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Dykema","submitted_at":"2009-05-04T16:44:18Z","abstract_excerpt":"We show that the polynomial S_{m,k}(A,B), that is the sum of all words in noncommuting variables A and B having length m and exactly k letters equal to B, is not equal to a sum of commutators and Hermitian squares in the algebra R<X,Y> where X^2=A and Y^2=B, for all even values of m and k with 6 <= k <= m-10, and also for (m,k)=(12,6). This leaves only the case (m,k)=(16,8) open. This topic is of interest in connection with the Lieb--Seiringer formulation of the Bessis--Moussa--Villani conjecture, which asks whether the trace of S_{m,k}(A,B)) is nonnegative for all positive semidefinite matric"},"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":"0905.0420","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-05-04T16:44:18Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"2e5f273f6651c150abc5e8e56246b7e3504a5ded9e76bdd0076687890f8e199c","abstract_canon_sha256":"c8d118f6095311b774652cc9bd9dc2eb0e7b391e7b32e15548eb690975d7e03b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:44.992587Z","signature_b64":"jMRvW8hN9vi5kaBfgokroYTXgwkhdjw/Z7m5Rk3+TJkwZuJOSqnK7GtonPSeoWJG38EApa991QT7NhzGskQzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"599e129b28238d912fdd640478451573a1ece7042db060c812ce697fb1c7fc59","last_reissued_at":"2026-05-17T23:52:44.992024Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:44.992024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum--of--squares results for polynomials related to the Bessis--Moussa--Villani conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.RA","authors_text":"Benoit Collins, Francisco Torres-Ayala, Kenneth J. 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This topic is of interest in connection with the Lieb--Seiringer formulation of the Bessis--Moussa--Villani conjecture, which asks whether the trace of S_{m,k}(A,B)) is nonnegative for all positive semidefinite matric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0420","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0905.0420","created_at":"2026-05-17T23:52:44.992091+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.0420v3","created_at":"2026-05-17T23:52:44.992091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0420","created_at":"2026-05-17T23:52:44.992091+00:00"},{"alias_kind":"pith_short_12","alias_value":"LGPBFGZIEOGZ","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"LGPBFGZIEOGZCL65","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"LGPBFGZI","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.17782","citing_title":"On the Failure of the Upper Bound in the Refined BMV Conjecture and a Pinching Correction","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO","json":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO.json","graph_json":"https://pith.science/api/pith-number/LGPBFGZIEOGZCL65MQCHQRIVOO/graph.json","events_json":"https://pith.science/api/pith-number/LGPBFGZIEOGZCL65MQCHQRIVOO/events.json","paper":"https://pith.science/paper/LGPBFGZI"},"agent_actions":{"view_html":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO","download_json":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO.json","view_paper":"https://pith.science/paper/LGPBFGZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.0420&json=true","fetch_graph":"https://pith.science/api/pith-number/LGPBFGZIEOGZCL65MQCHQRIVOO/graph.json","fetch_events":"https://pith.science/api/pith-number/LGPBFGZIEOGZCL65MQCHQRIVOO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO/action/storage_attestation","attest_author":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO/action/author_attestation","sign_citation":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO/action/citation_signature","submit_replication":"https://pith.science/pith/LGPBFGZIEOGZCL65MQCHQRIVOO/action/replication_record"}},"created_at":"2026-05-17T23:52:44.992091+00:00","updated_at":"2026-05-17T23:52:44.992091+00:00"}