{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AB65QQPMCXBDVK2YYKAJV5Z7G7","short_pith_number":"pith:AB65QQPM","canonical_record":{"source":{"id":"1207.1010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-07-04T15:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"9537554d01d209119f96115e0f7638ed3094f811ea1a67a4954f14f30c315ed1","abstract_canon_sha256":"9a79d3325401bd98de6281c02747147103b1d3dd1d6b079b99388ae40c1c3086"},"schema_version":"1.0"},"canonical_sha256":"007dd841ec15c23aab58c2809af73f37e6382f9acd282704670f4a5ae76bf4fe","source":{"kind":"arxiv","id":"1207.1010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1010","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1010v1","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1010","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"AB65QQPMCXBD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AB65QQPMCXBDVK2Y","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AB65QQPM","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AB65QQPMCXBDVK2YYKAJV5Z7G7","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-07-04T15:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"9537554d01d209119f96115e0f7638ed3094f811ea1a67a4954f14f30c315ed1","abstract_canon_sha256":"9a79d3325401bd98de6281c02747147103b1d3dd1d6b079b99388ae40c1c3086"},"schema_version":"1.0"},"canonical_sha256":"007dd841ec15c23aab58c2809af73f37e6382f9acd282704670f4a5ae76bf4fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.418944Z","signature_b64":"XUZS0ck5JfE6BXm2UEL/VDzIlONMMcVLWlMpOz13bw2xDTQDr2g2BCRr2yRpgju9c5gXYn3leDz9PWCVPqCBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"007dd841ec15c23aab58c2809af73f37e6382f9acd282704670f4a5ae76bf4fe","last_reissued_at":"2026-05-18T02:57:53.418362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.418362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1010","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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9o5gf/N7CYkfVOpwV81CQ43iA9WnpcvwDwWMWLya1E1i1bElBWM0rkF7+SfZiy+M+c/zRastxcFqbaa0erLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:56:17.303053Z"},"content_sha256":"e1169786a912d1ca0ba09ec5c0de0c4b128c119c9f4731fae8299cf364b2c18e","schema_version":"1.0","event_id":"sha256:e1169786a912d1ca0ba09ec5c0de0c4b128c119c9f4731fae8299cf364b2c18e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AB65QQPMCXBDVK2YYKAJV5Z7G7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exceptional Moufang quadrangles and structurable algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Lien Boelaert, Tom De Medts","submitted_at":"2012-07-04T15:02:06Z","abstract_excerpt":"In 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank two, also known as Moufang polygons. The hardest case in the classification consists of the Moufang quadrangles. They fall into different families, each of which can be described by an appropriate algebraic structure. For the exceptional quadrangles, this description is intricate and involves many different maps that are defined ad hoc and lack a proper explanation.\n  In this paper, we relate these algebraic structures to two other classes of algebraic structures that had already been studied before, namely to Fre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1010","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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zebVrsFXMJLKXfbewOqf/nM4QrMUI9fs36d5Zf9VIHVcQWcyMtn3KucBPX8hG8wJdAj65VeMbQZxdRdvGJhnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:56:17.303782Z"},"content_sha256":"1fcc7ebce5d8831bc565b853249027f17910cefc0a931515d66cc66ab82266a0","schema_version":"1.0","event_id":"sha256:1fcc7ebce5d8831bc565b853249027f17910cefc0a931515d66cc66ab82266a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7/bundle.json","state_url":"https://pith.science/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7/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":"2026-05-22T13:56:17Z","links":{"resolver":"https://pith.science/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7","bundle":"https://pith.science/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7/bundle.json","state":"https://pith.science/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AB65QQPMCXBDVK2YYKAJV5Z7G7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AB65QQPMCXBDVK2YYKAJV5Z7G7","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":"9a79d3325401bd98de6281c02747147103b1d3dd1d6b079b99388ae40c1c3086","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-07-04T15:02:06Z","title_canon_sha256":"9537554d01d209119f96115e0f7638ed3094f811ea1a67a4954f14f30c315ed1"},"schema_version":"1.0","source":{"id":"1207.1010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1010","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1010v1","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1010","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"AB65QQPMCXBD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AB65QQPMCXBDVK2Y","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AB65QQPM","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:1fcc7ebce5d8831bc565b853249027f17910cefc0a931515d66cc66ab82266a0","target":"graph","created_at":"2026-05-18T02:57:53Z","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 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank two, also known as Moufang polygons. The hardest case in the classification consists of the Moufang quadrangles. They fall into different families, each of which can be described by an appropriate algebraic structure. For the exceptional quadrangles, this description is intricate and involves many different maps that are defined ad hoc and lack a proper explanation.\n  In this paper, we relate these algebraic structures to two other classes of algebraic structures that had already been studied before, namely to Fre","authors_text":"Lien Boelaert, Tom De Medts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-07-04T15:02:06Z","title":"Exceptional Moufang quadrangles and structurable algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1010","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:e1169786a912d1ca0ba09ec5c0de0c4b128c119c9f4731fae8299cf364b2c18e","target":"record","created_at":"2026-05-18T02:57:53Z","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":"9a79d3325401bd98de6281c02747147103b1d3dd1d6b079b99388ae40c1c3086","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-07-04T15:02:06Z","title_canon_sha256":"9537554d01d209119f96115e0f7638ed3094f811ea1a67a4954f14f30c315ed1"},"schema_version":"1.0","source":{"id":"1207.1010","kind":"arxiv","version":1}},"canonical_sha256":"007dd841ec15c23aab58c2809af73f37e6382f9acd282704670f4a5ae76bf4fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"007dd841ec15c23aab58c2809af73f37e6382f9acd282704670f4a5ae76bf4fe","first_computed_at":"2026-05-18T02:57:53.418362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:53.418362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XUZS0ck5JfE6BXm2UEL/VDzIlONMMcVLWlMpOz13bw2xDTQDr2g2BCRr2yRpgju9c5gXYn3leDz9PWCVPqCBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:53.418944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1169786a912d1ca0ba09ec5c0de0c4b128c119c9f4731fae8299cf364b2c18e","sha256:1fcc7ebce5d8831bc565b853249027f17910cefc0a931515d66cc66ab82266a0"],"state_sha256":"c756ca679e92a24e793c85c93af7eb5750b7090d44c720154a9e6722bec06c33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r787UBSlhBpg9U/8aGtEzhwCrE1UWrtBe0Y2IcckcVFxWGK479clyj6ajUv0V1rZsVV79lnBOvM7zocdINlsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T13:56:17.308297Z","bundle_sha256":"19957d644bc7386ea98c9eda4755115726d08843fe5a23f1e363513c24af9b49"}}