{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RTNWZQIDA5DJKZKN36TEYVJZ34","short_pith_number":"pith:RTNWZQID","schema_version":"1.0","canonical_sha256":"8cdb6cc103074695654ddfa64c5539df3900e136a3437af928cf36ca5c65c3f7","source":{"kind":"arxiv","id":"2607.13511","version":1},"attestation_state":"computed","paper":{"title":"ExTernD: Expanded-Rank Ternary Decomposition Ternary LLM PTQ with Accuracy Approaching Any Quantization Level","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Chethan Reddy G.P","submitted_at":"2026-07-15T07:04:32Z","abstract_excerpt":"We introduce ExTernD (Expanded-rank Ternary Decomposition), a post-training factorization of each LLM weight matrix $A \\in \\mathbb{R}^{m \\times n}$ into $A \\approx B \\mathrm{diag}(D) C$ with ternary factors $B \\in \\{-1,0,+1\\}^{m \\times k}$, $C \\in \\{-1,0,+1\\}^{k \\times n}$ and a real scale vector $D \\in \\mathbb{R}^k$. The inner rank $k = \\mu \\min(m,n)$ is deliberately expanded beyond full rank ($\\mu > 1$), so that components past full rank correct the quantization error of earlier ones. We prove the residual decreases monotonically in $k$ and can be driven below any $\\varepsilon > 0$: ExTernD "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.13511","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T07:04:32Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0312a9d09254408e1df5b75ec5489c24fffea4c704d03b583b6cc630dc6bc056","abstract_canon_sha256":"fe6b0085a79fdf151f12f37a8332806bb11fd2fde59ae1f2c13771391939e508"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:16.635788Z","signature_b64":"/pzXzduaMSK7kLsjq3HSVa8f4lkYytpYEQDkFpzj8ZQxwZtLxkbpCWhDx1uVbEuDDlz903CCoaJ2MEmmGpsNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cdb6cc103074695654ddfa64c5539df3900e136a3437af928cf36ca5c65c3f7","last_reissued_at":"2026-07-16T01:22:16.634932Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:16.634932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"ExTernD: Expanded-Rank Ternary Decomposition Ternary LLM PTQ with Accuracy Approaching Any Quantization Level","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Chethan Reddy G.P","submitted_at":"2026-07-15T07:04:32Z","abstract_excerpt":"We introduce ExTernD (Expanded-rank Ternary Decomposition), a post-training factorization of each LLM weight matrix $A \\in \\mathbb{R}^{m \\times n}$ into $A \\approx B \\mathrm{diag}(D) C$ with ternary factors $B \\in \\{-1,0,+1\\}^{m \\times k}$, $C \\in \\{-1,0,+1\\}^{k \\times n}$ and a real scale vector $D \\in \\mathbb{R}^k$. The inner rank $k = \\mu \\min(m,n)$ is deliberately expanded beyond full rank ($\\mu > 1$), so that components past full rank correct the quantization error of earlier ones. We prove the residual decreases monotonically in $k$ and can be driven below any $\\varepsilon > 0$: ExTernD "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13511","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/2607.13511/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.13511","created_at":"2026-07-16T01:22:16.635384+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13511v1","created_at":"2026-07-16T01:22:16.635384+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13511","created_at":"2026-07-16T01:22:16.635384+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTNWZQIDA5DJ","created_at":"2026-07-16T01:22:16.635384+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTNWZQIDA5DJKZKN","created_at":"2026-07-16T01:22:16.635384+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTNWZQID","created_at":"2026-07-16T01:22:16.635384+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34","json":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34.json","graph_json":"https://pith.science/api/pith-number/RTNWZQIDA5DJKZKN36TEYVJZ34/graph.json","events_json":"https://pith.science/api/pith-number/RTNWZQIDA5DJKZKN36TEYVJZ34/events.json","paper":"https://pith.science/paper/RTNWZQID"},"agent_actions":{"view_html":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34","download_json":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34.json","view_paper":"https://pith.science/paper/RTNWZQID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13511&json=true","fetch_graph":"https://pith.science/api/pith-number/RTNWZQIDA5DJKZKN36TEYVJZ34/graph.json","fetch_events":"https://pith.science/api/pith-number/RTNWZQIDA5DJKZKN36TEYVJZ34/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34/action/storage_attestation","attest_author":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34/action/author_attestation","sign_citation":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34/action/citation_signature","submit_replication":"https://pith.science/pith/RTNWZQIDA5DJKZKN36TEYVJZ34/action/replication_record"}},"created_at":"2026-07-16T01:22:16.635384+00:00","updated_at":"2026-07-16T01:22:16.635384+00:00"}