{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ABIBUXL4G3C2DF4DQFUAH7D4D4","short_pith_number":"pith:ABIBUXL4","schema_version":"1.0","canonical_sha256":"00501a5d7c36c5a19783816803fc7c1f3af77775ed80de225826833b498c4ee6","source":{"kind":"arxiv","id":"1501.00602","version":2},"attestation_state":"computed","paper":{"title":"An analogue of Vosper's Theorem for Extension Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.NT","authors_text":"Christine Bachoc, Gilles Zemor, Oriol Serra","submitted_at":"2015-01-03T20:28:47Z","abstract_excerpt":"We are interested in characterising pairs $S,T$ of $F$-linear subspaces in a field extension $L/F$ such that the linear span $ST$ of the set of products of elements of $S$ and of elements of $T$ has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces $S, T$ in a prime extension $L$ of a finite field $F$ for which $\\dim_FST =\\dim_F S+\\dim_F T-1,$ when $\\dim_F S, \\dim_F T\\ge 2$ and $\\dim_F ST\\le [L:F]-2$."},"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":"1501.00602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-03T20:28:47Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"c2c22a67eda3bf00473691ed43abf0862a13f4e90bf0f458ad6b9bdf45875838","abstract_canon_sha256":"d7b50085585da5aba946c4876c2f32312c477e5980940602c3e51d0d7c656e7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.776397Z","signature_b64":"JZVObRlNTjkwcHa58CY0omRVnlp1eumdcgZVXA01DxeF5xBN5/g5MAYdiOe5PyVfr747DsiRP5Cw/Jsd+QelCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00501a5d7c36c5a19783816803fc7c1f3af77775ed80de225826833b498c4ee6","last_reissued_at":"2026-05-17T23:52:08.775877Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.775877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An analogue of Vosper's Theorem for Extension Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.NT","authors_text":"Christine Bachoc, Gilles Zemor, Oriol Serra","submitted_at":"2015-01-03T20:28:47Z","abstract_excerpt":"We are interested in characterising pairs $S,T$ of $F$-linear subspaces in a field extension $L/F$ such that the linear span $ST$ of the set of products of elements of $S$ and of elements of $T$ has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces $S, T$ in a prime extension $L$ of a finite field $F$ for which $\\dim_FST =\\dim_F S+\\dim_F T-1,$ when $\\dim_F S, \\dim_F T\\ge 2$ and $\\dim_F ST\\le [L:F]-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00602","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":"1501.00602","created_at":"2026-05-17T23:52:08.775953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00602v2","created_at":"2026-05-17T23:52:08.775953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00602","created_at":"2026-05-17T23:52:08.775953+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABIBUXL4G3C2","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABIBUXL4G3C2DF4D","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABIBUXL4","created_at":"2026-05-18T12:29:10.953037+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/ABIBUXL4G3C2DF4DQFUAH7D4D4","json":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4.json","graph_json":"https://pith.science/api/pith-number/ABIBUXL4G3C2DF4DQFUAH7D4D4/graph.json","events_json":"https://pith.science/api/pith-number/ABIBUXL4G3C2DF4DQFUAH7D4D4/events.json","paper":"https://pith.science/paper/ABIBUXL4"},"agent_actions":{"view_html":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4","download_json":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4.json","view_paper":"https://pith.science/paper/ABIBUXL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00602&json=true","fetch_graph":"https://pith.science/api/pith-number/ABIBUXL4G3C2DF4DQFUAH7D4D4/graph.json","fetch_events":"https://pith.science/api/pith-number/ABIBUXL4G3C2DF4DQFUAH7D4D4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4/action/storage_attestation","attest_author":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4/action/author_attestation","sign_citation":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4/action/citation_signature","submit_replication":"https://pith.science/pith/ABIBUXL4G3C2DF4DQFUAH7D4D4/action/replication_record"}},"created_at":"2026-05-17T23:52:08.775953+00:00","updated_at":"2026-05-17T23:52:08.775953+00:00"}