{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CHNFTS65VBMYH2CSEHX7643WE7","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":"322e12395fde55416d46dec3a00e68e7cb40259521dce4701bf91d5bda0c945d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-20T14:55:41Z","title_canon_sha256":"afd834cb4e657f8b983892a6354eff35cdf091f27fd883d3ceab3ff5895e0ecd"},"schema_version":"1.0","source":{"id":"1906.09147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09147","created_at":"2026-05-17T23:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09147v1","created_at":"2026-05-17T23:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09147","created_at":"2026-05-17T23:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"CHNFTS65VBMY","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CHNFTS65VBMYH2CS","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CHNFTS65","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:4cc7a18f79c3fb3309f8da06f1706c14ec35be66495d6cdc0c6a81dd7cf89c1c","target":"graph","created_at":"2026-05-17T23:42:44Z","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":"Supposing only that $\\displaystyle\\lim_{t \\to 0} \\frac{f(t)}{t} = 0$ and $\\displaystyle\\lim_{t \\to \\infty} \\frac{f(t)}{t^{p}} = 0$, for some $p \\in \\left(1,\\frac{N+1}{N-1}\\right)$, we prove that solutions to the extension problem \\begin{equation*}\\left\\{ \\begin{array}{rcll} -\\Delta u+ m^2u &=& 0, &\\mbox{in} \\ \\ \\mathbb{R}^{N+1}_{+} \\\\ -\\frac{\\partial u}{\\partial{x}} (0,y)& =& f(u(0,y)), & y \\in \\mathbb{R}^{N}, \\end{array}\\right. \\end{equation*} and also to the extension Hartree problem \\begin{equation*} \\left\\{\\begin{aligned} -\\Delta u +m^2u&=0, &&\\mbox{in} \\ \\mathbb{R}^{N+1}_+,\\\\ -\\displaysty","authors_text":"Aldo H. S. Medeiros, G. A. Pereira, Hamilton Bueno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-20T14:55:41Z","title":"Existence, regularity, asymptotic decay and radiality of solutions to some extension problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09147","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:d0e245a5de4d3ba8541f50dd2a50ab712c4e571cfcbe1f1805ae595b250e3bb4","target":"record","created_at":"2026-05-17T23:42:44Z","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":"322e12395fde55416d46dec3a00e68e7cb40259521dce4701bf91d5bda0c945d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-20T14:55:41Z","title_canon_sha256":"afd834cb4e657f8b983892a6354eff35cdf091f27fd883d3ceab3ff5895e0ecd"},"schema_version":"1.0","source":{"id":"1906.09147","kind":"arxiv","version":1}},"canonical_sha256":"11da59cbdda85983e85221efff737627edebed0c0ef573184e3f0bf73db41dd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11da59cbdda85983e85221efff737627edebed0c0ef573184e3f0bf73db41dd3","first_computed_at":"2026-05-17T23:42:44.362573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:44.362573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+aHVJuWQ23pf2gjvHGZcVd4S40d9xmM3ikZDY+gUjvuxI6i+bW2W77dVxsUne/l5g8KZk3z64XDp94Pwyj4rBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:44.363023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0e245a5de4d3ba8541f50dd2a50ab712c4e571cfcbe1f1805ae595b250e3bb4","sha256:4cc7a18f79c3fb3309f8da06f1706c14ec35be66495d6cdc0c6a81dd7cf89c1c"],"state_sha256":"940dd4d92ee0ed02c0957a8a573a563d74b0278deb6e2cebbefc955db3d457fe"}