{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BNPJSZEUWUKIU3ZMQ2PSGD4DUY","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":"b2a35b1142c7185028ef79255465a2e9b47d8c3b9728efbbe05c345def324498","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T15:35:28Z","title_canon_sha256":"48a10dd45598d641b884905f6a74eacf35e8a7e863db6e737f6181d1c9f70e91"},"schema_version":"1.0","source":{"id":"1606.08320","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08320","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08320v2","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08320","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"BNPJSZEUWUKI","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BNPJSZEUWUKIU3ZM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BNPJSZEU","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:3d29ab8b2a7eb2400428fff18122a21d846488d0aae771fe95e1d10c6333e5f6","target":"graph","created_at":"2026-05-18T01:11:40Z","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 metrically complete Riemannian manifold $(M,g)$ with smooth nonempty boundary and assuming that one of its curvatures is subject to a certain bound, we address the problem of whether it is possibile to realize $(M,g)$ as a domain inside a geodesically complete Riemannian manifold $(M',g')$ without boundary, by preserving the same curvature bounds. In this direction we provide three kind of results: (1) a general existence theorem showing that it is always possible to obtain a geodesically complete Riemannian extension without curvature constraints; (2) various topological obstructions ","authors_text":"Giona Veronelli, Stefano Pigola","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T15:35:28Z","title":"The smooth Riemannian extension problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08320","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":"sha256:9f74d65a9848eba095197e58b6cf1de912a45724716e525a4cf475f6f361d767","target":"record","created_at":"2026-05-18T01:11:40Z","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":"b2a35b1142c7185028ef79255465a2e9b47d8c3b9728efbbe05c345def324498","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T15:35:28Z","title_canon_sha256":"48a10dd45598d641b884905f6a74eacf35e8a7e863db6e737f6181d1c9f70e91"},"schema_version":"1.0","source":{"id":"1606.08320","kind":"arxiv","version":2}},"canonical_sha256":"0b5e996494b5148a6f2c869f230f83a61d7507656811dddd44d5986554b2758a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b5e996494b5148a6f2c869f230f83a61d7507656811dddd44d5986554b2758a","first_computed_at":"2026-05-18T01:11:40.801144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:40.801144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Y28+MhJ85DbSyriqGJ99p/XU2EEE4PimIRKOQBYuAta7RtFoLMXRnQ9xpiYTwOvgDTExMYik56mm1trRZSVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:40.801500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08320","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f74d65a9848eba095197e58b6cf1de912a45724716e525a4cf475f6f361d767","sha256:3d29ab8b2a7eb2400428fff18122a21d846488d0aae771fe95e1d10c6333e5f6"],"state_sha256":"b1cb603af506fcb93b6b5cf2227e4923835b998b44867ba07369eb36bcba2818"}