{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6JE6F55IB6BNYDZTGAJGVL3ADA","short_pith_number":"pith:6JE6F55I","canonical_record":{"source":{"id":"1704.02597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-09T12:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"f4a1198dbaa3f7e54ae0832bc4713a18e396f134fa57efa449145f78709f8786","abstract_canon_sha256":"ae99af8b735f1dd0157e06a8521b194337ed7687a620dfcc3807ee568c4874da"},"schema_version":"1.0"},"canonical_sha256":"f249e2f7a80f82dc0f3330126aaf6018339841ec4d9d7950727885b49a3adaec","source":{"kind":"arxiv","id":"1704.02597","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02597","created_at":"2026-05-18T00:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02597v2","created_at":"2026-05-18T00:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02597","created_at":"2026-05-18T00:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"6JE6F55IB6BN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6JE6F55IB6BNYDZT","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6JE6F55I","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6JE6F55IB6BNYDZTGAJGVL3ADA","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-09T12:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"f4a1198dbaa3f7e54ae0832bc4713a18e396f134fa57efa449145f78709f8786","abstract_canon_sha256":"ae99af8b735f1dd0157e06a8521b194337ed7687a620dfcc3807ee568c4874da"},"schema_version":"1.0"},"canonical_sha256":"f249e2f7a80f82dc0f3330126aaf6018339841ec4d9d7950727885b49a3adaec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:13.004035Z","signature_b64":"reZZdp47Y1/HhzIbzJESOSW18JLUsVxewrJrSU8kMfpV9ILV+8q4a+hmJND3F6505EPpE5L5uCPunN7SFnhIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f249e2f7a80f82dc0f3330126aaf6018339841ec4d9d7950727885b49a3adaec","last_reissued_at":"2026-05-18T00:43:13.003407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:13.003407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02597","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":"2026-05-18T00:43:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stEIFiKgPt6wFCCxMTNz3+n9TYFsEWk1o0GWxdtU+N3jgk2/lDfT91sIML9T8J2ll598NwtWftl41dBympaxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:24:20.275102Z"},"content_sha256":"7ed61f83a35eacba7a53f1bddeddf4d0555990c80ad652237dd6194ef285d2df","schema_version":"1.0","event_id":"sha256:7ed61f83a35eacba7a53f1bddeddf4d0555990c80ad652237dd6194ef285d2df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6JE6F55IB6BNYDZTGAJGVL3ADA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry results in the half space for a semi-linear fractional Laplace equation through a one-dimensional analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Quaas, B. Barrios, J. Garc\\'ia-Meli\\'an, L. Del Pezzo","submitted_at":"2017-04-09T12:51:01Z","abstract_excerpt":"In this paper we analyze the semi-linear fractional Laplace equation $$(-\\Delta)^s u = f(u) \\quad\\text{ in } \\mathbb{R}^N_+,\\quad u=0 \\quad\\text{ in } \\mathbb{R}^N\\setminus \\mathbb{R}^N_+,$$ where $\\mathbb{R}^N_+=\\{x=(x',x_N)\\in \\mathbb{R}^N:\\ x_N>0\\}$ stands for the half-space and $f$ is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if $u$ is a bounded solution with $\\rho:=\\sup_{\\mathbb{R}^N}u$ verifying $f(\\rho)=0$, then $u$ is necessarily one-dimensional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02597","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":"2026-05-18T00:43:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaCTUdPZNRFcLUsB6wSgvm1p9FtyySByAIephnV61hD23uC5JhJi0JpGEXAK8sqJQ0Ky7y+uDsXZezwfrgPUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:24:20.275467Z"},"content_sha256":"c41c510c6936e62175d560c4e74942f7d57400c25612245066348bd6f7c404cb","schema_version":"1.0","event_id":"sha256:c41c510c6936e62175d560c4e74942f7d57400c25612245066348bd6f7c404cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6JE6F55IB6BNYDZTGAJGVL3ADA/bundle.json","state_url":"https://pith.science/pith/6JE6F55IB6BNYDZTGAJGVL3ADA