{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GFHZ3NJGX7L75RGQYT5LSCE3WR","short_pith_number":"pith:GFHZ3NJG","canonical_record":{"source":{"id":"1710.02731","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-07T19:40:20Z","cross_cats_sorted":[],"title_canon_sha256":"0d554e4833bc56cd10045779c0c07021d94618d15aa63aea8e909eda1522a2b0","abstract_canon_sha256":"b30346b418fbaa569cfe35ce4965affd23171a2fed370a72856bd3bef040561d"},"schema_version":"1.0"},"canonical_sha256":"314f9db526bfd7fec4d0c4fab9089bb47a0fc827045615d4c6c20ddd493240b4","source":{"kind":"arxiv","id":"1710.02731","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02731","created_at":"2026-05-18T00:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02731v3","created_at":"2026-05-18T00:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02731","created_at":"2026-05-18T00:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"GFHZ3NJGX7L7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GFHZ3NJGX7L75RGQ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GFHZ3NJG","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GFHZ3NJGX7L75RGQYT5LSCE3WR","target":"record","payload":{"canonical_record":{"source":{"id":"1710.02731","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-07T19:40:20Z","cross_cats_sorted":[],"title_canon_sha256":"0d554e4833bc56cd10045779c0c07021d94618d15aa63aea8e909eda1522a2b0","abstract_canon_sha256":"b30346b418fbaa569cfe35ce4965affd23171a2fed370a72856bd3bef040561d"},"schema_version":"1.0"},"canonical_sha256":"314f9db526bfd7fec4d0c4fab9089bb47a0fc827045615d4c6c20ddd493240b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:52.856359Z","signature_b64":"Ivm9YZM4yAtflpuqLfUpDKdLBLY7ZbitAYh0k0nx/ujByTZKn61GyHKJoThS+bCKAas5cHL2TJQ8KR7HtYkxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"314f9db526bfd7fec4d0c4fab9089bb47a0fc827045615d4c6c20ddd493240b4","last_reissued_at":"2026-05-18T00:23:52.855665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:52.855665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.02731","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+0bEC9CADA96Znxa2x1MlHXY3uNZ7NFr/8iWRQ0AQfC3LBpZCjHyz2VtAxWR+l0Yf8sY9rfFQVym7gvVTsiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:13:11.149430Z"},"content_sha256":"dd99eecf7118753e6ce36097539c602b1017e8c8aa0dc406103aa94f97b3c2b6","schema_version":"1.0","event_id":"sha256:dd99eecf7118753e6ce36097539c602b1017e8c8aa0dc406103aa94f97b3c2b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GFHZ3NJGX7L75RGQYT5LSCE3WR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Juan Luis Vazquez, Matteo Bonforte","submitted_at":"2017-10-07T19:40:20Z","abstract_excerpt":"We investigate quantitative properties of nonnegative solutions $u(x)\\ge 0$ to the semilinear diffusion equation $\\mathcal{L} u= f(u)$, posed in a bounded domain $\\Omega\\subset {\\mathbb R}^N$ with appropriate homogeneous Dirichlet or outer boundary conditions. The operator $\\mathcal{L}$ may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian $(-\\Delta)^s$ ($0<s<1$) in a bounded domain with zero Dirichlet conditions, and a number of other nonlocal versions. The nonlinearity $f$ is increasing and loo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02731","kind":"arxiv","version":3},"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":"2026-05-18T00:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lptnjW27iMUewQOeNMsWeHLzjLTaBsZmqiK1UR/ibpS8RyrSHntXbh2fDUDN3C7Jru/l3gXOKpVM+phwIY6oDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:13:11.149833Z"},"content_sha256":"507711bf6ca678f97daf205e7a37072a9df4604d74b157a724c75b9cba2b352b","schema_version":"1.0","event_id":"sha256:507711bf6ca678f97daf205e7a37072a9df4604d74b157a724c75b9cba2b352b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR/bundle.json","state_url":"https://pith.science/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR/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":"2026-06-05T00:13:11Z","links":{"resolver":"https://pith.science/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR","bundle":"https://pith.science/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR/bundle.json","state":"https://pith.science/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFHZ3NJGX7L75RGQYT5LSCE3WR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GFHZ3NJGX7L75RGQYT5LSCE3WR","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":"b30346b418fbaa569cfe35ce4965affd23171a2fed370a72856bd3bef040561d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-07T19:40:20Z","title_canon_sha256":"0d554e4833bc56cd10045779c0c07021d94618d15aa63aea8e909eda1522a2b0"},"schema_version":"1.0","source":{"id":"1710.02731","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02731","created_at":"2026-05-18T00:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02731v3","created_at":"2026-05-18T00:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02731","created_at":"2026-05-18T00:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"GFHZ3NJGX7L7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GFHZ3NJGX7L75RGQ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GFHZ3NJG","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:507711bf6ca678f97daf205e7a37072a9df4604d74b157a724c75b9cba2b352b","target":"graph","created_at":"2026-05-18T00:23:52Z","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 investigate quantitative properties of nonnegative solutions $u(x)\\ge 0$ to the semilinear diffusion equation $\\mathcal{L} u= f(u)$, posed in a bounded domain $\\Omega\\subset {\\mathbb R}^N$ with appropriate homogeneous Dirichlet or outer boundary conditions. The operator $\\mathcal{L}$ may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian $(-\\Delta)^s$ ($0<s<1$) in a bounded domain with zero Dirichlet conditions, and a number of other nonlocal versions. The nonlinearity $f$ is increasing and loo","authors_text":"Alessio Figalli, Juan Luis Vazquez, Matteo Bonforte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-07T19:40:20Z","title":"Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02731","kind":"arxiv","version":3},"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:dd99eecf7118753e6ce36097539c602b1017e8c8aa0dc406103aa94f97b3c2b6","target":"record","created_at":"2026-05-18T00:23:52Z","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":"b30346b418fbaa569cfe35ce4965affd23171a2fed370a72856bd3bef040561d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-07T19:40:20Z","title_canon_sha256":"0d554e4833bc56cd10045779c0c07021d94618d15aa63aea8e909eda1522a2b0"},"schema_version":"1.0","source":{"id":"1710.02731","kind":"arxiv","version":3}},"canonical_sha256":"314f9db526bfd7fec4d0c4fab9089bb47a0fc827045615d4c6c20ddd493240b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"314f9db526bfd7fec4d0c4fab9089bb47a0fc827045615d4c6c20ddd493240b4","first_computed_at":"2026-05-18T00:23:52.855665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:52.855665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ivm9YZM4yAtflpuqLfUpDKdLBLY7ZbitAYh0k0nx/ujByTZKn61GyHKJoThS+bCKAas5cHL2TJQ8KR7HtYkxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:52.856359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02731","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd99eecf7118753e6ce36097539c602b1017e8c8aa0dc406103aa94f97b3c2b6","sha256:507711bf6ca678f97daf205e7a37072a9df4604d74b157a724c75b9cba2b352b"],"state_sha256":"0e10ccf40c8f6eded31202fd8f94454c6c8bcfb92c2c6da459376c2fd2996232"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsmqGvN8DSU7nOq2hmohQzHycEaXDag/rcLRtRherbRxtQWuI5XN2+mL/c+V57cctBLQ0iYeGLB/PqeYbFybCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:13:11.151922Z","bundle_sha256":"d522e5a24b6ad75f8e120f940e1821cc60dc8fc6433afa73ccd6fab9f5904c1b"}}