{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UUSBLLMW5HJQSYWTZFKCFRJAWZ","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":"9d3a5cd602ff5ad1c595a7aacabbaf9fa02591740fb4fdcaf63e9aaa857b436a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T16:48:30Z","title_canon_sha256":"7d1237019e041b59dcfc9adcd5a8067e7fb53566f6278fe58400b22f90d89e19"},"schema_version":"1.0","source":{"id":"1501.04039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04039","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04039v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04039","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"UUSBLLMW5HJQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UUSBLLMW5HJQSYWT","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UUSBLLMW","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:1a662d9bfaad6dade0ceaa6be2922a2b601049659f2128f763aa43c836bf4659","target":"graph","created_at":"2026-05-18T02:16:20Z","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 a rank 3 real arrangement $\\mathcal A$ of $n$ lines in the projective plane, the Dirac-Motzkin conjecture (proved by Green and Tao in 2013) states that for $n$ sufficiently large, the number of simple intersection points of $\\mathcal A$ is greater than or equal to $n/2$. With a much simpler proof we show that if $\\mathcal A$ is supersolvable, then the conjecture is true for any $n$ (a small improvement of original conjecture). The Slope problem (proved by Ungar in 1982) states that $n$ non-collinear points in the real plane determine at least $n-1$ slopes; we show that this is equivalent","authors_text":"Benjamin Anzis, Stefan Tohaneanu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T16:48:30Z","title":"On the geometry of real or complex supersolvable line arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04039","kind":"arxiv","version":2},"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":"sha256:418aebc8c8f7da8a9e1f565045a675052ec803f7c68f328214a64233fa869ec7","target":"record","created_at":"2026-05-18T02:16:20Z","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":"9d3a5cd602ff5ad1c595a7aacabbaf9fa02591740fb4fdcaf63e9aaa857b436a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-16T16:48:30Z","title_canon_sha256":"7d1237019e041b59dcfc9adcd5a8067e7fb53566f6278fe58400b22f90d89e19"},"schema_version":"1.0","source":{"id":"1501.04039","kind":"arxiv","version":2}},"canonical_sha256":"a52415ad96e9d30962d3c95422c520b654283cb4351733ad201e1a09f9963ff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a52415ad96e9d30962d3c95422c520b654283cb4351733ad201e1a09f9963ff1","first_computed_at":"2026-05-18T02:16:20.354078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:20.354078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6YpF3vDojdLaDkTWjKSwWcfUT55hgEz1stg4nPlrkGhd8B7bJGaoOuOXRUo5jVWUuxlX2Swj0fTWB+S46WQuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:20.354685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:418aebc8c8f7da8a9e1f565045a675052ec803f7c68f328214a64233fa869ec7","sha256:1a662d9bfaad6dade0ceaa6be2922a2b601049659f2128f763aa43c836bf4659"],"state_sha256":"b19eda82cebdca730975f7c4654d06b9a7638a67c7c8e37ee595e8c8f62998a8"}