{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q5HVHD4UKX5367RTBH3ER6XFQ7","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":"b8d847c01ac2ed85ab4d2ad6e1944d2f026b76bb166ad1a75f6d8a85316472e2","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T13:57:05Z","title_canon_sha256":"1df8a3c2e57e6fb9fb2f0aaac6f1079d386356f58b25a69f7a2243e5b3195a3d"},"schema_version":"1.0","source":{"id":"1504.06512","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06512","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06512v3","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06512","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"Q5HVHD4UKX53","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5HVHD4UKX5367RT","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5HVHD4U","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:5e064c9c149c62576c443b2481b451f63ed3b476a5131f593c437f8f0e89ef8d","target":"graph","created_at":"2026-05-18T00:57:44Z","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 design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on \"vertical strips\", namely searches on parallel lines in a given direction. Our results show that, on average, less than two searches suffice to obtain a rational point. We also analyze the probability distribution of outputs, using the notion of Shannon entropy, and prove that the algorithm is somewhat close to any \"ideal\" equidistributed algorithm.","authors_text":"Guillermo Matera, Mariana P\\'erez, Melina Privitelli","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T13:57:05Z","title":"On the computation of rational points of a hypersurface over a finite field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06512","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":"sha256:68c5af8b72b22eb8cd1f6126a0b0fb7c2e22337150cde94f867775fdb3492995","target":"record","created_at":"2026-05-18T00:57:44Z","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":"b8d847c01ac2ed85ab4d2ad6e1944d2f026b76bb166ad1a75f6d8a85316472e2","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T13:57:05Z","title_canon_sha256":"1df8a3c2e57e6fb9fb2f0aaac6f1079d386356f58b25a69f7a2243e5b3195a3d"},"schema_version":"1.0","source":{"id":"1504.06512","kind":"arxiv","version":3}},"canonical_sha256":"874f538f9455fbbf7e3309f648fae587edea3607fa7580cdd114a1378d50e562","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"874f538f9455fbbf7e3309f648fae587edea3607fa7580cdd114a1378d50e562","first_computed_at":"2026-05-18T00:57:44.419906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:44.419906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6oHXas0qNIkL9CetuLK6xYA9F8D+fZXrQCMnT/v8R5ADox7KBgcqACFTb3nhQyp2z08KBA21fd7e0NQIX+dRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:44.420492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06512","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68c5af8b72b22eb8cd1f6126a0b0fb7c2e22337150cde94f867775fdb3492995","sha256:5e064c9c149c62576c443b2481b451f63ed3b476a5131f593c437f8f0e89ef8d"],"state_sha256":"5187f379c8a9ab4794680ef5f61b1f955d6a4cc5a7dc92311b9b03b084231d55"}