{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6XZ6SGOBNIJC4UYP7PRDX3HAYQ","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":"1db8b65a12221f7c855b12a8b654b4917eeeca09fefbffb0e73a5984c785c8a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-14T03:14:10Z","title_canon_sha256":"778162569605634f5c55b5dc98e181147befacdc85bca2d4c502d39108cc80b8"},"schema_version":"1.0","source":{"id":"2505.09102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.09102","created_at":"2026-07-05T11:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.09102v1","created_at":"2026-07-05T11:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.09102","created_at":"2026-07-05T11:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"6XZ6SGOBNIJC","created_at":"2026-07-05T11:02:50Z"},{"alias_kind":"pith_short_16","alias_value":"6XZ6SGOBNIJC4UYP","created_at":"2026-07-05T11:02:50Z"},{"alias_kind":"pith_short_8","alias_value":"6XZ6SGOB","created_at":"2026-07-05T11:02:50Z"}],"graph_snapshots":[{"event_id":"sha256:58eadb7367bfafe2a42c5730ce6e2d075a2805c4d32a9e5d43c03f62df8ff6e1","target":"graph","created_at":"2026-07-05T11:02:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.09102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In R^3, let M be the infinite union of unit spheres whose centers lie at even integers on the x-axis; every pair of consecutive spheres touches at (2m+1, 0, 0). Desingularizing these point contacts yields Delaunay's classical constant mean curvature (CMC) surfaces, including unduloids and nodoids.\n  Motivated by this picture, we construct an analogue in the unit sphere S^4. We begin with the piecewise-smooth hypersurface M contained in S^4, obtained by gluing two carefully chosen totally umbilical 3-spheres to two specific Clifford hypersurfaces, all four components sharing the same constant m","authors_text":"Oscar Perdomo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-14T03:14:10Z","title":"Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09102","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":"sha256:1da489fe1852f25ddfd797bd669be8b17f94dea193cc56463c6a99cbc0184e9a","target":"record","created_at":"2026-07-05T11:02:50Z","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":"1db8b65a12221f7c855b12a8b654b4917eeeca09fefbffb0e73a5984c785c8a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-14T03:14:10Z","title_canon_sha256":"778162569605634f5c55b5dc98e181147befacdc85bca2d4c502d39108cc80b8"},"schema_version":"1.0","source":{"id":"2505.09102","kind":"arxiv","version":1}},"canonical_sha256":"f5f3e919c16a122e530ffbe23bece0c410771d0c01436e32e5e4fb8667e3c2a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5f3e919c16a122e530ffbe23bece0c410771d0c01436e32e5e4fb8667e3c2a1","first_computed_at":"2026-07-05T11:02:50.317791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:02:50.317791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XxLCl7OwjtJM+GV6Ps/W/Eat0gvpttkISWveUPX8xnwkAel6+3QvOfTeL6EYjKe3kn5z3UUlFELqcJR1DHmNBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:02:50.318240Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.09102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da489fe1852f25ddfd797bd669be8b17f94dea193cc56463c6a99cbc0184e9a","sha256:58eadb7367bfafe2a42c5730ce6e2d075a2805c4d32a9e5d43c03f62df8ff6e1"],"state_sha256":"cfe305067c5f63b901777b326c141d952c2f23a39dcd648da3b07de0477261b3"}