{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SXAEFLITWWXRACSSNFRUZPFWQ6","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":"188937e41871c50cf239a4fefde8344805565f9f4f52cbba99fbae80514e1d79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-10T13:56:21Z","title_canon_sha256":"f7ab0536b93fcadc7603185995fb883f272dfe1f5d2c0f4b34c45c53c3e54847"},"schema_version":"1.0","source":{"id":"1506.03309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03309","created_at":"2026-05-18T01:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03309v1","created_at":"2026-05-18T01:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03309","created_at":"2026-05-18T01:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"SXAEFLITWWXR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SXAEFLITWWXRACSS","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SXAEFLIT","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:e822d07583d511ed14b7983b6132002cd340b55c71b52a557c9a0307941ad256","target":"graph","created_at":"2026-05-18T01:55:25Z","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 prove that the number of real intersection points of a real line with a real plane curve defined by a polynomial with at most t monomials is either infinite or does not exceed 6t -7. This improves a result by M. Avendano. Furthermore, we prove that this bound is sharp for t = 3 with the help of Grothendieck's dessins d'enfant.","authors_text":"Boulos El Hilany, Fr\\'ed\\'eric Bihan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-10T13:56:21Z","title":"A sharp bound on the number of real intersection points of a sparse plane curve with a line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03309","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:ebd44e3ed6ab8b4562246814eae3a2bfa27c4b2ff8ce8480b75817e42de060c2","target":"record","created_at":"2026-05-18T01:55:25Z","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":"188937e41871c50cf239a4fefde8344805565f9f4f52cbba99fbae80514e1d79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-10T13:56:21Z","title_canon_sha256":"f7ab0536b93fcadc7603185995fb883f272dfe1f5d2c0f4b34c45c53c3e54847"},"schema_version":"1.0","source":{"id":"1506.03309","kind":"arxiv","version":1}},"canonical_sha256":"95c042ad13b5af100a5269634cbcb68791f5d24968ffa9da8b2afc3a1a5af997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95c042ad13b5af100a5269634cbcb68791f5d24968ffa9da8b2afc3a1a5af997","first_computed_at":"2026-05-18T01:55:25.063463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:25.063463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yj96fOMMxYmmq3vNtOzUbrqSAa4AABEH1nFJ/ulmYGoKfKwuTjCHNNFwP38sGTPSqv01JHwCyVnc36lMHvMbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:25.064031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebd44e3ed6ab8b4562246814eae3a2bfa27c4b2ff8ce8480b75817e42de060c2","sha256:e822d07583d511ed14b7983b6132002cd340b55c71b52a557c9a0307941ad256"],"state_sha256":"167492a81fb96145c324f38561868193e930a105d3cd85426e2ef9eec1e987de"}