{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3ZYS6ZGDNNSPGGZMGUTUXGLQCB","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":"122f85f8ff69eb71e31b38dd6c05b5bbaad7b545bf5fd6492520aa2f3a11806b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-01T15:05:26Z","title_canon_sha256":"9c1bf1d2a59db560ef14ff2105f3728814c8f36d4a121c029b5bdf31b7f82914"},"schema_version":"1.0","source":{"id":"2512.01760","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.01760","created_at":"2026-05-26T02:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2512.01760v3","created_at":"2026-05-26T02:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.01760","created_at":"2026-05-26T02:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"3ZYS6ZGDNNSP","created_at":"2026-05-26T02:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"3ZYS6ZGDNNSPGGZM","created_at":"2026-05-26T02:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"3ZYS6ZGD","created_at":"2026-05-26T02:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:8a3307427288ef4dc88971c4bd687e7839a1629adf1526884954202bc3fa40d6","target":"graph","created_at":"2026-05-26T02:04:00Z","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/2512.01760/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The chromatic number of the finite projective space $\\mathrm{PG}(n-1,q)$, denoted $\\chi_q(n)$, is the minimum number of colors needed to color its points so that no line is monochromatic. We prove subadditivity of $\\chi_q(n)$ with respect to $n$, and then establish the following stronger recursive bound: \\[ \\chi_q(n)\\le \\chi_q(d)+\\chi_q(n+1-d)-1 \\] for all $1 \\leq d < n$. We use it to prove new upper bounds on $\\chi_q(n)$. For $q = 2$, using this recursion we prove that \\[ \\chi_2(n) \\le \\lfloor 2n/3 \\rfloor + 1 \\] for all $n \\ge 2$, and we show that this bound is tight for all $n \\le 7$. In pa","authors_text":"Ananthakrishnan Ravi, Anurag Bishnoi, Wouter Cames van Batenburg","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-01T15:05:26Z","title":"The chromatic number of finite projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01760","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":"sha256:9f0c5c28475ffcd18ff62c067797868348bfa524b3e6fac354c694efa5dad048","target":"record","created_at":"2026-05-26T02:04:00Z","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":"122f85f8ff69eb71e31b38dd6c05b5bbaad7b545bf5fd6492520aa2f3a11806b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-01T15:05:26Z","title_canon_sha256":"9c1bf1d2a59db560ef14ff2105f3728814c8f36d4a121c029b5bdf31b7f82914"},"schema_version":"1.0","source":{"id":"2512.01760","kind":"arxiv","version":3}},"canonical_sha256":"de712f64c36b64f31b2c35274b997010711c64d0af092ab9eec9da2b7b5e987d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de712f64c36b64f31b2c35274b997010711c64d0af092ab9eec9da2b7b5e987d","first_computed_at":"2026-05-26T02:04:00.433351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:00.433351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0sBUpe3xy1k44mt07O2ON9R/VNOoW60+mMsqw1m8vuwjtZCjsbz8D2elUtkDUzfO3FFPHbLUEZUXsXD77s21DQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:00.434359Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.01760","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f0c5c28475ffcd18ff62c067797868348bfa524b3e6fac354c694efa5dad048","sha256:8a3307427288ef4dc88971c4bd687e7839a1629adf1526884954202bc3fa40d6"],"state_sha256":"d1b5ab818fff816f5aedb937e743afa58dc5608e5bc2b25740ef495f5ef28baa"}