{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GOTUXG4OPJRZPPMRJIPZ5Z6TVB","short_pith_number":"pith:GOTUXG4O","canonical_record":{"source":{"id":"2607.05803","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IR","submitted_at":"2026-07-07T03:56:18Z","cross_cats_sorted":[],"title_canon_sha256":"4987ee661371e3e92a74f5dd8331a85da3e97dcc1fed5560ce2d5b0f3c179081","abstract_canon_sha256":"3775a96e165355a18521e2cd098b32b559f19cc4f36dccb2fbcc57ebcd2a44a2"},"schema_version":"1.0"},"canonical_sha256":"33a74b9b8e7a6397bd914a1f9ee7d3a85811b0b152759b2fb32648821d4b77f5","source":{"kind":"arxiv","id":"2607.05803","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05803","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05803v1","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05803","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"GOTUXG4OPJRZ","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"pith_short_16","alias_value":"GOTUXG4OPJRZPPMR","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"pith_short_8","alias_value":"GOTUXG4O","created_at":"2026-07-08T01:18:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GOTUXG4OPJRZPPMRJIPZ5Z6TVB","target":"record","payload":{"canonical_record":{"source":{"id":"2607.05803","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IR","submitted_at":"2026-07-07T03:56:18Z","cross_cats_sorted":[],"title_canon_sha256":"4987ee661371e3e92a74f5dd8331a85da3e97dcc1fed5560ce2d5b0f3c179081","abstract_canon_sha256":"3775a96e165355a18521e2cd098b32b559f19cc4f36dccb2fbcc57ebcd2a44a2"},"schema_version":"1.0"},"canonical_sha256":"33a74b9b8e7a6397bd914a1f9ee7d3a85811b0b152759b2fb32648821d4b77f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:46.564673Z","signature_b64":"t9qSmofGEamM9jvpYSZBaXjzWJUWVevMUi5dNGMhACl+sptWubrTyld8xkLKHK9JEoUQFtKUmwNp512KgEpFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33a74b9b8e7a6397bd914a1f9ee7d3a85811b0b152759b2fb32648821d4b77f5","last_reissued_at":"2026-07-08T01:18:46.564227Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:46.564227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.05803","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":"2026-07-08T01:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9DKCod1OpfHT145bU9QjkE79iOwvD7LUDO0G4xGhH77ayEfin+W4aJUgaHNPLEYEQznftLDJIhMUBDqiNs2cBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T16:45:23.300818Z"},"content_sha256":"d7e03737cfbf02e653ca1e3f8e646969173cdef08623278e86fcb712e644ead9","schema_version":"1.0","event_id":"sha256:d7e03737cfbf02e653ca1e3f8e646969173cdef08623278e86fcb712e644ead9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GOTUXG4OPJRZPPMRJIPZ5Z6TVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantifying and Expanding the Theoretical Capacity of Late-Interaction Retrieval Models","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.IR","authors_text":"Cameron Musco, Hamed Zamani, Julian Killingback, Varad Ingale","submitted_at":"2026-07-07T03:56:18Z","abstract_excerpt":"Late-interaction retrieval models that use the MaxSim similarity function have shown strong empirical performance, often outperforming single-vector dense and sparse retrieval models. Despite these empirical findings, little is known about the theoretical representation power of MaxSim and how it compares to other retrieval approaches. This paper shows by construction that MaxSim similarity can exactly replicate the inner product between any two non-negative k-sparse vectors with possibly infinite dimension, requiring only O(k) representation space. Moreover, there exist similarities that MaxS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05803","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/2607.05803/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":"2026-07-08T01:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qCJXUmOv6EamXzvOpf7kqH+m4A16GE7epI+dpp7V+ufh7Y34az2KVLGNpcYl8DYjw8zJGn9xu3usqy8Ip+H9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T16:45:23.301177Z"},"content_sha256":"97b6c134516dfab4ec5cf009f1a643daf11c8b2b94834fa511e3d3a367d5e61c","schema_version":"1.0","event_id":"sha256:97b6c134516dfab4ec5cf009f1a643daf11c8b2b94834fa511e3d3a367d5e61c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB/bundle.json","state_url":"https://pith.science/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB/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":"2026-07-10T16:45:23Z","links":{"resolver":"https://pith.science/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB","bundle":"https://pith.science/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB/bundle.json","state":"https://pith.science/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOTUXG4OPJRZPPMRJIPZ5Z6TVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GOTUXG4OPJRZPPMRJIPZ5Z6TVB","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":"3775a96e165355a18521e2cd098b32b559f19cc4f36dccb2fbcc57ebcd2a44a2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IR","submitted_at":"2026-07-07T03:56:18Z","title_canon_sha256":"4987ee661371e3e92a74f5dd8331a85da3e97dcc1fed5560ce2d5b0f3c179081"},"schema_version":"1.0","source":{"id":"2607.05803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05803","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05803v1","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05803","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"GOTUXG4OPJRZ","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"pith_short_16","alias_value":"GOTUXG4OPJRZPPMR","created_at":"2026-07-08T01:18:46Z"},{"alias_kind":"pith_short_8","alias_value":"GOTUXG4O","created_at":"2026-07-08T01:18:46Z"}],"graph_snapshots":[{"event_id":"sha256:97b6c134516dfab4ec5cf009f1a643daf11c8b2b94834fa511e3d3a367d5e61c","target":"graph","created_at":"2026-07-08T01:18:46Z","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/2607.05803/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Late-interaction retrieval models that use the MaxSim similarity function have shown strong empirical performance, often outperforming single-vector dense and sparse retrieval models. Despite these empirical findings, little is known about the theoretical representation power of MaxSim and how it compares to other retrieval approaches. This paper shows by construction that MaxSim similarity can exactly replicate the inner product between any two non-negative k-sparse vectors with possibly infinite dimension, requiring only O(k) representation space. Moreover, there exist similarities that MaxS","authors_text":"Cameron Musco, Hamed Zamani, Julian Killingback, Varad Ingale","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IR","submitted_at":"2026-07-07T03:56:18Z","title":"Quantifying and Expanding the Theoretical Capacity of Late-Interaction Retrieval Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05803","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:d7e03737cfbf02e653ca1e3f8e646969173cdef08623278e86fcb712e644ead9","target":"record","created_at":"2026-07-08T01:18:46Z","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":"3775a96e165355a18521e2cd098b32b559f19cc4f36dccb2fbcc57ebcd2a44a2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IR","submitted_at":"2026-07-07T03:56:18Z","title_canon_sha256":"4987ee661371e3e92a74f5dd8331a85da3e97dcc1fed5560ce2d5b0f3c179081"},"schema_version":"1.0","source":{"id":"2607.05803","kind":"arxiv","version":1}},"canonical_sha256":"33a74b9b8e7a6397bd914a1f9ee7d3a85811b0b152759b2fb32648821d4b77f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33a74b9b8e7a6397bd914a1f9ee7d3a85811b0b152759b2fb32648821d4b77f5","first_computed_at":"2026-07-08T01:18:46.564227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:46.564227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t9qSmofGEamM9jvpYSZBaXjzWJUWVevMUi5dNGMhACl+sptWubrTyld8xkLKHK9JEoUQFtKUmwNp512KgEpFBA==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:46.564673Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e03737cfbf02e653ca1e3f8e646969173cdef08623278e86fcb712e644ead9","sha256:97b6c134516dfab4ec5cf009f1a643daf11c8b2b94834fa511e3d3a367d5e61c"],"state_sha256":"f08b8240008c5d3acf25651530deff37861a96b4b759a38777f0118d39c04bed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b77TAfIh/LeXTCdD9F3KaMqGaEdtSIcF7k62ZCTReFcgYwQaiQa9VVshZ2CFr89pqDrh1jAg9Bo+PvzpGaAdBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T16:45:23.303719Z","bundle_sha256":"e7cc5aa3b4caf798213775e66dc117e5e283179c29dc57a12ce2ba5f7da26418"}}