{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MTNPQ54ATTE2IB5VPRPILRBNHK","short_pith_number":"pith:MTNPQ54A","schema_version":"1.0","canonical_sha256":"64daf877809cc9a407b57c5e85c42d3a9fdf284b2ce3ed1793dcccfe7de2fe8b","source":{"kind":"arxiv","id":"2606.22451","version":1},"attestation_state":"computed","paper":{"title":"Exact Nonnegative Matrix Factorization via Cone-Ray Witnesses: Obtuseness Ranking, Saturation Curves, and an Augmented Alt-LP Breakthrough","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.NA"],"primary_cat":"math.NA","authors_text":"Mithil Ramteke","submitted_at":"2026-06-21T11:51:35Z","abstract_excerpt":"We study exact nonnegative matrix factorization (NMF) of small exact-rank-r matrices via a cone-ray pipeline combining the truncated SVD, the polyhedral cone of nonnegative preimages, the Double Description Method (DDM, via Fukuda's cddlib), and an alternating linear program (alt-LP) for slack minimisation. Under a uniform-support restriction the factorisation constraint Q P^T = I_r reduces to entrywise nonnegativity of an r x r witness matrix M_T = R_T^{-1} (R_K^T)^{-1} for an r-subset pair (T, K) of cone rays; this closed-form witness recovers an exact NMF in microseconds when feasible.\n  We"},"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":"2606.22451","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-21T11:51:35Z","cross_cats_sorted":["cs.CG","cs.NA"],"title_canon_sha256":"f4136e0eaef449ca4e8fdcb79eeb28601638b04618c28cc99446f0e81e9ec3d0","abstract_canon_sha256":"474b2d1fcc00034b746683bed242ba11d64f71fbef1fcd806d25c31a78ef11df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:38.705640Z","signature_b64":"/c0S+m4hFilEo9y0BT+jS/paOd6peItFTpCZ0ZR7BVvq0aX5prN7FYc++lk7XeA9vJyTYhnpS53oOkH+mJl0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64daf877809cc9a407b57c5e85c42d3a9fdf284b2ce3ed1793dcccfe7de2fe8b","last_reissued_at":"2026-06-23T02:13:38.705231Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:38.705231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Nonnegative Matrix Factorization via Cone-Ray Witnesses: Obtuseness Ranking, Saturation Curves, and an Augmented Alt-LP Breakthrough","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.NA"],"primary_cat":"math.NA","authors_text":"Mithil Ramteke","submitted_at":"2026-06-21T11:51:35Z","abstract_excerpt":"We study exact nonnegative matrix factorization (NMF) of small exact-rank-r matrices via a cone-ray pipeline combining the truncated SVD, the polyhedral cone of nonnegative preimages, the Double Description Method (DDM, via Fukuda's cddlib), and an alternating linear program (alt-LP) for slack minimisation. Under a uniform-support restriction the factorisation constraint Q P^T = I_r reduces to entrywise nonnegativity of an r x r witness matrix M_T = R_T^{-1} (R_K^T)^{-1} for an r-subset pair (T, K) of cone rays; this closed-form witness recovers an exact NMF in microseconds when feasible.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22451","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/2606.22451/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":"2606.22451","created_at":"2026-06-23T02:13:38.705296+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22451v1","created_at":"2026-06-23T02:13:38.705296+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22451","created_at":"2026-06-23T02:13:38.705296+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTNPQ54ATTE2","created_at":"2026-06-23T02:13:38.705296+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTNPQ54ATTE2IB5V","created_at":"2026-06-23T02:13:38.705296+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTNPQ54A","created_at":"2026-06-23T02:13:38.705296+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.25715","citing_title":"Gap-Aware Exact Nonnegative Matrix Factorization: A Two-Sided SVD Gauge and a Three-Regime W-Rank Taxonomy","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK","json":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK.json","graph_json":"https://pith.science/api/pith-number/MTNPQ54ATTE2IB5VPRPILRBNHK/graph.json","events_json":"https://pith.science/api/pith-number/MTNPQ54ATTE2IB5VPRPILRBNHK/events.json","paper":"https://pith.science/paper/MTNPQ54A"},"agent_actions":{"view_html":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK","download_json":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK.json","view_paper":"https://pith.science/paper/MTNPQ54A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22451&json=true","fetch_graph":"https://pith.science/api/pith-number/MTNPQ54ATTE2IB5VPRPILRBNHK/graph.json","fetch_events":"https://pith.science/api/pith-number/MTNPQ54ATTE2IB5VPRPILRBNHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK/action/storage_attestation","attest_author":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK/action/author_attestation","sign_citation":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK/action/citation_signature","submit_replication":"https://pith.science/pith/MTNPQ54ATTE2IB5VPRPILRBNHK/action/replication_record"}},"created_at":"2026-06-23T02:13:38.705296+00:00","updated_at":"2026-06-23T02:13:38.705296+00:00"}