{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2G5XI54V6Z5FQW2IAIAUH2LVAY","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":"9dbbec1c55b692054ee50dd828dca7a598c83ada756b5a75c047ec7217652202","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-05T21:17:11Z","title_canon_sha256":"d2fe60ec1418e0fd98b51d8bfa58c59b320983b3d51be6410ae8ed593915d5dd"},"schema_version":"1.0","source":{"id":"1201.1306","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1306","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1306v3","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1306","created_at":"2026-05-18T01:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"2G5XI54V6Z5F","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2G5XI54V6Z5FQW2I","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2G5XI54V","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:de25d9b6de874b744830bcf0e1117bcf6117f2f98bf712a4155ec5a2340ac81b","target":"graph","created_at":"2026-05-18T01:41:58Z","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":"To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completely determined by the oriented matroid. In this paper we study arrangements of pseudohyperplanes; they correspond to non-realizable oriented matroids. These arrangements arise as a consequence of the Folkman-Lawrence topological representation theorem. We propose a generalization of the complexification process in this context. In particular we construct a space naturally associated with these pseudo-arrangements which","authors_text":"Priyavrat Deshpande","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-05T21:17:11Z","title":"On Arrangements of Pseudohyperplanes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1306","kind":"arxiv","version":3},"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:ad40f1a586b816795e4aa6b88e76a9632762b20737484fd70b02d2db732c03e1","target":"record","created_at":"2026-05-18T01:41:58Z","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":"9dbbec1c55b692054ee50dd828dca7a598c83ada756b5a75c047ec7217652202","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-05T21:17:11Z","title_canon_sha256":"d2fe60ec1418e0fd98b51d8bfa58c59b320983b3d51be6410ae8ed593915d5dd"},"schema_version":"1.0","source":{"id":"1201.1306","kind":"arxiv","version":3}},"canonical_sha256":"d1bb747795f67a585b48020143e9750631bf3cb3fb97e00ca58ca2a1c2ef6225","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1bb747795f67a585b48020143e9750631bf3cb3fb97e00ca58ca2a1c2ef6225","first_computed_at":"2026-05-18T01:41:58.416274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:58.416274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sg7+YRnnXvVzoxdmKGsRjBF0UQgPZX2N6yqtfhImIKChCu/ikNqZy9T0RfBjwuGYvGG+5d2GN7m0Ngg3nf34Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:58.416890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1306","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad40f1a586b816795e4aa6b88e76a9632762b20737484fd70b02d2db732c03e1","sha256:de25d9b6de874b744830bcf0e1117bcf6117f2f98bf712a4155ec5a2340ac81b"],"state_sha256":"1039c6cd6069b3bcfffede14751b147befb4a1e87b8f2a095171f115a685882f"}