{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RRWJXPEGMBI4FRNH53NP6ZXQNN","short_pith_number":"pith:RRWJXPEG","canonical_record":{"source":{"id":"1206.3021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-14T07:24:26Z","cross_cats_sorted":["math.AC","math.DG","math.MG"],"title_canon_sha256":"277c41e1de52c716cf44ba581571a1e506ef56875b69c0457cadbba268d40e83","abstract_canon_sha256":"21cf98c7dea1746cd190388d2efc7561365d7d2741eda3e5a7b50248ccce4a06"},"schema_version":"1.0"},"canonical_sha256":"8c6c9bbc866051c2c5a7eedaff66f06b52a826e764f67c98711d0c8ca659c86f","source":{"kind":"arxiv","id":"1206.3021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3021","created_at":"2026-05-18T03:53:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3021v1","created_at":"2026-05-18T03:53:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3021","created_at":"2026-05-18T03:53:32Z"},{"alias_kind":"pith_short_12","alias_value":"RRWJXPEGMBI4","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RRWJXPEGMBI4FRNH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RRWJXPEG","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RRWJXPEGMBI4FRNH53NP6ZXQNN","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-14T07:24:26Z","cross_cats_sorted":["math.AC","math.DG","math.MG"],"title_canon_sha256":"277c41e1de52c716cf44ba581571a1e506ef56875b69c0457cadbba268d40e83","abstract_canon_sha256":"21cf98c7dea1746cd190388d2efc7561365d7d2741eda3e5a7b50248ccce4a06"},"schema_version":"1.0"},"canonical_sha256":"8c6c9bbc866051c2c5a7eedaff66f06b52a826e764f67c98711d0c8ca659c86f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:32.996825Z","signature_b64":"74DUzyJsZ2cUxKERdlMT5lbCMzR7+0xuott9wUbgmrzTFBqpkIv3z90K17nHc5tXG7hg4QZousw+L8OJWPZNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c6c9bbc866051c2c5a7eedaff66f06b52a826e764f67c98711d0c8ca659c86f","last_reissued_at":"2026-05-18T03:53:32.996216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:32.996216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3021","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lt6wig8AgNPLM1BARqtwAkMIsZwkK6RvynEtAaCSmfTvoAkau7c1l9U3lo2lZt+xcKZismUe3MRQUNI8fYpFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:13:55.924703Z"},"content_sha256":"a1e6f4fcdb33f67e13f6dce5e6e062ed00aa0526f27a1e038cfca14f548c2295","schema_version":"1.0","event_id":"sha256:a1e6f4fcdb33f67e13f6dce5e6e062ed00aa0526f27a1e038cfca14f548c2295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RRWJXPEGMBI4FRNH53NP6ZXQNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projective planes over quadratic 2-dimensional algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.DG","math.MG"],"primary_cat":"math.AG","authors_text":"Hendrik Van Maldeghem, Jeroen Schillewaert","submitted_at":"2012-06-14T07:24:26Z","abstract_excerpt":"The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [3, 17, 18]. The geometries appearing in the second row are Severi-Brauer varieties [20]. We provide an easy uniform axiomatization of these geometries and related ones, over an arbitrary field. In particular we investigate the entry A2 \\times A2 in the magic square, characterizing Hermitian Veronese varieties, Segre varieties and embeddings of Hjelmslev planes of level 2 over the dual numbers. In fact this amounts to a common characterization o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3021","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0iaGMOpDHjl6NtzZSfPOJmgoNd5dNHxCbN7IYAqzPKjsdTesSX4tLzuFmUNQhkrRTfi/birHgfpk6IIk6wvKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:13:55.925387Z"},"content_sha256":"055cd8586bdfaae6d14b7580106f8c58354c4b64daa894135ba1d1eb4b2d81b1","schema_version":"1.0","event_id":"sha256:055cd8586bdfaae6d14b7580106f8c58354c4b64daa894135ba1d1eb4b2d81b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN/bundle.json","state_url":"https://pith.science/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T07:13:55Z","links":{"resolver":"https://pith.science/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN","bundle":"https://pith.science/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN/bundle.json","state":"https://pith.science/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RRWJXPEGMBI4FRNH53NP6ZXQNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RRWJXPEGMBI4FRNH53NP6ZXQNN","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":"21cf98c7dea1746cd190388d2efc7561365d7d2741eda3e5a7b50248ccce4a06","cross_cats_sorted":["math.AC","math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-14T07:24:26Z","title_canon_sha256":"277c41e1de52c716cf44ba581571a1e506ef56875b69c0457cadbba268d40e83"},"schema_version":"1.0","source":{"id":"1206.3021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3021","created_at":"2026-05-18T03:53:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3021v1","created_at":"2026-05-18T03:53:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3021","created_at":"2026-05-18T03:53:32Z"},{"alias_kind":"pith_short_12","alias_value":"RRWJXPEGMBI4","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RRWJXPEGMBI4FRNH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RRWJXPEG","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:055cd8586bdfaae6d14b7580106f8c58354c4b64daa894135ba1d1eb4b2d81b1","target":"graph","created_at":"2026-05-18T03:53:32Z","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":"The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [3, 17, 18]. The geometries appearing in the second row are Severi-Brauer varieties [20]. We provide an easy uniform axiomatization of these geometries and related ones, over an arbitrary field. In particular we investigate the entry A2 \\times A2 in the magic square, characterizing Hermitian Veronese varieties, Segre varieties and embeddings of Hjelmslev planes of level 2 over the dual numbers. In fact this amounts to a common characterization o","authors_text":"Hendrik Van Maldeghem, Jeroen Schillewaert","cross_cats":["math.AC","math.DG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-14T07:24:26Z","title":"Projective planes over quadratic 2-dimensional algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3021","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:a1e6f4fcdb33f67e13f6dce5e6e062ed00aa0526f27a1e038cfca14f548c2295","target":"record","created_at":"2026-05-18T03:53:32Z","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":"21cf98c7dea1746cd190388d2efc7561365d7d2741eda3e5a7b50248ccce4a06","cross_cats_sorted":["math.AC","math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-14T07:24:26Z","title_canon_sha256":"277c41e1de52c716cf44ba581571a1e506ef56875b69c0457cadbba268d40e83"},"schema_version":"1.0","source":{"id":"1206.3021","kind":"arxiv","version":1}},"canonical_sha256":"8c6c9bbc866051c2c5a7eedaff66f06b52a826e764f67c98711d0c8ca659c86f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c6c9bbc866051c2c5a7eedaff66f06b52a826e764f67c98711d0c8ca659c86f","first_computed_at":"2026-05-18T03:53:32.996216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:32.996216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"74DUzyJsZ2cUxKERdlMT5lbCMzR7+0xuott9wUbgmrzTFBqpkIv3z90K17nHc5tXG7hg4QZousw+L8OJWPZNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:32.996825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1e6f4fcdb33f67e13f6dce5e6e062ed00aa0526f27a1e038cfca14f548c2295","sha256:055cd8586bdfaae6d14b7580106f8c58354c4b64daa894135ba1d1eb4b2d81b1"],"state_sha256":"193c90b1599b073ba6cba73054c9bac650223c43fea2cff7a17387233eeafddf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHJjy1weZFI39ePHlnH12gTt0aqSfae2ULRDgxaUUvhng0IaJy3EwmMsaHgTSi7Zm4KCSlL7Cl5LggXcSfvfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:13:55.928987Z","bundle_sha256":"084140c53681a86f58b5ef9cecc58aa5ef08912b1e6efe9e034aab5f75acde8b"}}