{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:3BQDTLZ2C6RCONWDSJ7WFMM6TH","short_pith_number":"pith:3BQDTLZ2","canonical_record":{"source":{"id":"0909.3216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-17T13:35:31Z","cross_cats_sorted":[],"title_canon_sha256":"d557a67d02649045e4a331ca55d87b058c42c2fed936c20acff6727cb673348a","abstract_canon_sha256":"1468ce5f77aba8f4ce9eabb4eedcdbddd63364644fa3e2b11c0ba6bd6f5ff19e"},"schema_version":"1.0"},"canonical_sha256":"d86039af3a17a22736c3927f62b19e99fed9ca9ff153e392dbc246b684d21f46","source":{"kind":"arxiv","id":"0909.3216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3216","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3216v1","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3216","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"pith_short_12","alias_value":"3BQDTLZ2C6RC","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"pith_short_16","alias_value":"3BQDTLZ2C6RCONWD","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"pith_short_8","alias_value":"3BQDTLZ2","created_at":"2026-07-04T15:50:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:3BQDTLZ2C6RCONWDSJ7WFMM6TH","target":"record","payload":{"canonical_record":{"source":{"id":"0909.3216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-17T13:35:31Z","cross_cats_sorted":[],"title_canon_sha256":"d557a67d02649045e4a331ca55d87b058c42c2fed936c20acff6727cb673348a","abstract_canon_sha256":"1468ce5f77aba8f4ce9eabb4eedcdbddd63364644fa3e2b11c0ba6bd6f5ff19e"},"schema_version":"1.0"},"canonical_sha256":"d86039af3a17a22736c3927f62b19e99fed9ca9ff153e392dbc246b684d21f46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:50:12.484947Z","signature_b64":"cQTlwpD87BUA7JOlPOs7Z9QtQnbWlceFNjIDvw5F2JagalH3gr0Xz6tuEGkHdMyBBNO38cDFkNH1v4lkv6aYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d86039af3a17a22736c3927f62b19e99fed9ca9ff153e392dbc246b684d21f46","last_reissued_at":"2026-07-04T15:50:12.484623Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:50:12.484623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.3216","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":"2026-07-04T15:50:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGI7MoIpK4kE828pOm9jW+czWUWRuofTFzIg33fXcPPYVB4Qo30QMTe1TlswIp6SMa1PzyPZAI81qJ4i2I+eCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:46:20.835429Z"},"content_sha256":"6351caf564ec549b07c9ee2f8c921c8c07a44e97bf2cbaf921e56668bbe70990","schema_version":"1.0","event_id":"sha256:6351caf564ec549b07c9ee2f8c921c8c07a44e97bf2cbaf921e56668bbe70990"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:3BQDTLZ2C6RCONWDSJ7WFMM6TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moufang sets related to polarities in exceptional Moufang quadrangles of type F_4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Koen Struyve","submitted_at":"2009-09-17T13:35:31Z","abstract_excerpt":"Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F_4, we construct a rank three geometry. The main property of this new geometry is that its automorphism group is identical to the one of the underlying Moufang set, providing a tool to study this Moufang set in a geometrical way. As a corollary we obtain that every automorphism of an exceptional Moufang quadrangle of type F_4 stabilizing the absolute points of a polarity, also centralizes the polarity. This handles the final case of a similar result for all polarities of Moufang n-gons."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3216","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0909.3216/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:50:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Im68KD1zywasvxGrfLwC+A/DFST/VxdtxOqgUohQHMeiUXDvm0I8sxkbak1PIZZuAgnBXDaOPy3pi83HJvweCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:46:20.836452Z"},"content_sha256":"66e97a7ecd6546b37a749bff7732992406d98bf6fd8d635fdecfcfbf63c236f2","schema_version":"1.0","event_id":"sha256:66e97a7ecd6546b37a749bff7732992406d98bf6fd8d635fdecfcfbf63c236f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH/bundle.json","state_url":"https://pith.science/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH/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":"2026-08-06T03:46:20Z","links":{"resolver":"https://pith.science/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH","bundle":"https://pith.science/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH/bundle.json","state":"https://pith.science/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BQDTLZ2C6RCONWDSJ7WFMM6TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3BQDTLZ2C6RCONWDSJ7WFMM6TH","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":"1468ce5f77aba8f4ce9eabb4eedcdbddd63364644fa3e2b11c0ba6bd6f5ff19e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-17T13:35:31Z","title_canon_sha256":"d557a67d02649045e4a331ca55d87b058c42c2fed936c20acff6727cb673348a"},"schema_version":"1.0","source":{"id":"0909.3216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3216","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3216v1","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3216","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"pith_short_12","alias_value":"3BQDTLZ2C6RC","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"pith_short_16","alias_value":"3BQDTLZ2C6RCONWD","created_at":"2026-07-04T15:50:12Z"},{"alias_kind":"pith_short_8","alias_value":"3BQDTLZ2","created_at":"2026-07-04T15:50:12Z"}],"graph_snapshots":[{"event_id":"sha256:66e97a7ecd6546b37a749bff7732992406d98bf6fd8d635fdecfcfbf63c236f2","target":"graph","created_at":"2026-07-04T15:50:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0909.3216/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F_4, we construct a rank three geometry. The main property of this new geometry is that its automorphism group is identical to the one of the underlying Moufang set, providing a tool to study this Moufang set in a geometrical way. As a corollary we obtain that every automorphism of an exceptional Moufang quadrangle of type F_4 stabilizing the absolute points of a polarity, also centralizes the polarity. This handles the final case of a similar result for all polarities of Moufang n-gons.","authors_text":"Koen Struyve","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-17T13:35:31Z","title":"Moufang sets related to polarities in exceptional Moufang quadrangles of type F_4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3216","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":"sha256:6351caf564ec549b07c9ee2f8c921c8c07a44e97bf2cbaf921e56668bbe70990","target":"record","created_at":"2026-07-04T15:50:12Z","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":"1468ce5f77aba8f4ce9eabb4eedcdbddd63364644fa3e2b11c0ba6bd6f5ff19e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-17T13:35:31Z","title_canon_sha256":"d557a67d02649045e4a331ca55d87b058c42c2fed936c20acff6727cb673348a"},"schema_version":"1.0","source":{"id":"0909.3216","kind":"arxiv","version":1}},"canonical_sha256":"d86039af3a17a22736c3927f62b19e99fed9ca9ff153e392dbc246b684d21f46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d86039af3a17a22736c3927f62b19e99fed9ca9ff153e392dbc246b684d21f46","first_computed_at":"2026-07-04T15:50:12.484623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:50:12.484623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQTlwpD87BUA7JOlPOs7Z9QtQnbWlceFNjIDvw5F2JagalH3gr0Xz6tuEGkHdMyBBNO38cDFkNH1v4lkv6aYCA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:50:12.484947Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6351caf564ec549b07c9ee2f8c921c8c07a44e97bf2cbaf921e56668bbe70990","sha256:66e97a7ecd6546b37a749bff7732992406d98bf6fd8d635fdecfcfbf63c236f2"],"state_sha256":"318e9712ed82c782268af5f232cff1685980e240862d7aeb99917c1d5a8e0a7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5eI4PVszyuDDwkX6owOw5IT4yj3ph7GoA+O5JeWFgjmKhhWSYBbHy9UgmwQdf4JyvFo94JOKF/Wz5mLjsRKlBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T03:46:20.846093Z","bundle_sha256":"8802e83e6d613e22692e3a5775b8e4a860fb8e0be47d265d6e8093859bb222eb"}}