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We show that when $1\\leq\\dim_{\\mathbb{F}_q}(\\Gamma_F/q\\Gamma_F)\\leq 3$, the reduced Whitehead group of $D$ is trivial."},"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":"1609.01403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-06T06:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"67097253539aa6c724b6e72d424a508401b2d3845e380e4eb32172ddf61b8c1c","abstract_canon_sha256":"0fc69112b16b65f60b6553bf20cb53ec83f753c5613c0512d1524c24aabadb41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:40.375396Z","signature_b64":"F0kkFQuuwoul2qpihnK7GWdTMYcSf5Pb8aHe8QyCNrcqgn3ciuBqcLnvUCZS8W/TWEOSh7hD3rAUBSFLYXkeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5879ce97f2a7aef1b5a696a95a6d60d184f21589a7185c2937f43e6b2ba8a77a","last_reissued_at":"2026-05-17T23:47:40.374954Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:40.374954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On triviality of reduced Whitehead group over Henselian fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A. Soman","submitted_at":"2016-09-06T06:06:54Z","abstract_excerpt":"Let $F$ be a Henselian field of $q$-cohomological dimension $3$, where $q$ is a prime. Let $\\Gamma_F$ be the totally ordered abelian value group of $F$ and let $D$ be a central division algebra over $F$ of index a power of $q$ such that the characteristic of the residue field, $\\overline{F}$ is coprime to $q$. We show that when $1\\leq\\dim_{\\mathbb{F}_q}(\\Gamma_F/q\\Gamma_F)\\leq 3$, the reduced Whitehead group of $D$ is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01403","kind":"arxiv","version":2},"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":"1609.01403","created_at":"2026-05-17T23:47:40.375016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01403v2","created_at":"2026-05-17T23:47:40.375016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01403","created_at":"2026-05-17T23:47:40.375016+00:00"},{"alias_kind":"pith_short_12","alias_value":"LB445F7SU6XP","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LB445F7SU6XPDNNG","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LB445F7S","created_at":"2026-05-18T12:30:29.479603+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/LB445F7SU6XPDNNGS2UVU3LA2G","json":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G.json","graph_json":"https://pith.science/api/pith-number/LB445F7SU6XPDNNGS2UVU3LA2G/graph.json","events_json":"https://pith.science/api/pith-number/LB445F7SU6XPDNNGS2UVU3LA2G/events.json","paper":"https://pith.science/paper/LB445F7S"},"agent_actions":{"view_html":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G","download_json":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G.json","view_paper":"https://pith.science/paper/LB445F7S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01403&json=true","fetch_graph":"https://pith.science/api/pith-number/LB445F7SU6XPDNNGS2UVU3LA2G/graph.json","fetch_events":"https://pith.science/api/pith-number/LB445F7SU6XPDNNGS2UVU3LA2G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G/action/storage_attestation","attest_author":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G/action/author_attestation","sign_citation":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G/action/citation_signature","submit_replication":"https://pith.science/pith/LB445F7SU6XPDNNGS2UVU3LA2G/action/replication_record"}},"created_at":"2026-05-17T23:47:40.375016+00:00","updated_at":"2026-05-17T23:47:40.375016+00:00"}