{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IDUNJG4GQXKS33YAMNWVZ7CN2C","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":"4067165a0ef4f0ebf174f4da618853e321a4de420de3c3429621ff33325c29c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-31T23:08:15Z","title_canon_sha256":"9c5bc670c3d138b0e8331b01c8e635cd1bb4aa687e5fbc474615acc4a29d2b2f"},"schema_version":"1.0","source":{"id":"0906.0189","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.0189","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"0906.0189v3","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0189","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"IDUNJG4GQXKS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IDUNJG4GQXKS33YA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IDUNJG4G","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:f3756cf2804760a694691a853f5229ce40521e5b8c4958144dcfd4736bca737e","target":"graph","created_at":"2026-05-18T03:29:28Z","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 an m-dimensional minimal variety in a Riemannian manifold cannot touch the boundary at a point where the sum of the smallest m principal curvatures is greater than 0. We also prove an analogous result for varieties with bounded mean curvature.","authors_text":"Brian White","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-31T23:08:15Z","title":"The Maximum Principle for Minimal Varieties of Arbitrary Codimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0189","kind":"arxiv","version":3},"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":"sha256:06a8e700046dcf2c78da6a97fa6bcdcc902290aaf2ac81da0071453e0a690626","target":"record","created_at":"2026-05-18T03:29:28Z","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":"4067165a0ef4f0ebf174f4da618853e321a4de420de3c3429621ff33325c29c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-31T23:08:15Z","title_canon_sha256":"9c5bc670c3d138b0e8331b01c8e635cd1bb4aa687e5fbc474615acc4a29d2b2f"},"schema_version":"1.0","source":{"id":"0906.0189","kind":"arxiv","version":3}},"canonical_sha256":"40e8d49b8685d52def00636d5cfc4dd0825498d938c476a3768ddb592011b328","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40e8d49b8685d52def00636d5cfc4dd0825498d938c476a3768ddb592011b328","first_computed_at":"2026-05-18T03:29:28.166127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:28.166127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mb2CDiTtplHWNCQ0I7uZSYCukP66dSfKBewKOWcLQUkOJnXjjAY0tLLktjKkxOxaElhdGCTRHugA3PwUIiLfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:28.166988Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.0189","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06a8e700046dcf2c78da6a97fa6bcdcc902290aaf2ac81da0071453e0a690626","sha256:f3756cf2804760a694691a853f5229ce40521e5b8c4958144dcfd4736bca737e"],"state_sha256":"c191f7d8d34e8a395a3f2349d3bef38fbf78029b2c959ffc8a1f2d8fb6fbb042"}