{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CAGJYSVQ2OX66SUIGNF6IZXTN6","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":"bb0b99463b565e2ddaad5f8ab4f819e34dcde0167fa33ec3fd0120107f0a84fd","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T20:00:01Z","title_canon_sha256":"8f6849f9432d8e73e6bfa019ffac84ebf167bd4c61b7f6118e1e7ac1d4a43e0b"},"schema_version":"1.0","source":{"id":"1610.01596","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01596","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01596v2","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01596","created_at":"2026-05-17T23:59:39Z"},{"alias_kind":"pith_short_12","alias_value":"CAGJYSVQ2OX6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CAGJYSVQ2OX66SUI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CAGJYSVQ","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:1ff1e4b8550fb180e66739926f57464b16e7592688434f97978ae0e3e08a2eb9","target":"graph","created_at":"2026-05-17T23:59:39Z","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":"In this note, we study the cut locus of the free, step two Carnot groups $\\mathbb{G}_k$ with $k$ generators, equipped with their left-invariant Carnot-Carath\\'eodory metric. In particular, we disprove the conjectures on the shape of the cut loci proposed in [Myasnichenko - 2002] and [Montanari, Morbidelli - 2016], by exhibiting sets of cut points $C_k \\subset \\mathbb{G}_k$ which, for $k \\geq 4$, are strictly larger than conjectured ones. While the latter were, respectively, smooth semi-algebraic sets of codimension $\\Theta(k^2)$ and semi-algebraic sets of codimension $\\Theta(k)$, the sets $C_k","authors_text":"Luca Rizzi, Ulysse Serres","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T20:00:01Z","title":"On the cut locus of free, step two Carnot groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01596","kind":"arxiv","version":2},"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":"sha256:633d08ce427f1dfe2b8041c6f038d1403b7f89791bd862add80d9cbadcb63054","target":"record","created_at":"2026-05-17T23:59:39Z","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":"bb0b99463b565e2ddaad5f8ab4f819e34dcde0167fa33ec3fd0120107f0a84fd","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T20:00:01Z","title_canon_sha256":"8f6849f9432d8e73e6bfa019ffac84ebf167bd4c61b7f6118e1e7ac1d4a43e0b"},"schema_version":"1.0","source":{"id":"1610.01596","kind":"arxiv","version":2}},"canonical_sha256":"100c9c4ab0d3afef4a88334be466f36f9229918655fc746d007e760579d02ef4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"100c9c4ab0d3afef4a88334be466f36f9229918655fc746d007e760579d02ef4","first_computed_at":"2026-05-17T23:59:39.797257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:39.797257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r3evPrjoft6ueW8UyZmdrTzCsVOSSyu0Oe7BrkXYTTuV+WsgpaYULcewjx0HKHw3u6x3YfM7E3KrzTsl/kyGCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:39.797929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01596","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:633d08ce427f1dfe2b8041c6f038d1403b7f89791bd862add80d9cbadcb63054","sha256:1ff1e4b8550fb180e66739926f57464b16e7592688434f97978ae0e3e08a2eb9"],"state_sha256":"5bd3065a6bf9ceb2a28791db162040138cbff1e605305e2834ad2b2b79d98203"}