d268b33c20fb4cd5340a98277f1cb0c642"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:Z7JAZOCUISE5ZH7BBF5OK64Q7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Better Spherical Sliced-Wasserstein Distance Learning with Data-Adaptive Discriminative Projection Direction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Hongliang Zhang, Jian Yang, Lei Luo, Shuo Chen","submitted_at":"2024-12-26T13:23:37Z","abstract_excerpt":"Spherical Sliced-Wasserstein (SSW) has recently been proposed to measure the discrepancy between spherical data distributions in various fields, such as geology, medical domains, computer vision, and deep representation learning. However, in the original SSW, all projection directions are treated equally, which is too idealistic and cannot accurately reflect the importance of different projection directions for various data distributions. To address this issue, we propose a novel data-adaptive Discriminative Spherical Sliced-Wasserstein (DSSW) distance, which utilizes a projected energy functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19212","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/2412.19212/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":"2026-07-05T09:54:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AkuOcZVopYBNtt8UuPJXblbDHzt9U7Gl8ovSJ81cfh7PwgG9GDYJgkXYbe4s4eNcGLSxJO1dB4E7S3cQALRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:32:43.749930Z"},"content_sha256":"a42bd74ecd58b41d2309172ac9479988c641372e6d870dfd9a1db857b6ba73f8","schema_version":"1.0","event_id":"sha256:a42bd74ecd58b41d2309172ac9479988c641372e6d870dfd9a1db857b6ba73f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q/bundle.json","state_url":"https://pith.science/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q/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":"2026-08-16T18:32:43Z","links":{"resolver":"https://pith.science/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q","bundle":"https://pith.science/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q/bundle.json","state":"https://pith.science/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7JAZOCUISE5ZH7BBF5OK64Q7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:Z7JAZOCUISE5ZH7BBF5OK64Q7Q","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":"c37aeb41b79eb76da74738a2d95a8913175277f4125f97901fcdbfbc8fff4884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-26T13:23:37Z","title_canon_sha256":"e389a74ed128451b46a06b42735c1ebd75d2e18abca83382106b6d9a656232d2"},"schema_version":"1.0","source":{"id":"2412.19212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19212","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19212v1","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19212","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"Z7JAZOCUISE5","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"pith_short_16","alias_value":"Z7JAZOCUISE5ZH7B","created_at":"2026-07-05T09:54:32Z"},{"alias_kind":"pith_short_8","alias_value":"Z7JAZOCU","created_at":"2026-07-05T09:54:32Z"}],"graph_snapshots":[{"event_id":"sha256:a42bd74ecd58b41d2309172ac9479988c641372e6d870dfd9a1db857b6ba73f8","target":"graph","created_at":"2026-07-05T09:54:32Z","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/2412.19212/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Spherical Sliced-Wasserstein (SSW) has recently been proposed to measure the discrepancy between spherical data distributions in various fields, such as geology, medical domains, computer vision, and deep representation learning. However, in the original SSW, all projection directions are treated equally, which is too idealistic and cannot accurately reflect the importance of different projection directions for various data distributions. To address this issue, we propose a novel data-adaptive Discriminative Spherical Sliced-Wasserstein (DSSW) distance, which utilizes a projected energy functi","authors_text":"Hongliang Zhang, Jian Yang, Lei Luo, Shuo Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-26T13:23:37Z","title":"Towards Better Spherical Sliced-Wasserstein Distance Learning with Data-Adaptive Discriminative Projection Direction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19212","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":"sha256:81ce3fcdfb39aaadd6724b960953f5d268b33c20fb4cd5340a98277f1cb0c642","target":"record","created_at":"2026-07-05T09:54:32Z","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":"c37aeb41b79eb76da74738a2d95a8913175277f4125f97901fcdbfbc8fff4884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-26T13:23:37Z","title_canon_sha256":"e389a74ed128451b46a06b42735c1ebd75d2e18abca83382106b6d9a656232d2"},"schema_version":"1.0","source":{"id":"2412.19212","kind":"arxiv","version":1}},"canonical_sha256":"cfd20cb8544489dc9fe1097ae57b90fc161bbaa103ac25684f671e1cefef7aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfd20cb8544489dc9fe1097ae57b90fc161bbaa103ac25684f671e1cefef7aaf","first_computed_at":"2026-07-05T09:54:32.474590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:32.474590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qpVYEbKQxQfS4w3VHv6B+VjOBsjUP4ii4F/3Q/WkezIHD6PzTgNVUtyy0Y/xKdUqQzx/ko2YIc2kQgKpjh0gCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:32.474944Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81ce3fcdfb39aaadd6724b960953f5d268b33c20fb4cd5340a98277f1cb0c642","sha256:a42bd74ecd58b41d2309172ac9479988c641372e6d870dfd9a1db857b6ba73f8"],"state_sha256":"10f9dffe0423c6fe7e7de16acbfa279362743588c6346c66464139d83022c15e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNZGjblu5rSSAWWyOXVMYqr/5mHFkkxo2UDH56YO+zdMelCm2fwSlufVnYcobvhTx2/4FBNlxMoNE7KpfyfXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:32:43.754613Z","bundle_sha256":"f2288a5939e31a88921d30ad47354632c0db0fa1b9db74337e54a0b6fa930544"}}