{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EOS6F26TUFLI2LRPJ75OOIRNCA","short_pith_number":"pith:EOS6F26T","canonical_record":{"source":{"id":"1604.06137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-20T22:50:41Z","cross_cats_sorted":[],"title_canon_sha256":"110a81c604586abde3e1b07743c6b884d50541fafa43a2b35ce0354a4db78506","abstract_canon_sha256":"1bcae534d0ad6f50448ea76092405ba017ca81b52c6c114ccf20453b55106624"},"schema_version":"1.0"},"canonical_sha256":"23a5e2ebd3a1568d2e2f4ffae7222d102ebc8e4efedc9dabc7f0b88caa3dbb9e","source":{"kind":"arxiv","id":"1604.06137","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EOS6F26TUFLI2LRPJ75OOIRNCA","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-20T22:50:41Z","cross_cats_sorted":[],"title_canon_sha256":"110a81c604586abde3e1b07743c6b884d50541fafa43a2b35ce0354a4db78506","abstract_canon_sha256":"1bcae534d0ad6f50448ea76092405ba017ca81b52c6c114ccf20453b55106624"},"schema_version":"1.0"},"canonical_sha256":"23a5e2ebd3a1568d2e2f4ffae7222d102ebc8e4efedc9dabc7f0b88caa3dbb9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:32.524495Z","signature_b64":"n+jWIKu/Pd3HMJD2bQ9b55XXJD2+N/YqXk3+FqtPo3U74hzML8CFhmVeCPCHx9fFsrP5lJJUL00T3lm7mdoBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23a5e2ebd3a1568d2e2f4ffae7222d102ebc8e4efedc9dabc7f0b88caa3dbb9e","last_reissued_at":"2026-05-18T01:16:32.523880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:32.523880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06137","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":"2026-05-18T01:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pCX6Zg64t/iVReeddEnXA1JYPhcRZ8qGgBtcnOtN1PR5zIH8/TeUMzgYCJ6SChD97ImlFqaz4tA5HWUgh8z7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:01:03.093089Z"},"content_sha256":"707eb8028a1407ea398d2d74e512954122fd477e07126ef44bfa0fa39c4fe2df","schema_version":"1.0","event_id":"sha256:707eb8028a1407ea398d2d74e512954122fd477e07126ef44bfa0fa39c4fe2df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EOS6F26TUFLI2LRPJ75OOIRNCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Feet in Orthogonal-Buekenhout-Metz Unitals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nicolas Abarzua, Oscar Vega, Rolando Pomareda","submitted_at":"2016-04-20T22:50:41Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06137","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":"2026-05-18T01:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kuq3Pc+qj7pOi/sPLK2+YYaf01dPBF/WDyu/1Zv9xE/GNVWkcvxOqmCk7nOtA8CEwZxlge7Anb9V2drJtz1ZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:01:03.093448Z"},"content_sha256":"b3df24f797d125379f52d44c909024fd7d00aade8c5ef13f54d1efcf5e323c87","schema_version":"1.0","event_id":"sha256:b3df24f797d125379f52d44c909024fd7d00aade8c5ef13f54d1efcf5e323c87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOS6F26TUFLI2LRPJ75OOIRNCA/bundle.json","state_url":"https://pith.science/pith/EOS6F26TUFLI2LRPJ75OOIRNCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOS6F26TUFLI2LRPJ75OOIRNCA/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":"2026-06-11T09:01:03Z","links":{"resolver":"https://pith.science/pith/EOS6F26TUFLI2LRPJ75OOIRNCA","bundle":"https://pith.science/pith/EOS6F26TUFLI2LRPJ75OOIRNCA/bundle.json","state":"https://pith.science/pith/EOS6F26TUFLI2LRPJ75OOIRNCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOS6F26TUFLI2LRPJ75OOIRNCA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+vRTN8mMRF7LgR7nL5fPlaTT54XvvQzLvlbA89mB5LuU+DV0cr8/tMQsPfPvPnXP/Bur6n8eUgYu2ELLVQfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:01:03.095633Z","bundle_sha256":"a4a7a92078f8783071bbe2f4a09970f954278705759689818dadd90f43f4386e"}}