{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:C32ZIRDE2IWJO4RSXRCFFHTTGK","short_pith_number":"pith:C32ZIRDE","schema_version":"1.0","canonical_sha256":"16f5944464d22c977232bc44529e7332abda6964f47c7a81c2c143f12f14ad0a","source":{"kind":"arxiv","id":"1610.09328","version":1},"attestation_state":"computed","paper":{"title":"Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"G. M. Figueiredo, G. Siciliano","submitted_at":"2016-10-28T17:54:46Z","abstract_excerpt":"We prove existence of multiple positive solutions for a {\\sl fractional scalar field equation} in a bounded domain, whenever $p$ tends to the critical Sobolev exponent. By means of the \"photography method\", we prove that the topology of the domain furnishes a lower bound on the number of positive solutions."},"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":"1610.09328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T17:54:46Z","cross_cats_sorted":[],"title_canon_sha256":"79b0a54b70f5dd28af44e89d57044400bdfa19d812e5569d5cd61dfe05c91bce","abstract_canon_sha256":"fe4172993e74478bd0371c0627c247910e95b003c5f815a4068c435ec4054297"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:54.466179Z","signature_b64":"hhFBTN3rWRVsh8MgEXXGM5HkOsTOaiBVVpRJkH77Sfvm7YkWqLdZhNelvw4r/jZvpVDDQg2MxEmost3/ovARCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16f5944464d22c977232bc44529e7332abda6964f47c7a81c2c143f12f14ad0a","last_reissued_at":"2026-05-18T01:00:54.465556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:54.465556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"G. M. Figueiredo, G. Siciliano","submitted_at":"2016-10-28T17:54:46Z","abstract_excerpt":"We prove existence of multiple positive solutions for a {\\sl fractional scalar field equation} in a bounded domain, whenever $p$ tends to the critical Sobolev exponent. By means of the \"photography method\", we prove that the topology of the domain furnishes a lower bound on the number of positive solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09328","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":"1610.09328","created_at":"2026-05-18T01:00:54.465669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09328v1","created_at":"2026-05-18T01:00:54.465669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09328","created_at":"2026-05-18T01:00:54.465669+00:00"},{"alias_kind":"pith_short_12","alias_value":"C32ZIRDE2IWJ","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C32ZIRDE2IWJO4RS","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C32ZIRDE","created_at":"2026-05-18T12:30:09.641336+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/C32ZIRDE2IWJO4RSXRCFFHTTGK","json":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK.json","graph_json":"https://pith.science/api/pith-number/C32ZIRDE2IWJO4RSXRCFFHTTGK/graph.json","events_json":"https://pith.science/api/pith-number/C32ZIRDE2IWJO4RSXRCFFHTTGK/events.json","paper":"https://pith.science/paper/C32ZIRDE"},"agent_actions":{"view_html":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK","download_json":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK.json","view_paper":"https://pith.science/paper/C32ZIRDE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09328&json=true","fetch_graph":"https://pith.science/api/pith-number/C32ZIRDE2IWJO4RSXRCFFHTTGK/graph.json","fetch_events":"https://pith.science/api/pith-number/C32ZIRDE2IWJO4RSXRCFFHTTGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK/action/storage_attestation","attest_author":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK/action/author_attestation","sign_citation":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK/action/citation_signature","submit_replication":"https://pith.science/pith/C32ZIRDE2IWJO4RSXRCFFHTTGK/action/replication_record"}},"created_at":"2026-05-18T01:00:54.465669+00:00","updated_at":"2026-05-18T01:00:54.465669+00:00"}