{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:U7G2FTFKUMV4RV2URS5RBBMBHM","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":"6654b200aba3538391654b945658cde0b3c158809e0eab8bfdeec1fb15e76c99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-16T14:55:22Z","title_canon_sha256":"1e26977024b268a4f1fc1e53cb9f457c9979ad01e6f549ada088143360be3063"},"schema_version":"1.0","source":{"id":"2410.12637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.12637","created_at":"2026-07-05T09:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"2410.12637v1","created_at":"2026-07-05T09:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.12637","created_at":"2026-07-05T09:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"U7G2FTFKUMV4","created_at":"2026-07-05T09:21:31Z"},{"alias_kind":"pith_short_16","alias_value":"U7G2FTFKUMV4RV2U","created_at":"2026-07-05T09:21:31Z"},{"alias_kind":"pith_short_8","alias_value":"U7G2FTFK","created_at":"2026-07-05T09:21:31Z"}],"graph_snapshots":[{"event_id":"sha256:78678d91e91b743b761ad52b7a5045d2112459f1627c7e2c563319a11fd98cc5","target":"graph","created_at":"2026-07-05T09:21:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.12637/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Grushin Laplacian $- \\Delta_\\alpha $ is a degenerate elliptic operator in $\\mathbb{R}^{h+k}$ that degenerates on $\\{0\\} \\times \\mathbb{R}^k$. We consider weak solutions of $- \\Delta_\\alpha u= Vu$ in an open bounded connected domain $\\Omega$ with $V \\in W^{1,\\sigma}(\\Omega)$ and $\\sigma > Q/2$, where $Q = h + (1+\\alpha)k$ is the so-called homogeneous dimension of $\\mathbb{R}^{h+k}$. By means of an Almgren-type monotonicity formula we identify the exact asymptotic blow-up profile of solutions on degenerate points of $\\Omega$. As an application we derive strong unique continuation properties ","authors_text":"Alberto Ferrero, Laura Abatangelo, Paolo Luzzini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-16T14:55:22Z","title":"On solutions to a class of degenerate equations with the Grushin operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.12637","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":"sha256:99f3f7a89c10a40125d1107592878b2b55f01dde1c0c14e86fa56556a3450fa9","target":"record","created_at":"2026-07-05T09:21:31Z","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":"6654b200aba3538391654b945658cde0b3c158809e0eab8bfdeec1fb15e76c99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-16T14:55:22Z","title_canon_sha256":"1e26977024b268a4f1fc1e53cb9f457c9979ad01e6f549ada088143360be3063"},"schema_version":"1.0","source":{"id":"2410.12637","kind":"arxiv","version":1}},"canonical_sha256":"a7cda2ccaaa32bc8d7548cbb1085813b1efd52353985adb8c419d532919e07d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7cda2ccaaa32bc8d7548cbb1085813b1efd52353985adb8c419d532919e07d9","first_computed_at":"2026-07-05T09:21:31.892307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:31.892307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rV6eA+LRmquq7pPI8xUzhMAYZF4GKtFbbP9Uk0f0boEEJlowahZQJEy5L2XjUyM83FbyTapKR7VPzC3Qi3v5AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:31.892782Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.12637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99f3f7a89c10a40125d1107592878b2b55f01dde1c0c14e86fa56556a3450fa9","sha256:78678d91e91b743b761ad52b7a5045d2112459f1627c7e2c563319a11fd98cc5"],"state_sha256":"1ea1456babd56cd0cc702c4c4f1c48ff8e7f379bf29a23292f31a9765cdc3002"}