{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DJYJ4YLJ3KECFXQOIRDPL7EM2G","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":"53e8d1e37b50d35fc1c7e249ccd6a3e041ae2d35438ed40483584b51220af9cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T17:41:42Z","title_canon_sha256":"5b517d11b0e17cc20d889814ecf30f7972c90d59bdf5f3b9a749141b68277ebc"},"schema_version":"1.0","source":{"id":"1009.3899","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3899","created_at":"2026-05-18T04:31:22Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3899v3","created_at":"2026-05-18T04:31:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3899","created_at":"2026-05-18T04:31:22Z"},{"alias_kind":"pith_short_12","alias_value":"DJYJ4YLJ3KEC","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DJYJ4YLJ3KECFXQO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DJYJ4YLJ","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:98471f551d573bc08d62cdb6997f73a8d5655a32741f62006db02c4951d467c0","target":"graph","created_at":"2026-05-18T04:31:22Z","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":"Let $\\mathbb{F}_{q}$ be a finite field of order $q=p^k$ where $p$ is prime. Let $P$ and $L$ be sets of points and lines respectively in $\\mathbb{F}_{q} \\times \\mathbb{F}_{q}$ with $|P|=|L|=n$. We establish the incidence bound $I(P,L) \\leq \\gamma n^{3/2 - 1/12838}$, where $\\gamma$ is an absolute constant, so long as $P$ satisfies the conditions of being an `antifield'. We define this to mean that the projection of $P$ onto some coordinate axis has no more than half-dimensional interaction with large subfields of $\\mathbb{F}_q$. In addition, we give examples of sets satisfying these conditions i","authors_text":"Timothy G. F. Jones","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T17:41:42Z","title":"Explicit incidence bounds over general finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3899","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:bbbc69210cb030dafd403bd154f33ea3389994087f9b7a28956b8e532e046c48","target":"record","created_at":"2026-05-18T04:31:22Z","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":"53e8d1e37b50d35fc1c7e249ccd6a3e041ae2d35438ed40483584b51220af9cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T17:41:42Z","title_canon_sha256":"5b517d11b0e17cc20d889814ecf30f7972c90d59bdf5f3b9a749141b68277ebc"},"schema_version":"1.0","source":{"id":"1009.3899","kind":"arxiv","version":3}},"canonical_sha256":"1a709e6169da8822de0e4446f5fc8cd1b6473a276b1cf58a2644fd4f76e47721","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a709e6169da8822de0e4446f5fc8cd1b6473a276b1cf58a2644fd4f76e47721","first_computed_at":"2026-05-18T04:31:22.275982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:22.275982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8PNfEJ53b9Ak5mXaPSFWmdAAH/Tz0jUZnl8WbZjkbdoWHVGnEwnthMaZTNaZtVADWC41GffdbW3ThwkXSuoQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:22.276446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3899","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbbc69210cb030dafd403bd154f33ea3389994087f9b7a28956b8e532e046c48","sha256:98471f551d573bc08d62cdb6997f73a8d5655a32741f62006db02c4951d467c0"],"state_sha256":"c3080fd186be92f25334f4e0afcf0a12154756d2812aaf7b649e62c609333ab7"}