{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:F7FAC7HNV3LG2GSHK6NHVWUP5X","short_pith_number":"pith:F7FAC7HN","canonical_record":{"source":{"id":"2602.19393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-23T00:00:57Z","cross_cats_sorted":[],"title_canon_sha256":"93434d8ad7b3eb77cafb41d930d23f76daf2d3541ae2eb1298360de78dfeaa5b","abstract_canon_sha256":"38b46101d4da72afbc6034e359f02c1a343798f907a39c09b2633bf4d36b8a06"},"schema_version":"1.0"},"canonical_sha256":"2fca017cedaed66d1a47579a7ada8fedce644d41de2abc8a442cbe087c4a83f5","source":{"kind":"arxiv","id":"2602.19393","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.19393","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"2602.19393v2","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.19393","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"F7FAC7HNV3LG","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"pith_short_16","alias_value":"F7FAC7HNV3LG2GSH","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"pith_short_8","alias_value":"F7FAC7HN","created_at":"2026-06-10T01:09:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:F7FAC7HNV3LG2GSHK6NHVWUP5X","target":"record","payload":{"canonical_record":{"source":{"id":"2602.19393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-23T00:00:57Z","cross_cats_sorted":[],"title_canon_sha256":"93434d8ad7b3eb77cafb41d930d23f76daf2d3541ae2eb1298360de78dfeaa5b","abstract_canon_sha256":"38b46101d4da72afbc6034e359f02c1a343798f907a39c09b2633bf4d36b8a06"},"schema_version":"1.0"},"canonical_sha256":"2fca017cedaed66d1a47579a7ada8fedce644d41de2abc8a442cbe087c4a83f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:09:56.989600Z","signature_b64":"M9agRxjA9/sCtea80izLdg1oaL5Wwo06PJKoqN2x9H2pQp5wHUDDyookJ6zRHpCueHU+pTHy2mIRGwtyZHW2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fca017cedaed66d1a47579a7ada8fedce644d41de2abc8a442cbe087c4a83f5","last_reissued_at":"2026-06-10T01:09:56.988604Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:09:56.988604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.19393","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":"2026-06-10T01:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ntele1Ah9b0VZfhEH0vCSlFNpq5budpBlQ6gsfWbSBs6CCe4PqkvR3zWlCle3QhxMMdEk900iF7HiX/+RJHmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:18:11.340615Z"},"content_sha256":"5e34890a588e04506e866a9091b15c1522476a11a3d7701c96d3c0210de798a5","schema_version":"1.0","event_id":"sha256:5e34890a588e04506e866a9091b15c1522476a11a3d7701c96d3c0210de798a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:F7FAC7HNV3LG2GSHK6NHVWUP5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"In Defense of Cosine Similarity: Normalization Eliminates the Gauge Freedom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Taha Bouhsine","submitted_at":"2026-02-23T00:00:57Z","abstract_excerpt":"Steck, Ekanadham, and Kallus [arXiv:2403.05440] demonstrate that cosine similarity of learned embeddings from matrix factorization models can be rendered arbitrary by a diagonal ``gauge'' matrix $D$. Their result is correct and important for practitioners who compute cosine similarity on embeddings trained with dot-product objectives. However, we argue that their conclusion, cautioning against cosine similarity in general, conflates the pathology of an incompatible training objective with the geometric validity of cosine distance on the unit sphere. We prove that when embeddings are constraine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.19393","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/2602.19393/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":"2026-06-10T01:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZ2oBVuSoiWo80s+UOJgjxavwIqIi1lY/IAHIIYSh0TdPfeNt/DzRkLZg3HKsDFhg/NBnXYnVHMRH3nBzIjLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:18:11.341210Z"},"content_sha256":"475b9061d5d4723b1ded346aa504b7a4c48ea948742d87fd8ff2f056db5f8779","schema_version":"1.0","event_id":"sha256:475b9061d5d4723b1ded346aa504b7a4c48ea948742d87fd8ff2f056db5f8779"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X/bundle.json","state_url":"https://