{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A34XSPY4TMIA53LKHHORIU22FX","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":"06c4fd42cb480bdfb0f9b3727db8bdca59c19a275808503131402d0bbfa3db34","cross_cats_sorted":["math.AG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-14T18:23:57Z","title_canon_sha256":"9d338137616bdd2c38ecd0449ae3fb056070e27fb08521eea0f26932957afc36"},"schema_version":"1.0","source":{"id":"1608.04122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04122","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04122v1","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04122","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"A34XSPY4TMIA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A34XSPY4TMIA53LK","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A34XSPY4","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:0c3c298e6f9cb85506b7235041c52ae8140db370b110a5c8a6e387570a47cf17","target":"graph","created_at":"2026-05-18T00:10:32Z","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":"Given a totally nonholonomic distribution of rank two on a three-dimensional manifold we investigate the size of the set of points that can be reached by singular horizontal paths starting from a same point. In this setting, the Sard conjecture states that that set should be a subset of the so-called Martinet surface of 2-dimensional Hausdorff measure zero. We prove that the conjecture holds in the case where the Martinet surface is smooth. Moreover, we address the case of singular real-analytic Martinet surfaces and show that the result holds true under an assumption of non-transversality of ","authors_text":"Andr\\'e Belotto da Silva, Ludovic Rifford","cross_cats":["math.AG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-14T18:23:57Z","title":"The Sard conjecture on Martinet surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04122","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":"sha256:76ab1f746dbb3b5339baf75ac817d50fa5b8cb7ffcbdd8b490a40aa40004bffe","target":"record","created_at":"2026-05-18T00:10:32Z","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":"06c4fd42cb480bdfb0f9b3727db8bdca59c19a275808503131402d0bbfa3db34","cross_cats_sorted":["math.AG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-14T18:23:57Z","title_canon_sha256":"9d338137616bdd2c38ecd0449ae3fb056070e27fb08521eea0f26932957afc36"},"schema_version":"1.0","source":{"id":"1608.04122","kind":"arxiv","version":1}},"canonical_sha256":"06f9793f1c9b100eed6a39dd14535a2df02e180a4c57a3d7a3e215f6e31479ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06f9793f1c9b100eed6a39dd14535a2df02e180a4c57a3d7a3e215f6e31479ed","first_computed_at":"2026-05-18T00:10:32.493089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:32.493089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PX46c6C6OI9NgPaYof7meISdjPSTchnXixzUjm4Hn5Ll+tA5DeInTYd6QKX3wFZmoe41zVr0ABpA0C9ebSoHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:32.493711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76ab1f746dbb3b5339baf75ac817d50fa5b8cb7ffcbdd8b490a40aa40004bffe","sha256:0c3c298e6f9cb85506b7235041c52ae8140db370b110a5c8a6e387570a47cf17"],"state_sha256":"e50b7fd111de405aa0684a389793175aa447dd60201744048f1d5a74a5ce77ee"}