{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AOWGAFGTNMMJSIW6YYT27RIMDP","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":"0515fc09d49a0e300a31b311e8d6875128b419b2e0e6827b2fbf27909082ec70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-22T08:03:36Z","title_canon_sha256":"b7cdec4becaf0d3b7e4b9c62cb75b522d0f746139af389126ac248c6c746d66b"},"schema_version":"1.0","source":{"id":"1405.5657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5657","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5657v1","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5657","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"pith_short_12","alias_value":"AOWGAFGTNMMJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AOWGAFGTNMMJSIW6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AOWGAFGT","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:4473dbfe11fb60c5ca892666e9a4b74938b79d1530649c315067faacd7f7c2a2","target":"graph","created_at":"2026-05-18T02:51:16Z","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 show that a realization of the operator $L=|x|^\\alpha\\Delta +c|x|^{\\alpha-1}\\frac{x}{|x|}\\cdot\\nabla -b|x|^{\\alpha-2}$ generates a semigroup in $L^p(\\mathbb {R}^N)$ if and only if $D_c=b+(N-2+c)^2/4 > 0$ and $s_1+\\min\\{0,2-\\alpha\\}<N/p<s_2+\\max\\{0,2-\\alpha\\}$, where $s_i$ are the roots of the equation $b+s(N-2+c-s)=0$, or $D_c=0$ and $s_0+\\min\\{0,2-\\alpha\\} \\le N/p \\le s_0+\\max\\{0,2-\\alpha\\}$, where $s_0$ is the unique root of the above equation. The domain of the generator is also characterized.","authors_text":"C. Spina, G. Metafune, M. Sobajima, N. Okazawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-22T08:03:36Z","title":"Scale invariant elliptic operators with singular coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5657","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":"sha256:75a6f76273ac9b8fa986278702bd60f01cbf22e77c94fae64eb44b0d1962ec2a","target":"record","created_at":"2026-05-18T02:51:16Z","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":"0515fc09d49a0e300a31b311e8d6875128b419b2e0e6827b2fbf27909082ec70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-22T08:03:36Z","title_canon_sha256":"b7cdec4becaf0d3b7e4b9c62cb75b522d0f746139af389126ac248c6c746d66b"},"schema_version":"1.0","source":{"id":"1405.5657","kind":"arxiv","version":1}},"canonical_sha256":"03ac6014d36b189922dec627afc50c1bd923d5d81926b23118571be8886c29ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03ac6014d36b189922dec627afc50c1bd923d5d81926b23118571be8886c29ab","first_computed_at":"2026-05-18T02:51:16.004005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:16.004005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"brCzMAAWX7RjtLWGtGG0OHuRAJjD9wWNZRnZNnO7uqu0r+MSK8zx67xKt7iHbKFvnoNeCZhAzUyWj2p2N1dHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:16.004530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75a6f76273ac9b8fa986278702bd60f01cbf22e77c94fae64eb44b0d1962ec2a","sha256:4473dbfe11fb60c5ca892666e9a4b74938b79d1530649c315067faacd7f7c2a2"],"state_sha256":"8bd99a1f11fbfad218770879b4edc85a89200742ac757ee047fb121ae7cb023c"}