{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AKRNRNE76TJIA5HG2CPJSST7BH","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":"60734bd1361cb2aa367839897e24cd19d1f91ff6df8a3367844fc306b035eece","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-16T15:56:34Z","title_canon_sha256":"0db103b22c083a635eb8b7faceb9c309065fab7ded396bbad5472fe2aceebdd0"},"schema_version":"1.0","source":{"id":"1201.3296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3296","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3296v1","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3296","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"AKRNRNE76TJI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKRNRNE76TJIA5HG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKRNRNE7","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:781defe0abd6579b6fa2186f7f4c755d547d6db30a99299b6f405c76e6979274","target":"graph","created_at":"2026-05-18T04:04:31Z","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":"In this paper, we show that a small minimal k-blocking set in PG(n, q3), q = p^h, h >= 1, p prime, p >=7, intersecting every (n-k)-space in 1 (mod q) points, is linear. As a corollary, this result shows that all small minimal k-blocking sets in PG(n, p^3), p prime, p >=7, are Fp-linear, proving the linearity conjecture (see [7]) in the case PG(n, p3), p prime, p >= 7.","authors_text":"Geertrui Van de Voorde, Leo Storme, Michel Lavrauw","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-16T15:56:34Z","title":"A proof of the linearity conjecture for k-blocking sets in PG(n, p3), p prime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3296","kind":"arxiv","version":1},"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:a27cd20b3990763ead4f2f0b3bf4e93aef3670c3d5ea241d1fbe6962f568a02a","target":"record","created_at":"2026-05-18T04:04:31Z","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":"60734bd1361cb2aa367839897e24cd19d1f91ff6df8a3367844fc306b035eece","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-16T15:56:34Z","title_canon_sha256":"0db103b22c083a635eb8b7faceb9c309065fab7ded396bbad5472fe2aceebdd0"},"schema_version":"1.0","source":{"id":"1201.3296","kind":"arxiv","version":1}},"canonical_sha256":"02a2d8b49ff4d28074e6d09e994a7f09c8990f97cd1ce43353ca317250da5a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02a2d8b49ff4d28074e6d09e994a7f09c8990f97cd1ce43353ca317250da5a88","first_computed_at":"2026-05-18T04:04:31.687244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:31.687244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YC/wHuAC3GM4ZFRfXL6pmcagXPJiKyB2mvGlAGCleSGfXRCdbsa/yBS0CgGhPWdQ4R0GO3P4Rbz85BM2AW1sBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:31.687879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a27cd20b3990763ead4f2f0b3bf4e93aef3670c3d5ea241d1fbe6962f568a02a","sha256:781defe0abd6579b6fa2186f7f4c755d547d6db30a99299b6f405c76e6979274"],"state_sha256":"16121ffd9f531b6bcf1c60eb97aa4c405cc0b89ce31a175048222ab1d942d6d8"}