{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G7A7VFWRUBNKNVT3G4V3JM2YYE","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":"8b6a81f9b5bcc4d83b558c440ebeb70b7907f31b7be5bab062d5828c69c7b313","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-27T17:02:34Z","title_canon_sha256":"b9e5ef29198d591703525cf5514d94c02df58840fd6f935f7d4e51ce1a2a193a"},"schema_version":"1.0","source":{"id":"1704.08658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08658","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08658v1","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08658","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"G7A7VFWRUBNK","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7A7VFWRUBNKNVT3","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7A7VFWR","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:da69113fd02f8e077788c1daaba4e4ff7da4f5752aad1358ffb91c244c516022","target":"graph","created_at":"2026-05-18T00:45:27Z","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 consider linear and non-linear boundary value problems associated to the fractional Hardy-Schr\\\"odinger operator $ L_{\\gamma,\\alpha}: = ({-}{ \\Delta})^{\\frac{\\alpha}{2}}- \\frac{\\gamma}{|x|^{\\alpha}}$ on domains of $\\mathbb{R}^n$ containing the singularity $0$, where $0<\\alpha<2$ and $ 0 \\le \\gamma < \\gamma_H(\\alpha)$, the latter being the best constant in the fractional Hardy inequality on $\\mathbb{R}^n$. We tackle the existence of least-energy solutions for the borderline boundary value problem $(L_{\\gamma,\\alpha}-\\lambda I)u= {\\frac{u^{2^\\star_\\alpha(s)-1}}{|x|^s}}$ on $\\Omega$, where $0\\","authors_text":"Fr\\'ed\\'eric Robert, Mingefeng Zhao, Nassif Ghoussoub, Shaya Shakerian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-27T17:02:34Z","title":"Mass and Asymptotics associated to Fractional Hardy-Schr\\\"odinger Operators in Critical Regimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08658","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":"sha256:7825169bab8f9015ced26f93f1a834ffd05fb0479e016294ddd561aa1bd5b55b","target":"record","created_at":"2026-05-18T00:45:27Z","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":"8b6a81f9b5bcc4d83b558c440ebeb70b7907f31b7be5bab062d5828c69c7b313","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-27T17:02:34Z","title_canon_sha256":"b9e5ef29198d591703525cf5514d94c02df58840fd6f935f7d4e51ce1a2a193a"},"schema_version":"1.0","source":{"id":"1704.08658","kind":"arxiv","version":1}},"canonical_sha256":"37c1fa96d1a05aa6d67b372bb4b358c134535a410e09cbaa66d8e7fe411349a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37c1fa96d1a05aa6d67b372bb4b358c134535a410e09cbaa66d8e7fe411349a0","first_computed_at":"2026-05-18T00:45:27.225412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:27.225412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"01YHbbKoMSSPWxnnHF8LxJqQ/3CGu8Sdk1c00Dw5EK94WLUopJdRFhdza/7KK8W2xjLaDP2qVli4nZeCVV2hBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:27.225872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7825169bab8f9015ced26f93f1a834ffd05fb0479e016294ddd561aa1bd5b55b","sha256:da69113fd02f8e077788c1daaba4e4ff7da4f5752aad1358ffb91c244c516022"],"state_sha256":"cfc77fbbb7fbdab70f11c8ecc151630a8f72bd9fe7fbc544119aeae3bd2188a7"}