{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3WYK3NRUKMCOITA3DERUNZQKVL","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":"e0aa6e2ea1f0d02530b0d42f5d1f7734c5b8387e2f97aa400b8dc9faa7fc98c5","cross_cats_sorted":["cs.CV","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-09-14T02:45:56Z","title_canon_sha256":"83f83531ce44f62685bfb268615df0de78ff3051ecb2972500519f1bb14b945f"},"schema_version":"1.0","source":{"id":"2509.11054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.11054","created_at":"2026-07-05T12:11:32Z"},{"alias_kind":"arxiv_version","alias_value":"2509.11054v1","created_at":"2026-07-05T12:11:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.11054","created_at":"2026-07-05T12:11:32Z"},{"alias_kind":"pith_short_12","alias_value":"3WYK3NRUKMCO","created_at":"2026-07-05T12:11:32Z"},{"alias_kind":"pith_short_16","alias_value":"3WYK3NRUKMCOITA3","created_at":"2026-07-05T12:11:32Z"},{"alias_kind":"pith_short_8","alias_value":"3WYK3NRU","created_at":"2026-07-05T12:11:32Z"}],"graph_snapshots":[{"event_id":"sha256:f3bd5851740ffa6bc4aa3509b4f01f22970810dfdc45e8af7df52f5a5083dc0f","target":"graph","created_at":"2026-07-05T12:11:32Z","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/2509.11054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the first information-theoretic limits for multimodal retrieval. Casting ranking as lossy source coding, we derive a single-letter rate-distortion function $R(D)$ for reciprocal-rank distortion and prove a converse bound that splits into a modality-balanced term plus a skew penalty $\\kappa\\,\\Delta H$ capturing entropy imbalance and cross-modal redundancy. We then construct an explicit entropy-weighted stochastic quantizer with an adaptive, per-modality temperature decoder; a Blahut-Arimoto argument shows this scheme achieves distortion within $O(n^{-1})$ of $R(D)$ using $n$ traini","authors_text":"Thomas Y. Chen","cross_cats":["cs.CV","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-09-14T02:45:56Z","title":"Rate-Distortion Limits for Multimodal Retrieval: Theory, Optimal Codes, and Finite-Sample Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11054","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":"sha256:6dd78c2082f48a6a6cd6f2ef90ba0da2ee9390b46900072c72f6d3f3120d9f23","target":"record","created_at":"2026-07-05T12:11:32Z","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":"e0aa6e2ea1f0d02530b0d42f5d1f7734c5b8387e2f97aa400b8dc9faa7fc98c5","cross_cats_sorted":["cs.CV","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-09-14T02:45:56Z","title_canon_sha256":"83f83531ce44f62685bfb268615df0de78ff3051ecb2972500519f1bb14b945f"},"schema_version":"1.0","source":{"id":"2509.11054","kind":"arxiv","version":1}},"canonical_sha256":"ddb0adb6345304e44c1b192346e60aaacfe65de17b1a4bd0ce2e50c9fe852b13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddb0adb6345304e44c1b192346e60aaacfe65de17b1a4bd0ce2e50c9fe852b13","first_computed_at":"2026-07-05T12:11:32.742268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:11:32.742268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GfjUoZp98WSBCDaJHoFtjeTb3QOcEGPISVtmKBV+IqaCWkJo7RHWkfOUOoHfUUx0nnFNUbtxW/hIrkyhFpD4CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:11:32.742787Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.11054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dd78c2082f48a6a6cd6f2ef90ba0da2ee9390b46900072c72f6d3f3120d9f23","sha256:f3bd5851740ffa6bc4aa3509b4f01f22970810dfdc45e8af7df52f5a5083dc0f"],"state_sha256":"0cf817cff7e1528662b906dc948b74b071c81d9143a76bb111806e1f8b902bcd"}