pith.science/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X/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":"2026-07-04T13:18:11Z","links":{"resolver":"https://pith.science/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X","bundle":"https://pith.science/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X/bundle.json","state":"https://pith.science/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7FAC7HNV3LG2GSHK6NHVWUP5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F7FAC7HNV3LG2GSHK6NHVWUP5X","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":"38b46101d4da72afbc6034e359f02c1a343798f907a39c09b2633bf4d36b8a06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-23T00:00:57Z","title_canon_sha256":"93434d8ad7b3eb77cafb41d930d23f76daf2d3541ae2eb1298360de78dfeaa5b"},"schema_version":"1.0","source":{"id":"2602.19393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.19393","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"2602.19393v2","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.19393","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"F7FAC7HNV3LG","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"pith_short_16","alias_value":"F7FAC7HNV3LG2GSH","created_at":"2026-06-10T01:09:56Z"},{"alias_kind":"pith_short_8","alias_value":"F7FAC7HN","created_at":"2026-06-10T01:09:56Z"}],"graph_snapshots":[{"event_id":"sha256:475b9061d5d4723b1ded346aa504b7a4c48ea948742d87fd8ff2f056db5f8779","target":"graph","created_at":"2026-06-10T01:09:56Z","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/2602.19393/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Steck, Ekanadham, and Kallus [arXiv:2403.05440] demonstrate that cosine similarity of learned embeddings from matrix factorization models can be rendered arbitrary by a diagonal ``gauge'' matrix $D$. Their result is correct and important for practitioners who compute cosine similarity on embeddings trained with dot-product objectives. However, we argue that their conclusion, cautioning against cosine similarity in general, conflates the pathology of an incompatible training objective with the geometric validity of cosine distance on the unit sphere. We prove that when embeddings are constraine","authors_text":"Taha Bouhsine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-23T00:00:57Z","title":"In Defense of Cosine Similarity: Normalization Eliminates the Gauge Freedom"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.19393","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":"sha256:5e34890a588e04506e866a9091b15c1522476a11a3d7701c96d3c0210de798a5","target":"record","created_at":"2026-06-10T01:09:56Z","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":"38b46101d4da72afbc6034e359f02c1a343798f907a39c09b2633bf4d36b8a06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-02-23T00:00:57Z","title_canon_sha256":"93434d8ad7b3eb77cafb41d930d23f76daf2d3541ae2eb1298360de78dfeaa5b"},"schema_version":"1.0","source":{"id":"2602.19393","kind":"arxiv","version":2}},"canonical_sha256":"2fca017cedaed66d1a47579a7ada8fedce644d41de2abc8a442cbe087c4a83f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fca017cedaed66d1a47579a7ada8fedce644d41de2abc8a442cbe087c4a83f5","first_computed_at":"2026-06-10T01:09:56.988604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:56.988604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9agRxjA9/sCtea80izLdg1oaL5Wwo06PJKoqN2x9H2pQp5wHUDDyookJ6zRHpCueHU+pTHy2mIRGwtyZHW2BA==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:56.989600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.19393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e34890a588e04506e866a9091b15c1522476a11a3d7701c96d3c0210de798a5","sha256:475b9061d5d4723b1ded346aa504b7a4c48ea948742d87fd8ff2f056db5f8779"],"state_sha256":"e61f1d5e4ae281427a0e3615c02b691be9db384c9eabc28616a29a39e4f5d4f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"557I14kCEdE4IuIcldzlygB9keLR2ZlWs0jVhDRT27WTpEFpf+m8915XY6eh/1Y/Ta0Qru/VU6ZEj2UmfxdrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T13:18:11.343863Z","bundle_sha256":"853fbb6026c9a5f79359ac0b30a535122993a6e3f5bcdd188b268782f2aebc6b"}}