{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2JGJAOYRP4FQWFPUKD3YQK3ILW","short_pith_number":"pith:2JGJAOYR","canonical_record":{"source":{"id":"1407.2397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-09T09:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"9257e506d7f6e8fc5584f952666115ff33bdbc17555fb8a069c2d27dad25899c","abstract_canon_sha256":"631df3b0b04a4b1acd4bb1f03c37e4b21e25ede23765c072525e0de813418208"},"schema_version":"1.0"},"canonical_sha256":"d24c903b117f0b0b15f450f7882b685db98d39a8f95a678519c1bd3e8ef08f12","source":{"kind":"arxiv","id":"1407.2397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2397","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2397v2","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2397","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"pith_short_12","alias_value":"2JGJAOYRP4FQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2JGJAOYRP4FQWFPU","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2JGJAOYR","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2JGJAOYRP4FQWFPUKD3YQK3ILW","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-09T09:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"9257e506d7f6e8fc5584f952666115ff33bdbc17555fb8a069c2d27dad25899c","abstract_canon_sha256":"631df3b0b04a4b1acd4bb1f03c37e4b21e25ede23765c072525e0de813418208"},"schema_version":"1.0"},"canonical_sha256":"d24c903b117f0b0b15f450f7882b685db98d39a8f95a678519c1bd3e8ef08f12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:03.944307Z","signature_b64":"gCONbB+PiVBTYS/B4woe98M7ldKRWVZd1O4LY7JaKv2obHkPEJNrEZVIKmG2T9acUGccV4Zmxy/ndVkpfZGNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d24c903b117f0b0b15f450f7882b685db98d39a8f95a678519c1bd3e8ef08f12","last_reissued_at":"2026-05-18T02:45:03.943680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:03.943680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2397","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wur3TBRwe05fhNFQOz/6DZxzdKGmU1w1G+/rfA8mt4dF3WKYKEilnEiAhEcp6jF5/cviP+JCGgkdBLAyRSHvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:25:55.691594Z"},"content_sha256":"bf3cb54a0be21b7507d78d4c7b72e433c12e0f69af4a99e27add3a04359c7e6d","schema_version":"1.0","event_id":"sha256:bf3cb54a0be21b7507d78d4c7b72e433c12e0f69af4a99e27add3a04359c7e6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2JGJAOYRP4FQWFPUKD3YQK3ILW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elementary methods for incidence problems in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Iosevich, Ben Lund, Javier Cilleruelo, Misha Rudnev, Oliver Roche-Newton","submitted_at":"2014-07-09T09:16:52Z","abstract_excerpt":"We use elementary methods to prove an incidence theorem for points and spheres in $\\mathbb{F}_q^n$. As an application, we show that any point set of $P\\subset \\mathbb{F}_q^2$ with $|P|\\geq 5q$ determines a positive proportion of all circles. The latter result is an analogue of Beck's Theorem for circles which is optimal up to multiplicative constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2397","kind":"arxiv","version":2},"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":"2026-05-18T02:45:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GTkuFcfDcjk9BK5cMNYowh896I5XNmdyZ6Do21hbRMiK/XGXDXisoEdEBqx6Ff3VLiKU7PiBQadhy7nuAbGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:25:55.692238Z"},"content_sha256":"a5ab8ce7c257adf17c456bb23929472db480b0ca54ea737f2481d15c7b3cdbbf","schema_version":"1.0","event_id":"sha256:a5ab8ce7c257adf17c456bb23929472db480b0ca54ea737f2481d15c7b3cdbbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW/bundle.json","state_url":"https://pith.science/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW/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":"2026-05-26T21:25:55Z","links":{"resolver":"https://pith.science/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW","bundle":"https://pith.science/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW/bundle.json","state":"https://pith.science/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JGJAOYRP4FQWFPUKD3YQK3ILW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2JGJAOYRP4FQWFPUKD3YQK3ILW","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":"631df3b0b04a4b1acd4bb1f03c37e4b21e25ede23765c072525e0de813418208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-09T09:16:52Z","title_canon_sha256":"9257e506d7f6e8fc5584f952666115ff33bdbc17555fb8a069c2d27dad25899c"},"schema_version":"1.0","source":{"id":"1407.2397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2397","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2397v2","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2397","created_at":"2026-05-18T02:45:03Z"},{"alias_kind":"pith_short_12","alias_value":"2JGJAOYRP4FQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2JGJAOYRP4FQWFPU","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2JGJAOYR","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:a5ab8ce7c257adf17c456bb23929472db480b0ca54ea737f2481d15c7b3cdbbf","target":"graph","created_at":"2026-05-18T02:45:03Z","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":"We use elementary methods to prove an incidence theorem for points and spheres in $\\mathbb{F}_q^n$. As an application, we show that any point set of $P\\subset \\mathbb{F}_q^2$ with $|P|\\geq 5q$ determines a positive proportion of all circles. The latter result is an analogue of Beck's Theorem for circles which is optimal up to multiplicative constants.","authors_text":"Alex Iosevich, Ben Lund, Javier Cilleruelo, Misha Rudnev, Oliver Roche-Newton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-09T09:16:52Z","title":"Elementary methods for incidence problems in finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2397","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:bf3cb54a0be21b7507d78d4c7b72e433c12e0f69af4a99e27add3a04359c7e6d","target":"record","created_at":"2026-05-18T02:45:03Z","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":"631df3b0b04a4b1acd4bb1f03c37e4b21e25ede23765c072525e0de813418208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-09T09:16:52Z","title_canon_sha256":"9257e506d7f6e8fc5584f952666115ff33bdbc17555fb8a069c2d27dad25899c"},"schema_version":"1.0","source":{"id":"1407.2397","kind":"arxiv","version":2}},"canonical_sha256":"d24c903b117f0b0b15f450f7882b685db98d39a8f95a678519c1bd3e8ef08f12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d24c903b117f0b0b15f450f7882b685db98d39a8f95a678519c1bd3e8ef08f12","first_computed_at":"2026-05-18T02:45:03.943680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:03.943680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCONbB+PiVBTYS/B4woe98M7ldKRWVZd1O4LY7JaKv2obHkPEJNrEZVIKmG2T9acUGccV4Zmxy/ndVkpfZGNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:03.944307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf3cb54a0be21b7507d78d4c7b72e433c12e0f69af4a99e27add3a04359c7e6d","sha256:a5ab8ce7c257adf17c456bb23929472db480b0ca54ea737f2481d15c7b3cdbbf"],"state_sha256":"95657f076d947be03d736fb5242a9ffab31d4bfce78d972e64a4f473f1304364"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obQ2LWwRKK6Hcxabh12fCETn37tXWMLvSBYq9f6WGqDvQJ3H6/W/rvVu0FKc+nd0wqj5z+bE9QxCYFxAJvFOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:25:55.695656Z","bundle_sha256":"48e580aa1c5be2fa9608429020c0f3cf9434a9fa085ff279da37193542152436"}}