{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CPX7FWOLCJ4HXF4DUDMN3DER72","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":"9f67d8964f6e4728fa01164c1dba4b936dcf43c5d6dff6fc8644b674172edb79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-29T20:25:19Z","title_canon_sha256":"1bf415677e4c9ad7709d5f59f5389ad16ad0554117a7742391906fb04d179a58"},"schema_version":"1.0","source":{"id":"1110.6551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6551","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6551v1","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6551","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"CPX7FWOLCJ4H","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CPX7FWOLCJ4HXF4D","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CPX7FWOL","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:fad8b352f8e9f713af573f76c0854903f0feb1256653897991415d1b5880ef96","target":"graph","created_at":"2026-05-18T04:09:55Z","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":"By analyzing the affine Taylor expansion of a non-degenerate plane curve, we obtain characterizations of classes of such curves via curvature properties of the gravity curve. The proof is based on an analysis of the degree parity and leading coefficients of polynomials occurring in the expansion.","authors_text":"Thomas Binder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-29T20:25:19Z","title":"An affine characterization of quadratic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6551","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:fac79de4ca799b29cbb06b1d68539d2e627b0bcde5b273e346c725e026b89048","target":"record","created_at":"2026-05-18T04:09:55Z","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":"9f67d8964f6e4728fa01164c1dba4b936dcf43c5d6dff6fc8644b674172edb79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-29T20:25:19Z","title_canon_sha256":"1bf415677e4c9ad7709d5f59f5389ad16ad0554117a7742391906fb04d179a58"},"schema_version":"1.0","source":{"id":"1110.6551","kind":"arxiv","version":1}},"canonical_sha256":"13eff2d9cb12787b9783a0d8dd8c91fe9c96ccb2375a42fb757188ef5b8c5c49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13eff2d9cb12787b9783a0d8dd8c91fe9c96ccb2375a42fb757188ef5b8c5c49","first_computed_at":"2026-05-18T04:09:55.321101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:55.321101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JXs1r3uqxstx+ljl1/7ZBN2LF80slLX6gtzsgwWLp/Ab3aoytN/JjLNx/f78vcOZfY+ZkAxUFR3r5u4YGKyWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:55.321588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fac79de4ca799b29cbb06b1d68539d2e627b0bcde5b273e346c725e026b89048","sha256:fad8b352f8e9f713af573f76c0854903f0feb1256653897991415d1b5880ef96"],"state_sha256":"ab1ec48405ae4f94bdcdda3d1c6a6f20b9c0d274a8dfdefae0279e85bd4dd06e"}