{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:G4HMLNEVZJGIINIVKBZBPZR7TT","short_pith_number":"pith:G4HMLNEV","schema_version":"1.0","canonical_sha256":"370ec5b495ca4c843515507217e63f9cf74548e6812f946c681073e079894fc8","source":{"kind":"arxiv","id":"1501.02639","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic Cones of Embedded Singular Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jean-Marie Morvan, Xiang Sun","submitted_at":"2015-01-12T13:38:37Z","abstract_excerpt":"We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We get a simple expression of these cones for polyhedra in E^3, as well as convergence and approximation theorems. In particular, if a sequence of singular spaces tends to a smooth submanifold, the corresponding sequence of asymptotic cones tends to the asymptotic cone of the smooth one for a suitable distance function. Moreover, we apply these results to appro"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.02639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-12T13:38:37Z","cross_cats_sorted":[],"title_canon_sha256":"c43a55b9307fa233fc181e5fd48a260fbf81814be8912c26d0c1f8b570ccfe75","abstract_canon_sha256":"43b1fc32ea7c881c7780a6b0b6054b804131581a811045f549449af2a4432ab9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:37.587958Z","signature_b64":"nTeJwp2ZAxpc/SK8Gq/q07ImeR4w49JnJlvrVi46ZWCYA7bMbe7hafdtYTbpcQoHM3TprG3JBhf3ugqFcY1uCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"370ec5b495ca4c843515507217e63f9cf74548e6812f946c681073e079894fc8","last_reissued_at":"2026-05-18T02:29:37.587521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:37.587521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Cones of Embedded Singular Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jean-Marie Morvan, Xiang Sun","submitted_at":"2015-01-12T13:38:37Z","abstract_excerpt":"We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We get a simple expression of these cones for polyhedra in E^3, as well as convergence and approximation theorems. In particular, if a sequence of singular spaces tends to a smooth submanifold, the corresponding sequence of asymptotic cones tends to the asymptotic cone of the smooth one for a suitable distance function. Moreover, we apply these results to appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02639","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.02639","created_at":"2026-05-18T02:29:37.587582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02639v1","created_at":"2026-05-18T02:29:37.587582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02639","created_at":"2026-05-18T02:29:37.587582+00:00"},{"alias_kind":"pith_short_12","alias_value":"G4HMLNEVZJGI","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G4HMLNEVZJGIINIV","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G4HMLNEV","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT","json":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT.json","graph_json":"https://pith.science/api/pith-number/G4HMLNEVZJGIINIVKBZBPZR7TT/graph.json","events_json":"https://pith.science/api/pith-number/G4HMLNEVZJGIINIVKBZBPZR7TT/events.json","paper":"https://pith.science/paper/G4HMLNEV"},"agent_actions":{"view_html":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT","download_json":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT.json","view_paper":"https://pith.science/paper/G4HMLNEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02639&json=true","fetch_graph":"https://pith.science/api/pith-number/G4HMLNEVZJGIINIVKBZBPZR7TT/graph.json","fetch_events":"https://pith.science/api/pith-number/G4HMLNEVZJGIINIVKBZBPZR7TT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT/action/storage_attestation","attest_author":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT/action/author_attestation","sign_citation":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT/action/citation_signature","submit_replication":"https://pith.science/pith/G4HMLNEVZJGIINIVKBZBPZR7TT/action/replication_record"}},"created_at":"2026-05-18T02:29:37.587582+00:00","updated_at":"2026-05-18T02:29:37.587582+00:00"}