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6JE6F55IB6BNYDZTGAJGVL3ADA/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":"2026-07-01T02:24:20Z","links":{"resolver":"https://pith.science/pith/6JE6F55IB6BNYDZTGAJGVL3ADA","bundle":"https://pith.science/pith/6JE6F55IB6BNYDZTGAJGVL3ADA/bundle.json","state":"https://pith.science/pith/6JE6F55IB6BNYDZTGAJGVL3ADA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6JE6F55IB6BNYDZTGAJGVL3ADA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6JE6F55IB6BNYDZTGAJGVL3ADA","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":"ae99af8b735f1dd0157e06a8521b194337ed7687a620dfcc3807ee568c4874da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-09T12:51:01Z","title_canon_sha256":"f4a1198dbaa3f7e54ae0832bc4713a18e396f134fa57efa449145f78709f8786"},"schema_version":"1.0","source":{"id":"1704.02597","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02597","created_at":"2026-05-18T00:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02597v2","created_at":"2026-05-18T00:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02597","created_at":"2026-05-18T00:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"6JE6F55IB6BN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6JE6F55IB6BNYDZT","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6JE6F55I","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:c41c510c6936e62175d560c4e74942f7d57400c25612245066348bd6f7c404cb","target":"graph","created_at":"2026-05-18T00:43:13Z","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 analyze the semi-linear fractional Laplace equation $$(-\\Delta)^s u = f(u) \\quad\\text{ in } \\mathbb{R}^N_+,\\quad u=0 \\quad\\text{ in } \\mathbb{R}^N\\setminus \\mathbb{R}^N_+,$$ where $\\mathbb{R}^N_+=\\{x=(x',x_N)\\in \\mathbb{R}^N:\\ x_N>0\\}$ stands for the half-space and $f$ is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if $u$ is a bounded solution with $\\rho:=\\sup_{\\mathbb{R}^N}u$ verifying $f(\\rho)=0$, then $u$ is necessarily one-dimensional.","authors_text":"A. Quaas, B. Barrios, J. Garc\\'ia-Meli\\'an, L. Del Pezzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-09T12:51:01Z","title":"Symmetry results in the half space for a semi-linear fractional Laplace equation through a one-dimensional analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02597","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":"sha256:7ed61f83a35eacba7a53f1bddeddf4d0555990c80ad652237dd6194ef285d2df","target":"record","created_at":"2026-05-18T00:43:13Z","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":"ae99af8b735f1dd0157e06a8521b194337ed7687a620dfcc3807ee568c4874da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-09T12:51:01Z","title_canon_sha256":"f4a1198dbaa3f7e54ae0832bc4713a18e396f134fa57efa449145f78709f8786"},"schema_version":"1.0","source":{"id":"1704.02597","kind":"arxiv","version":2}},"canonical_sha256":"f249e2f7a80f82dc0f3330126aaf6018339841ec4d9d7950727885b49a3adaec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f249e2f7a80f82dc0f3330126aaf6018339841ec4d9d7950727885b49a3adaec","first_computed_at":"2026-05-18T00:43:13.003407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:13.003407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"reZZdp47Y1/HhzIbzJESOSW18JLUsVxewrJrSU8kMfpV9ILV+8q4a+hmJND3F6505EPpE5L5uCPunN7SFnhIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:13.004035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02597","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ed61f83a35eacba7a53f1bddeddf4d0555990c80ad652237dd6194ef285d2df","sha256:c41c510c6936e62175d560c4e74942f7d57400c25612245066348bd6f7c404cb"],"state_sha256":"6249d0387c53a1769759e74ac8373870e51827e285528d895ae48c8dc5f17f39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0sSAe+23ZSTLFmX4Tpw2b3t1c/g9tRtmc2f0CGI0iD95wRW8v0vhyHuPK573U15LAE+C8ZKHD3Ffplfp6d4YCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T02:24:20.277344Z","bundle_sha256":"b82189388c1bb8f8301c97933399dc0d6ea1efc784ef0e464812b414b17851a8"}}