{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4R76QCNLEIMU2F2XRHAVZGZMOD","short_pith_number":"pith:4R76QCNL","schema_version":"1.0","canonical_sha256":"e47fe809ab22194d175789c15c9b2c70e292efebee83c3007ce23f2779a524fd","source":{"kind":"arxiv","id":"1601.03981","version":3},"attestation_state":"computed","paper":{"title":"A point-line incidence identity in finite fields, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan Murphy, Giorgis Petridis","submitted_at":"2016-01-15T16:06:27Z","abstract_excerpt":"Let $E \\subseteq \\mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the literature, not all naturally associated with lines in $\\mathbb{F}_q^2$, in a unified and elementary way."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.03981","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-15T16:06:27Z","cross_cats_sorted":[],"title_canon_sha256":"30e69ba2416773eb731f182951dd0d9494e84f76f40ea5e4e057d4667b148fd0","abstract_canon_sha256":"abf56f67e91f2c06161bb1f00efc7d4da4daad82c4e40d38bde0f9c698e05b7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:34.279536Z","signature_b64":"0NWBvWM9W1C6LQq0PyOZWMdcQGkAORJLAFzSgKcYFhPyKCO/Owk2/tWfAu8ZZxdyedxyocEdQLg+iJgh5veXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e47fe809ab22194d175789c15c9b2c70e292efebee83c3007ce23f2779a524fd","last_reissued_at":"2026-05-18T00:58:34.278906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:34.278906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A point-line incidence identity in finite fields, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan Murphy, Giorgis Petridis","submitted_at":"2016-01-15T16:06:27Z","abstract_excerpt":"Let $E \\subseteq \\mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the literature, not all naturally associated with lines in $\\mathbb{F}_q^2$, in a unified and elementary way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03981","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.03981","created_at":"2026-05-18T00:58:34.278996+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.03981v3","created_at":"2026-05-18T00:58:34.278996+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03981","created_at":"2026-05-18T00:58:34.278996+00:00"},{"alias_kind":"pith_short_12","alias_value":"4R76QCNLEIMU","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4R76QCNLEIMU2F2X","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4R76QCNL","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD","json":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD.json","graph_json":"https://pith.science/api/pith-number/4R76QCNLEIMU2F2XRHAVZGZMOD/graph.json","events_json":"https://pith.science/api/pith-number/4R76QCNLEIMU2F2XRHAVZGZMOD/events.json","paper":"https://pith.science/paper/4R76QCNL"},"agent_actions":{"view_html":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD","download_json":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD.json","view_paper":"https://pith.science/paper/4R76QCNL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.03981&json=true","fetch_graph":"https://pith.science/api/pith-number/4R76QCNLEIMU2F2XRHAVZGZMOD/graph.json","fetch_events":"https://pith.science/api/pith-number/4R76QCNLEIMU2F2XRHAVZGZMOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD/action/storage_attestation","attest_author":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD/action/author_attestation","sign_citation":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD/action/citation_signature","submit_replication":"https://pith.science/pith/4R76QCNLEIMU2F2XRHAVZGZMOD/action/replication_record"}},"created_at":"2026-05-18T00:58:34.278996+00:00","updated_at":"2026-05-18T00:58:34.278996+00:00"}