{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PRJG7ZG5S62B2ZDVVIDYQAAGHY","short_pith_number":"pith:PRJG7ZG5","canonical_record":{"source":{"id":"2603.21437","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-03-22T22:58:11Z","cross_cats_sorted":["cs.IR"],"title_canon_sha256":"8c44474e3b8d9215650e8783be41260f2d59b1a589d9558473cb055ea979c0bc","abstract_canon_sha256":"ff357964bf7791c397d1fc3fa28b08b89b469b74133f55686070f17bc21ccb8b"},"schema_version":"1.0"},"canonical_sha256":"7c526fe4dd97b41d6475aa078800063e37b555ab121a109f2ed0345b35364b25","source":{"kind":"arxiv","id":"2603.21437","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.21437","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"arxiv_version","alias_value":"2603.21437v2","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.21437","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"pith_short_12","alias_value":"PRJG7ZG5S62B","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"pith_short_16","alias_value":"PRJG7ZG5S62B2ZDV","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"pith_short_8","alias_value":"PRJG7ZG5","created_at":"2026-05-25T02:01:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PRJG7ZG5S62B2ZDVVIDYQAAGHY","target":"record","payload":{"canonical_record":{"source":{"id":"2603.21437","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-03-22T22:58:11Z","cross_cats_sorted":["cs.IR"],"title_canon_sha256":"8c44474e3b8d9215650e8783be41260f2d59b1a589d9558473cb055ea979c0bc","abstract_canon_sha256":"ff357964bf7791c397d1fc3fa28b08b89b469b74133f55686070f17bc21ccb8b"},"schema_version":"1.0"},"canonical_sha256":"7c526fe4dd97b41d6475aa078800063e37b555ab121a109f2ed0345b35364b25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:17.968405Z","signature_b64":"5UpgZINUAMdqEQ9rdjy3g5WqPzPSsi4dwyMipM+tb/GV6QnmXjsQi/8xbyeMfjD19m1QJZ7OBkUpKv6ENpQcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c526fe4dd97b41d6475aa078800063e37b555ab121a109f2ed0345b35364b25","last_reissued_at":"2026-05-25T02:01:17.967493Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:17.967493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.21437","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":"2026-05-25T02:01:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8xsNIHrEBkxcHznYjUkvxydONUgjb8CkvRuXQkK8F4uCMwS3yHB+87V+CW9Y3biXt4aKyvRQfpqu8v3Tuy7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:26:22.750134Z"},"content_sha256":"db2e3fa362b35a1c352626127e2a9cf858ae8c3ab545349f47953468d8f5e4ea","schema_version":"1.0","event_id":"sha256:db2e3fa362b35a1c352626127e2a9cf858ae8c3ab545349f47953468d8f5e4ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PRJG7ZG5S62B2ZDVVIDYQAAGHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pooling and Semantic Shift: The Fundamental Challenges in Long Text Embedding and Retrieval","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IR"],"primary_cat":"cs.CL","authors_text":"Dimitris N. Metaxas, Hang Gao, Kai Mei, Wujiang Xu","submitted_at":"2026-03-22T22:58:11Z","abstract_excerpt":"Transformer-based embedding models frequently exhibit geometric pathologies, such as anisotropy and length-induced representation collapse, which can degrade downstream retrieval performance. While prior work often attributes these issues directly to text length or attention mechanisms, we argue that the fundamental drivers are instead the inherent pooling operations coupled with internal semantic shift. In this paper, we establish a unified theoretical framework proving that contextual pooling intrinsically causes embedding collapse. Specifically, we mathematically prove that pooling semantic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21437","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/2603.21437/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":"2026-05-25T02:01:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HN++6uLXVhDRqKtDvyoE6hUrELx9g60kS8Mqu531CdYPun4ct3FgEYyZtIlnqtSRy9vOec0Fj8gwBPfi18MzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:26:22.750553Z"},"content_sha256":"c54401521cd2fd4c2bda58877c2b273a00b18cec342d56e14ea7ccaf915f1a40","schema_version":"1.0","event_id":"sha256:c54401521cd2fd4c2bda58877c2b273a00b18cec342d56e14ea7ccaf915f1a40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY/bundle.json","state_url":"https://pith