{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FJ5VFVEZLTANT2DIOXBLIIUMG7","short_pith_number":"pith:FJ5VFVEZ","schema_version":"1.0","canonical_sha256":"2a7b52d4995cc0d9e86875c2b4228c37e1a6c2dc65052979d00fd719883c9cc3","source":{"kind":"arxiv","id":"1510.01354","version":2},"attestation_state":"computed","paper":{"title":"Revisiting Kneser's Theorem for Field Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Christine Bachoc, Gilles Z\\'emor, Oriol Serra","submitted_at":"2015-10-05T20:47:05Z","abstract_excerpt":"A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the non-separable case, thus solving Hou's conjecture. This result is a consequence of a strengthening of Hou et al.'s theorem that is a transposition to extension fields of an addition theorem of Balandraud."},"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":"1510.01354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-05T20:47:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f32dcb52c14e7789ae4c533a550561fe56f39af9254b1f509cc6dbc87a98fa61","abstract_canon_sha256":"73d776bc29153c6b6f15466fce1368fc800b7c771a7628319bc3b1dacf3bfe8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.747007Z","signature_b64":"rX1zLZ2hj0HqLjMovtmgSoXfOdc8q4YknOQLeJh1iLiEgRBih4NzXdiaRkyCj+dWMPZtj2udFSCF2sLd/+8aDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a7b52d4995cc0d9e86875c2b4228c37e1a6c2dc65052979d00fd719883c9cc3","last_reissued_at":"2026-05-17T23:52:08.746546Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.746546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting Kneser's Theorem for Field Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Christine Bachoc, Gilles Z\\'emor, Oriol Serra","submitted_at":"2015-10-05T20:47:05Z","abstract_excerpt":"A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the non-separable case, thus solving Hou's conjecture. This result is a consequence of a strengthening of Hou et al.'s theorem that is a transposition to extension fields of an addition theorem of Balandraud."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01354","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":"1510.01354","created_at":"2026-05-17T23:52:08.746614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01354v2","created_at":"2026-05-17T23:52:08.746614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01354","created_at":"2026-05-17T23:52:08.746614+00:00"},{"alias_kind":"pith_short_12","alias_value":"FJ5VFVEZLTAN","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FJ5VFVEZLTANT2DI","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FJ5VFVEZ","created_at":"2026-05-18T12:29:19.899920+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/FJ5VFVEZLTANT2DIOXBLIIUMG7","json":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7.json","graph_json":"https://pith.science/api/pith-number/FJ5VFVEZLTANT2DIOXBLIIUMG7/graph.json","events_json":"https://pith.science/api/pith-number/FJ5VFVEZLTANT2DIOXBLIIUMG7/events.json","paper":"https://pith.science/paper/FJ5VFVEZ"},"agent_actions":{"view_html":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7","download_json":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7.json","view_paper":"https://pith.science/paper/FJ5VFVEZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01354&json=true","fetch_graph":"https://pith.science/api/pith-number/FJ5VFVEZLTANT2DIOXBLIIUMG7/graph.json","fetch_events":"https://pith.science/api/pith-number/FJ5VFVEZLTANT2DIOXBLIIUMG7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7/action/storage_attestation","attest_author":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7/action/author_attestation","sign_citation":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7/action/citation_signature","submit_replication":"https://pith.science/pith/FJ5VFVEZLTANT2DIOXBLIIUMG7/action/replication_record"}},"created_at":"2026-05-17T23:52:08.746614+00:00","updated_at":"2026-05-17T23:52:08.746614+00:00"}