{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U5PUX3LT257M36HUUGTT3MSD5P","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":"027a59a8b7c23be7595eff186566c7a8c061a5c1b9e382f008c00fc7624a62b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-17T06:56:33Z","title_canon_sha256":"3ca8c520ba04f7608924f165d9a70ac406cca6901c06699446b0da0f465d9a00"},"schema_version":"1.0","source":{"id":"1108.3408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3408","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3408v1","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3408","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"pith_short_12","alias_value":"U5PUX3LT257M","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U5PUX3LT257M36HU","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U5PUX3LT","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:d30f4a34b162220a2a88f2b3c88c8bd34667504f65a58986e212fef2066ce678","target":"graph","created_at":"2026-05-18T04:15:17Z","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 investigate dual 3-nets realizing the groups $C_3 \\times C_3$, $C_2 \\times C_4$, $\\Alt_4$ and that can be embedded in a projective plane $PG(2,\\mathbb K)$, where $\\mathbb K$ is an algebraically closed field. We give a symbolically verifiable computational proof that every dual 3-net realizing the groups $C_3 \\times C_3$ and $C_2 \\times C_4$ is algebraic, namely, that its points lie on a plane cubic. Moreover, we present two computer programs whose calculations show that the group $\\Alt_4$ cannot be realized if the characteristic of $\\mathbb K$ is zero.","authors_text":"Gabor P. Nagy, Nicola Pace","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-17T06:56:33Z","title":"Some computational results on small 3-nets embedded in a projective plane over a field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3408","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":"sha256:63db133c71fee77b0dfd7bad7939c8adf462ce0e0049ff618536037cb747c68b","target":"record","created_at":"2026-05-18T04:15:17Z","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":"027a59a8b7c23be7595eff186566c7a8c061a5c1b9e382f008c00fc7624a62b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-17T06:56:33Z","title_canon_sha256":"3ca8c520ba04f7608924f165d9a70ac406cca6901c06699446b0da0f465d9a00"},"schema_version":"1.0","source":{"id":"1108.3408","kind":"arxiv","version":1}},"canonical_sha256":"a75f4bed73d77ecdf8f4a1a73db243ebcbfcd7b13b83fa91273d77d23bcaef9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a75f4bed73d77ecdf8f4a1a73db243ebcbfcd7b13b83fa91273d77d23bcaef9e","first_computed_at":"2026-05-18T04:15:17.992040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:17.992040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wxSDbp9a0nQF8oZlyJwrghaUCGpMLx5KQhAVoMwHMG6Nk52xCrEtw03JMtsn558KxQy7lwTQroLYkOmIzapvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:17.992727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63db133c71fee77b0dfd7bad7939c8adf462ce0e0049ff618536037cb747c68b","sha256:d30f4a34b162220a2a88f2b3c88c8bd34667504f65a58986e212fef2066ce678"],"state_sha256":"01b78b1abda10e215bf83556659d1a757b4368a87faa0abbcd0695fd7d80d8e3"}