{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EGUWO4U2BQ4HTXQFI2W3HFFIBV","short_pith_number":"pith:EGUWO4U2","canonical_record":{"source":{"id":"1708.06149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T11:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"cc1e5ac84d6aaff4c4e8299ee98b7713a922a827bdd936b8b8b9dd1ad0727cc4","abstract_canon_sha256":"d87d21ae942f9bb838d37b79ecfbf0911b84857c6ba54a6b8ec16e8475a695dd"},"schema_version":"1.0"},"canonical_sha256":"21a967729a0c3879de0546adb394a80d5a6482d5ccd7cd09c141e36aea229ba9","source":{"kind":"arxiv","id":"1708.06149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06149","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06149v2","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06149","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"pith_short_12","alias_value":"EGUWO4U2BQ4H","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EGUWO4U2BQ4HTXQF","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EGUWO4U2","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EGUWO4U2BQ4HTXQFI2W3HFFIBV","target":"record","payload":{"canonical_record":{"source":{"id":"1708.06149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T11:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"cc1e5ac84d6aaff4c4e8299ee98b7713a922a827bdd936b8b8b9dd1ad0727cc4","abstract_canon_sha256":"d87d21ae942f9bb838d37b79ecfbf0911b84857c6ba54a6b8ec16e8475a695dd"},"schema_version":"1.0"},"canonical_sha256":"21a967729a0c3879de0546adb394a80d5a6482d5ccd7cd09c141e36aea229ba9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:32.466128Z","signature_b64":"/P9KGNfeeKXmIBLPHIFkswMwPR+GKsW0XurwpV6StT5aTGRKv+EHilsPdD48LYo+qLyA0pve0ZZjyCruZRG+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21a967729a0c3879de0546adb394a80d5a6482d5ccd7cd09c141e36aea229ba9","last_reissued_at":"2026-05-18T00:11:32.465608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:32.465608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.06149","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nO1fnNz/J6XQW/4YmX2Me96v72PZ2Am6QZTeVzVtEZpDddZyZ+iJEkObnFN5YKkVpTFJGZGvD3kwuy35GUQNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:28:07.422166Z"},"content_sha256":"cd93b2f930b85f917ed68becea57ce39e157e7703a27447c0b9739b17c608c53","schema_version":"1.0","event_id":"sha256:cd93b2f930b85f917ed68becea57ce39e157e7703a27447c0b9739b17c608c53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EGUWO4U2BQ4HTXQFI2W3HFFIBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of the nodal set and asymptotics of least energy sign-changing radial solutions of the fractional Brezis-Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti, Gabriele Cora","submitted_at":"2017-08-21T11:06:24Z","abstract_excerpt":"In this paper we study the asymptotic and qualitative properties of least energy radial sign-changing solutions of the fractional Brezis--Nirenberg problem ruled by the s-laplacian, in a ball of $\\mathbb{R}^n$, when $s \\in (0,1)$ and $n > 6s$. As usual, $\\lambda$ is the (positive) parameter in the linear part in $u$, and we consider $\\lambda$ close to zero. We prove that if such solutions vanish at the center of the ball then they vanish everywhere, we establish a bound on the number of sign-changes and, when $s$ is close to $1$, for a suitable value of the parameter $\\lambda$ such solutions c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06149","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJmL5g8ljiDUVCICJ59IWvdXB3Zipbh6YZnf20AyAhIFuPg9EdNrv4Z/xKSB+Glxq/Z9M4mJZ3oFqT/91D/cDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:28:07.422610Z"},"content_sha256":"44f72bcfea075f82b0c3ae04655ce4db9ab18d988efb528487603d5a8cd7234b","schema_version":"1.0","event_id":"sha256:44f72bcfea075f82b0c3ae04655ce4db9ab18d988efb528487603d5a8cd7234b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV/bundle.json","state_url":"https://pith.science/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T08:28:07Z","links":{"resolver":"https://pith.science/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV","bundle":"https://pith.science/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV/bundle.json","state":"https://pith.science/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGUWO4U2BQ4HTXQFI2W3HFFIBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EGUWO4U2BQ4HTXQFI2W3HFFIBV","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":"d87d21ae942f9bb838d37b79ecfbf0911b84857c6ba54a6b8ec16e8475a695dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T11:06:24Z","title_canon_sha256":"cc1e5ac84d6aaff4c4e8299ee98b7713a922a827bdd936b8b8b9dd1ad0727cc4"},"schema_version":"1.0","source":{"id":"1708.06149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06149","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06149v2","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06149","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"pith_short_12","alias_value":"EGUWO4U2BQ4H","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EGUWO4U2BQ4HTXQF","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EGUWO4U2","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:44f72bcfea075f82b0c3ae04655ce4db9ab18d988efb528487603d5a8cd7234b","target":"graph","created_at":"2026-05-18T00:11:32Z","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":"In this paper we study the asymptotic and qualitative properties of least energy radial sign-changing solutions of the fractional Brezis--Nirenberg problem ruled by the s-laplacian, in a ball of $\\mathbb{R}^n$, when $s \\in (0,1)$ and $n > 6s$. As usual, $\\lambda$ is the (positive) parameter in the linear part in $u$, and we consider $\\lambda$ close to zero. We prove that if such solutions vanish at the center of the ball then they vanish everywhere, we establish a bound on the number of sign-changes and, when $s$ is close to $1$, for a suitable value of the parameter $\\lambda$ such solutions c","authors_text":"Alessandro Iacopetti, Gabriele Cora","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T11:06:24Z","title":"On the structure of the nodal set and asymptotics of least energy sign-changing radial solutions of the fractional Brezis-Nirenberg problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06149","kind":"arxiv","version":2},"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:cd93b2f930b85f917ed68becea57ce39e157e7703a27447c0b9739b17c608c53","target":"record","created_at":"2026-05-18T00:11:32Z","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":"d87d21ae942f9bb838d37b79ecfbf0911b84857c6ba54a6b8ec16e8475a695dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T11:06:24Z","title_canon_sha256":"cc1e5ac84d6aaff4c4e8299ee98b7713a922a827bdd936b8b8b9dd1ad0727cc4"},"schema_version":"1.0","source":{"id":"1708.06149","kind":"arxiv","version":2}},"canonical_sha256":"21a967729a0c3879de0546adb394a80d5a6482d5ccd7cd09c141e36aea229ba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a967729a0c3879de0546adb394a80d5a6482d5ccd7cd09c141e36aea229ba9","first_computed_at":"2026-05-18T00:11:32.465608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:32.465608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/P9KGNfeeKXmIBLPHIFkswMwPR+GKsW0XurwpV6StT5aTGRKv+EHilsPdD48LYo+qLyA0pve0ZZjyCruZRG+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:32.466128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd93b2f930b85f917ed68becea57ce39e157e7703a27447c0b9739b17c608c53","sha256:44f72bcfea075f82b0c3ae04655ce4db9ab18d988efb528487603d5a8cd7234b"],"state_sha256":"59d7ff4bf94595d2e96dddf68ae1538d113df9581c13ff7ccc0428c23c3f4390"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SjsR3boNbVHVyf2dC0kmbyDAyG3VWs7HVKlwtculB4dJr7XFva+c6vcIsmmt2C4IXAqhm2sAJxCKoPSHo/ceAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:28:07.424578Z","bundle_sha256":"4a30e0e5606e76277ebfc6f182268cc97895f836ee847d6679d9b62c0fa0d982"}}