{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SBEOSLHOADBYUYMR536QVYGYNT","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":"45ca8d22a139edaf29f80abaa3246469aa4dbad183a06943fb7cc9617bc7c03c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-17T15:58:31Z","title_canon_sha256":"3be388a3eb3afbf7099ad389b7114f773e8b0a9d6b1ea64b600d3fb57143eba4"},"schema_version":"1.0","source":{"id":"1212.4041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4041","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4041v1","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4041","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"SBEOSLHOADBY","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SBEOSLHOADBYUYMR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SBEOSLHO","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:99fd2f4a2491319495e5a88e1ccd56078a164521822535f83130ad3e2d1bafa5","target":"graph","created_at":"2026-05-18T00:01:01Z","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 study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is compact, we deduce spectral information on the natural drifted Laplacian associated to the self-shrinker. These results go in the direction of verifying the validity of a conjecture by H. D. Cao concerning the polynomial volume growth of complete self-shrinkers. A finite strong maxim","authors_text":"Michele Rimoldi, Stefano Pigola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-17T15:58:31Z","title":"Complete self-shrinkers confined into some regions of the space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4041","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:c86cf4e0743e75a208bfa0233a83b7b423b9b2e9a2d3891a4a1c9cc39d284e16","target":"record","created_at":"2026-05-18T00:01:01Z","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":"45ca8d22a139edaf29f80abaa3246469aa4dbad183a06943fb7cc9617bc7c03c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-17T15:58:31Z","title_canon_sha256":"3be388a3eb3afbf7099ad389b7114f773e8b0a9d6b1ea64b600d3fb57143eba4"},"schema_version":"1.0","source":{"id":"1212.4041","kind":"arxiv","version":1}},"canonical_sha256":"9048e92cee00c38a6191eefd0ae0d86cdb1798a68b67944ebc00e8b9ea8c2ce9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9048e92cee00c38a6191eefd0ae0d86cdb1798a68b67944ebc00e8b9ea8c2ce9","first_computed_at":"2026-05-18T00:01:01.063919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:01.063919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uiPnn3aBOrYpwD9e5fVneIhEOykWr1pVDnG2iIf17w4f0NCacusfqSG4x/8Ld0408A7Yk6PBCTNpKO0oMbQRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:01.064568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c86cf4e0743e75a208bfa0233a83b7b423b9b2e9a2d3891a4a1c9cc39d284e16","sha256:99fd2f4a2491319495e5a88e1ccd56078a164521822535f83130ad3e2d1bafa5"],"state_sha256":"2ac8be14cf3873d51cce55eea78094b2abae03c77ea6ff5b3fcec2e7abe71e02"}