{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NKJKAWNWCFUMDLQX25US64JKZY","short_pith_number":"pith:NKJKAWNW","canonical_record":{"source":{"id":"1802.10486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-28T15:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"a7bdeef880c855ff3f992071302a0225ef27b47c0278ffe8d521caf68047fb44","abstract_canon_sha256":"4163fe288ebe3690b72b12bcce7772d9c2a1372e53c92641e8fa0e40fe6060dc"},"schema_version":"1.0"},"canonical_sha256":"6a92a059b61168c1ae17d7692f712ace0fe59f3f4a35f1192a378dc8185e92c3","source":{"kind":"arxiv","id":"1802.10486","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10486","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10486v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10486","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"NKJKAWNWCFUM","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NKJKAWNWCFUMDLQX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NKJKAWNW","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NKJKAWNWCFUMDLQX25US64JKZY","target":"record","payload":{"canonical_record":{"source":{"id":"1802.10486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-28T15:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"a7bdeef880c855ff3f992071302a0225ef27b47c0278ffe8d521caf68047fb44","abstract_canon_sha256":"4163fe288ebe3690b72b12bcce7772d9c2a1372e53c92641e8fa0e40fe6060dc"},"schema_version":"1.0"},"canonical_sha256":"6a92a059b61168c1ae17d7692f712ace0fe59f3f4a35f1192a378dc8185e92c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:17.014307Z","signature_b64":"n4njjFCaGSwOXfCBzSjIm5AuURE6Nk9O2A/IiVl09fwkTyH0h8QrRP8Qt49Srv1hzfAX7tWE0fNchoID3To8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a92a059b61168c1ae17d7692f712ace0fe59f3f4a35f1192a378dc8185e92c3","last_reissued_at":"2026-05-18T00:22:17.013820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:17.013820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.10486","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWyIt2l6aXcNtpHUPRXTIEw04Qn92uDREh4Nn1t8iLRdwg+A27fCDoTmN60vdvwkImeE+6XKDUx8oVXRedHRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:11:09.282992Z"},"content_sha256":"467b3c11b1e821b9d847576d811dfa01d712934e5d9155a8f8eb7d480c7fe884","schema_version":"1.0","event_id":"sha256:467b3c11b1e821b9d847576d811dfa01d712934e5d9155a8f8eb7d480c7fe884"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NKJKAWNWCFUMDLQX25US64JKZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On quadratic curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas Aabrandt, Vagn Lundsgaard Hansen","submitted_at":"2018-02-28T15:46:25Z","abstract_excerpt":"The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of solutions of the circle equation depends on the characteristic $p$ and the degree $n\\geq 1$ of the finite field $\\mathbb{F}_{p^n}$. In this paper, we make a similar study of the geometry over finite fields of the quadratic curves defined by the quadratic equations in two variables for the classical conic sections. In particular the quadratic equation with mixed ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10486","kind":"arxiv","version":1},"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":"2026-05-18T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4IrAW2Pj+TIO+WuDwrhQEi20+tvIsosJJBNbLfU7zclPAb5FeisC+TLmYwEquf/vcXTlLjQIZYnwF8pOTnRqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:11:09.283559Z"},"content_sha256":"b895596539c36ea5a028ec82d54c1758e003ef4bada581651a1d62bbfa9ed0ff","schema_version":"1.0","event_id":"sha256:b895596539c36ea5a028ec82d54c1758e003ef4bada581651a1d62bbfa9ed0ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKJKAWNWCFUMDLQX25US64JKZY/bundle.json","state_url":"https://pith.science/pith/NKJKAWNWCFUMDLQX25US64JKZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKJKAWNWCFUMDLQX25US64JKZY/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":"2026-08-11T22:11:09Z","links":{"resolver":"https://pith.science/pith/NKJKAWNWCFUMDLQX25US64JKZY","bundle":"https://pith.science/pith/NKJKAWNWCFUMDLQX25US64JKZY/bundle.json","state":"https://pith.science/pith/NKJKAWNWCFUMDLQX25US64JKZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKJKAWNWCFUMDLQX25US64JKZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NKJKAWNWCFUMDLQX25US64JKZY","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":"4163fe288ebe3690b72b12bcce7772d9c2a1372e53c92641e8fa0e40fe6060dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-28T15:46:25Z","title_canon_sha256":"a7bdeef880c855ff3f992071302a0225ef27b47c0278ffe8d521caf68047fb44"},"schema_version":"1.0","source":{"id":"1802.10486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10486","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10486v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10486","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"NKJKAWNWCFUM","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NKJKAWNWCFUMDLQX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NKJKAWNW","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:b895596539c36ea5a028ec82d54c1758e003ef4bada581651a1d62bbfa9ed0ff","target":"graph","created_at":"2026-05-18T00:22:17Z","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":"The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of solutions of the circle equation depends on the characteristic $p$ and the degree $n\\geq 1$ of the finite field $\\mathbb{F}_{p^n}$. In this paper, we make a similar study of the geometry over finite fields of the quadratic curves defined by the quadratic equations in two variables for the classical conic sections. In particular the quadratic equation with mixed ter","authors_text":"Andreas Aabrandt, Vagn Lundsgaard Hansen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-28T15:46:25Z","title":"On quadratic curves over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10486","kind":"arxiv","version":1},"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":"sha256:467b3c11b1e821b9d847576d811dfa01d712934e5d9155a8f8eb7d480c7fe884","target":"record","created_at":"2026-05-18T00:22:17Z","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":"4163fe288ebe3690b72b12bcce7772d9c2a1372e53c92641e8fa0e40fe6060dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-28T15:46:25Z","title_canon_sha256":"a7bdeef880c855ff3f992071302a0225ef27b47c0278ffe8d521caf68047fb44"},"schema_version":"1.0","source":{"id":"1802.10486","kind":"arxiv","version":1}},"canonical_sha256":"6a92a059b61168c1ae17d7692f712ace0fe59f3f4a35f1192a378dc8185e92c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a92a059b61168c1ae17d7692f712ace0fe59f3f4a35f1192a378dc8185e92c3","first_computed_at":"2026-05-18T00:22:17.013820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:17.013820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n4njjFCaGSwOXfCBzSjIm5AuURE6Nk9O2A/IiVl09fwkTyH0h8QrRP8Qt49Srv1hzfAX7tWE0fNchoID3To8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:17.014307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.10486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:467b3c11b1e821b9d847576d811dfa01d712934e5d9155a8f8eb7d480c7fe884","sha256:b895596539c36ea5a028ec82d54c1758e003ef4bada581651a1d62bbfa9ed0ff"],"state_sha256":"4f37f6c9051affd4a81c9f1a4bc656a8a2b27dbbf3e6811daaf5ae5f6e2d44c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HplCrdeQBPPx4Z7IALHBN+1gaPa0STfAxS/pm88/+Vdu6NmuU1r6KZOhvf440a0hRyjdVMNb0wUP8n/Oeh7LCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T22:11:09.288628Z","bundle_sha256":"d357f20d53cb39c11973778dbdce356d5ad54a2b06f3f7659f3393c1497a9bd0"}}