{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MBCVMHAWQ77DFVHYIO7QM5UGNR","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":"82711e2c4bab8d1b9e04a81494732062495ab70c5297edfbec463f8200d90819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-26T01:32:33Z","title_canon_sha256":"dddf9615cada2dde286999b42b696d1c733cbd64cadc72ecbdb759d4b108875a"},"schema_version":"1.0","source":{"id":"1707.08268","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08268","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08268v2","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08268","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"MBCVMHAWQ77D","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MBCVMHAWQ77DFVHY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MBCVMHAW","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:068bda56e9b638ddbee7cbb8c0f9e19515f806ecd4ebada2c73626db092e2c46","target":"graph","created_at":"2026-05-18T00:36:19Z","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 give a new bound on the number of collinear triples for two arbitrary subsets of a finite field. This improves on existing results which rely on the Cauchy inequality. We then us this to provide a new bound on trilinear and quadrilinear exponential sums.","authors_text":"Simon Macourt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-26T01:32:33Z","title":"Incidence Results and Bounds of Trilinear and Quadrilinear Exponential Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08268","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":"sha256:142afdbbbffd620ead225cd073b42e3d4ecc34b681e4173f1525f7cd945f1085","target":"record","created_at":"2026-05-18T00:36:19Z","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":"82711e2c4bab8d1b9e04a81494732062495ab70c5297edfbec463f8200d90819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-26T01:32:33Z","title_canon_sha256":"dddf9615cada2dde286999b42b696d1c733cbd64cadc72ecbdb759d4b108875a"},"schema_version":"1.0","source":{"id":"1707.08268","kind":"arxiv","version":2}},"canonical_sha256":"6045561c1687fe32d4f843bf0676866c5377d278751a0cba0f55617c57caeca2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6045561c1687fe32d4f843bf0676866c5377d278751a0cba0f55617c57caeca2","first_computed_at":"2026-05-18T00:36:19.035112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:19.035112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2CWAh+IstNNH1G1xUyMgsP5EPsn10aXXNZFDWEL3LeTTsI2h3Tx6E8gLRSLsuMzua+eLdQK6oyrrH7y8d55JBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:19.035787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08268","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142afdbbbffd620ead225cd073b42e3d4ecc34b681e4173f1525f7cd945f1085","sha256:068bda56e9b638ddbee7cbb8c0f9e19515f806ecd4ebada2c73626db092e2c46"],"state_sha256":"4d5e165796451690eb662bafdc83171c5467a892585a0a4ea53bb17115c458ef"}