{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XWMJ4DGYPGPNYY3GAECCTV6HU5","short_pith_number":"pith:XWMJ4DGY","canonical_record":{"source":{"id":"2606.22249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-20T22:22:26Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"8a39ff5a3a701dff938abb93cd5c5c39a688d85e9629508aeeb98f468ff08bf8","abstract_canon_sha256":"65cc771399d693986823c7ba63f58b6f1147d27f0935966107901bedba618036"},"schema_version":"1.0"},"canonical_sha256":"bd989e0cd8799edc6366010429d7c7a758545564158fe39c550c86614cda20f9","source":{"kind":"arxiv","id":"2606.22249","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22249","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22249v1","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22249","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"XWMJ4DGYPGPN","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"pith_short_16","alias_value":"XWMJ4DGYPGPNYY3G","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"pith_short_8","alias_value":"XWMJ4DGY","created_at":"2026-06-23T02:13:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XWMJ4DGYPGPNYY3GAECCTV6HU5","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-20T22:22:26Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"8a39ff5a3a701dff938abb93cd5c5c39a688d85e9629508aeeb98f468ff08bf8","abstract_canon_sha256":"65cc771399d693986823c7ba63f58b6f1147d27f0935966107901bedba618036"},"schema_version":"1.0"},"canonical_sha256":"bd989e0cd8799edc6366010429d7c7a758545564158fe39c550c86614cda20f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:32.966788Z","signature_b64":"BEob3EiK2TFRO53naOpVWdziL3nnoYmLMoJfV3+FE4hQNlfvizGvrfNE1HmyVKSSwBqvMJa8UCl+claYt9YZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd989e0cd8799edc6366010429d7c7a758545564158fe39c550c86614cda20f9","last_reissued_at":"2026-06-23T02:13:32.966385Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:32.966385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22249","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":"2026-06-23T02:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0oA9sonySc530ibAPuatoIjqx2xphTJNHh17OQZZ321IYWtZhdJLIeUrXXZXJHb2OFLBlySBv2BRIha2JdzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:21:29.041226Z"},"content_sha256":"5879bcc69a400e3c42736f354ff5a73ac3879b690e09be11861633720ff3c79d","schema_version":"1.0","event_id":"sha256:5879bcc69a400e3c42736f354ff5a73ac3879b690e09be11861633720ff3c79d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XWMJ4DGYPGPNYY3GAECCTV6HU5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Expressive Power of Weight Quantization in Large Language Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Shao-Qun Zhang","submitted_at":"2026-06-20T22:22:26Z","abstract_excerpt":"In recent years, weight quantization that encodes the learnable parameters of large language models in an $n$-bit format has garnered significant attention due to its potential for model compression and inference acceleration. Many practical techniques have been developed; however, the theoretical understanding of many aspects, especially the approximation and degradation of expressive power as the number of quantization bits decreases, remains unclear. In this paper, we provide a theoretical investigation into the expressive capability of large language models relative to the number of quanti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22249","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/2606.22249/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":"2026-06-23T02:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+kjQ+XOq23sWoGD0l2EYA3USKU2453+13vMadrB4Nm0sI1RfKesyPD7kW3BHXXsGxbjLGhpkwJ0QBF6KFRUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:21:29.041636Z"},"content_sha256":"42eaabad61046aec8dc9b4c9f88979892ad48b601d240d53fb66a37184a5222d","schema_version":"1.0","event_id":"sha256:42eaabad61046aec8dc9b4c9f88979892ad48b601d240d53fb66a37184a5222d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5/bundle.json","state_url":"https://pith.science/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5/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":"2026-07-05T03:21:29Z","links":{"resolver":"https://pith.science/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5","bundle":"https://pith.science/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5/bundle.json","state":"https://pith.science/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWMJ4DGYPGPNYY3GAECCTV6HU5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XWMJ4DGYPGPNYY3GAECCTV6HU5","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":"65cc771399d693986823c7ba63f58b6f1147d27f0935966107901bedba618036","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-20T22:22:26Z","title_canon_sha256":"8a39ff5a3a701dff938abb93cd5c5c39a688d85e9629508aeeb98f468ff08bf8"},"schema_version":"1.0","source":{"id":"2606.22249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22249","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22249v1","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22249","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"XWMJ4DGYPGPN","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"pith_short_16","alias_value":"XWMJ4DGYPGPNYY3G","created_at":"2026-06-23T02:13:32Z"},{"alias_kind":"pith_short_8","alias_value":"XWMJ4DGY","created_at":"2026-06-23T02:13:32Z"}],"graph_snapshots":[{"event_id":"sha256:42eaabad61046aec8dc9b4c9f88979892ad48b601d240d53fb66a37184a5222d","target":"graph","created_at":"2026-06-23T02:13:32Z","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/2606.22249/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In recent years, weight quantization that encodes the learnable parameters of large language models in an $n$-bit format has garnered significant attention due to its potential for model compression and inference acceleration. Many practical techniques have been developed; however, the theoretical understanding of many aspects, especially the approximation and degradation of expressive power as the number of quantization bits decreases, remains unclear. In this paper, we provide a theoretical investigation into the expressive capability of large language models relative to the number of quanti","authors_text":"Shao-Qun Zhang","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-20T22:22:26Z","title":"On the Expressive Power of Weight Quantization in Large Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22249","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":"sha256:5879bcc69a400e3c42736f354ff5a73ac3879b690e09be11861633720ff3c79d","target":"record","created_at":"2026-06-23T02:13:32Z","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":"65cc771399d693986823c7ba63f58b6f1147d27f0935966107901bedba618036","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-20T22:22:26Z","title_canon_sha256":"8a39ff5a3a701dff938abb93cd5c5c39a688d85e9629508aeeb98f468ff08bf8"},"schema_version":"1.0","source":{"id":"2606.22249","kind":"arxiv","version":1}},"canonical_sha256":"bd989e0cd8799edc6366010429d7c7a758545564158fe39c550c86614cda20f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd989e0cd8799edc6366010429d7c7a758545564158fe39c550c86614cda20f9","first_computed_at":"2026-06-23T02:13:32.966385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:32.966385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BEob3EiK2TFRO53naOpVWdziL3nnoYmLMoJfV3+FE4hQNlfvizGvrfNE1HmyVKSSwBqvMJa8UCl+claYt9YZCw==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:32.966788Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5879bcc69a400e3c42736f354ff5a73ac3879b690e09be11861633720ff3c79d","sha256:42eaabad61046aec8dc9b4c9f88979892ad48b601d240d53fb66a37184a5222d"],"state_sha256":"27e134698f455d938c401f5152f3ef49399d7f9e201f2abccbd212d803255490"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5zaD9TjKrCV2JTh0Ru5SLt5fGJh9CAd5jriPeGzupL8C1x9fe0Ktp6oX3HofnKmZE7JXusALIE/kWDqxSfgDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T03:21:29.043700Z","bundle_sha256":"b253970c8a16afd35b8aed7837f67222d4c5adab847a7b0a7bde442d46dbe4b2"}}