.science/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY/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":"2026-06-12T06:26:22Z","links":{"resolver":"https://pith.science/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY","bundle":"https://pith.science/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY/bundle.json","state":"https://pith.science/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PRJG7ZG5S62B2ZDVVIDYQAAGHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PRJG7ZG5S62B2ZDVVIDYQAAGHY","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":"ff357964bf7791c397d1fc3fa28b08b89b469b74133f55686070f17bc21ccb8b","cross_cats_sorted":["cs.IR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-03-22T22:58:11Z","title_canon_sha256":"8c44474e3b8d9215650e8783be41260f2d59b1a589d9558473cb055ea979c0bc"},"schema_version":"1.0","source":{"id":"2603.21437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.21437","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"arxiv_version","alias_value":"2603.21437v2","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.21437","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"pith_short_12","alias_value":"PRJG7ZG5S62B","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"pith_short_16","alias_value":"PRJG7ZG5S62B2ZDV","created_at":"2026-05-25T02:01:17Z"},{"alias_kind":"pith_short_8","alias_value":"PRJG7ZG5","created_at":"2026-05-25T02:01:17Z"}],"graph_snapshots":[{"event_id":"sha256:c54401521cd2fd4c2bda58877c2b273a00b18cec342d56e14ea7ccaf915f1a40","target":"graph","created_at":"2026-05-25T02:01:17Z","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/2603.21437/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformer-based embedding models frequently exhibit geometric pathologies, such as anisotropy and length-induced representation collapse, which can degrade downstream retrieval performance. While prior work often attributes these issues directly to text length or attention mechanisms, we argue that the fundamental drivers are instead the inherent pooling operations coupled with internal semantic shift. In this paper, we establish a unified theoretical framework proving that contextual pooling intrinsically causes embedding collapse. Specifically, we mathematically prove that pooling semantic","authors_text":"Dimitris N. Metaxas, Hang Gao, Kai Mei, Wujiang Xu","cross_cats":["cs.IR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-03-22T22:58:11Z","title":"Pooling and Semantic Shift: The Fundamental Challenges in Long Text Embedding and Retrieval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21437","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:db2e3fa362b35a1c352626127e2a9cf858ae8c3ab545349f47953468d8f5e4ea","target":"record","created_at":"2026-05-25T02:01:17Z","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":"ff357964bf7791c397d1fc3fa28b08b89b469b74133f55686070f17bc21ccb8b","cross_cats_sorted":["cs.IR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-03-22T22:58:11Z","title_canon_sha256":"8c44474e3b8d9215650e8783be41260f2d59b1a589d9558473cb055ea979c0bc"},"schema_version":"1.0","source":{"id":"2603.21437","kind":"arxiv","version":2}},"canonical_sha256":"7c526fe4dd97b41d6475aa078800063e37b555ab121a109f2ed0345b35364b25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c526fe4dd97b41d6475aa078800063e37b555ab121a109f2ed0345b35364b25","first_computed_at":"2026-05-25T02:01:17.967493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:17.967493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5UpgZINUAMdqEQ9rdjy3g5WqPzPSsi4dwyMipM+tb/GV6QnmXjsQi/8xbyeMfjD19m1QJZ7OBkUpKv6ENpQcBA==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:17.968405Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.21437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db2e3fa362b35a1c352626127e2a9cf858ae8c3ab545349f47953468d8f5e4ea","sha256:c54401521cd2fd4c2bda58877c2b273a00b18cec342d56e14ea7ccaf915f1a40"],"state_sha256":"d5c5064909f0b46072ed402c051f84b844e9f602e8da27f98e2bea95c29de635"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PjpcfMDA5NzE9QMLRLdmCrJelCtEJ+rZN/dz1to5Jv+k9U8KWcDUZmpEWmtJrGxdoC36H0Ly1dmwvR3BubWfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:26:22.753180Z","bundle_sha256":"5a4bddca37e4e6eb16bbff788dad3a3c7c59d68e761ef4f256270231948c7656"}}