{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EOS6F26TUFLI2LRPJ75OOIRNCA","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":"1bcae534d0ad6f50448ea76092405ba017ca81b52c6c114ccf20453b55106624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-20T22:50:41Z","title_canon_sha256":"110a81c604586abde3e1b07743c6b884d50541fafa43a2b35ce0354a4db78506"},"schema_version":"1.0","source":{"id":"1604.06137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06137","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06137v1","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06137","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"EOS6F26TUFLI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EOS6F26TUFLI2LRP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EOS6F26T","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:b3df24f797d125379f52d44c909024fd7d00aade8c5ef13f54d1efcf5e323c87","target":"graph","created_at":"2026-05-18T01:16:32Z","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":"Given an Orthogonal-Buekenhout-Metz unital $U_{\\alpha,\\beta}$, embedded in $PG(2,q^2)$, and a point $P\\notin U_{\\alpha,\\beta}$, we study the set of feet, $\\tau_{P}(U_{\\alpha,\\beta})$, of $P$ in $U_{\\alpha,\\beta}$. We characterize geometrically each of these sets as either $q+1$ collinear points or as $q+1$ points partitioned into two arcs. Other results about the geometry of these sets are also given.","authors_text":"Nicolas Abarzua, Oscar Vega, Rolando Pomareda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-20T22:50:41Z","title":"Feet in Orthogonal-Buekenhout-Metz Unitals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06137","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":"sha256:707eb8028a1407ea398d2d74e512954122fd477e07126ef44bfa0fa39c4fe2df","target":"record","created_at":"2026-05-18T01:16:32Z","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":"1bcae534d0ad6f50448ea76092405ba017ca81b52c6c114ccf20453b55106624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-20T22:50:41Z","title_canon_sha256":"110a81c604586abde3e1b07743c6b884d50541fafa43a2b35ce0354a4db78506"},"schema_version":"1.0","source":{"id":"1604.06137","kind":"arxiv","version":1}},"canonical_sha256":"23a5e2ebd3a1568d2e2f4ffae7222d102ebc8e4efedc9dabc7f0b88caa3dbb9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23a5e2ebd3a1568d2e2f4ffae7222d102ebc8e4efedc9dabc7f0b88caa3dbb9e","first_computed_at":"2026-05-18T01:16:32.523880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:32.523880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n+jWIKu/Pd3HMJD2bQ9b55XXJD2+N/YqXk3+FqtPo3U74hzML8CFhmVeCPCHx9fFsrP5lJJUL00T3lm7mdoBAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:32.524495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:707eb8028a1407ea398d2d74e512954122fd477e07126ef44bfa0fa39c4fe2df","sha256:b3df24f797d125379f52d44c909024fd7d00aade8c5ef13f54d1efcf5e323c87"],"state_sha256":"900b0f8ebe03db6c06d7183b190bd76d671b0249bb11352bf749038f4c426456"}