{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ABIBUXL4G3C2DF4DQFUAH7D4D4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d7b50085585da5aba946c4876c2f32312c477e5980940602c3e51d0d7c656e7b","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-03T20:28:47Z","title_canon_sha256":"c2c22a67eda3bf00473691ed43abf0862a13f4e90bf0f458ad6b9bdf45875838"},"schema_version":"1.0","source":{"id":"1501.00602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00602","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00602v2","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00602","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"ABIBUXL4G3C2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABIBUXL4G3C2DF4D","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABIBUXL4","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:dd6578a1dc221a1324186835b2fc94cde09946ad2de0e4b2a111e8ba926cfa36","target":"graph","created_at":"2026-05-17T23:52:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $\\dim_F ST\\le [L:F]-2$.","authors_text":"Christine Bachoc, Gilles Zemor, Oriol Serra","cross_cats":["cs.IT","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-03T20:28:47Z","title":"An analogue of Vosper's Theorem for Extension Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00602","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:15010e890b1eea4ab893d3a3bcc00b7d1bb116f4223af939d88a5ea0aebf9023","target":"record","created_at":"2026-05-17T23:52:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d7b50085585da5aba946c4876c2f32312c477e5980940602c3e51d0d7c656e7b","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-03T20:28:47Z","title_canon_sha256":"c2c22a67eda3bf00473691ed43abf0862a13f4e90bf0f458ad6b9bdf45875838"},"schema_version":"1.0","source":{"id":"1501.00602","kind":"arxiv","version":2}},"canonical_sha256":"00501a5d7c36c5a19783816803fc7c1f3af77775ed80de225826833b498c4ee6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00501a5d7c36c5a19783816803fc7c1f3af77775ed80de225826833b498c4ee6","first_computed_at":"2026-05-17T23:52:08.775877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:08.775877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JZVObRlNTjkwcHa58CY0omRVnlp1eumdcgZVXA01DxeF5xBN5/g5MAYdiOe5PyVfr747DsiRP5Cw/Jsd+QelCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:08.776397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15010e890b1eea4ab893d3a3bcc00b7d1bb116f4223af939d88a5ea0aebf9023","sha256:dd6578a1dc221a1324186835b2fc94cde09946ad2de0e4b2a111e8ba926cfa36"],"state_sha256":"4b67a91dfa090da90373da61000ebc701f89c7db4b342b74a56223a72ae9f32b"}