{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:M33TACLW47IUDDH6F555FMZ44Z","short_pith_number":"pith:M33TACLW","canonical_record":{"source":{"id":"1902.01606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-05T09:37:06Z","cross_cats_sorted":[],"title_canon_sha256":"d9ef0e193185d1e4e1e43a3029546e1808d80379c423d6518de6cf75d555b2d3","abstract_canon_sha256":"e52ce38abad31f780bf7cc551a7633896f35220b67dd4a6ef956b334ca9c95ef"},"schema_version":"1.0"},"canonical_sha256":"66f7300976e7d1418cfe2f7bd2b33ce67bb180f34ec79493c702f14d2702e117","source":{"kind":"arxiv","id":"1902.01606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01606","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01606v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01606","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"M33TACLW47IU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M33TACLW47IUDDH6","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M33TACLW","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:M33TACLW47IUDDH6F555FMZ44Z","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-05T09:37:06Z","cross_cats_sorted":[],"title_canon_sha256":"d9ef0e193185d1e4e1e43a3029546e1808d80379c423d6518de6cf75d555b2d3","abstract_canon_sha256":"e52ce38abad31f780bf7cc551a7633896f35220b67dd4a6ef956b334ca9c95ef"},"schema_version":"1.0"},"canonical_sha256":"66f7300976e7d1418cfe2f7bd2b33ce67bb180f34ec79493c702f14d2702e117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:47.167218Z","signature_b64":"QUC7auZnC9BK4M2hFAWUmUCj6j7SUDRmFMFYk1OfvUWFC+0CGZMNbxuV7cHMG+i8Mc0cTGAqqor+2Uqa7zkdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66f7300976e7d1418cfe2f7bd2b33ce67bb180f34ec79493c702f14d2702e117","last_reissued_at":"2026-05-17T23:54:47.166487Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:47.166487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01606","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G3VxJuGZuBwu+eYopRwfgwCManqK0EZh0zi5UVTemqE/kscoMp0xzmtla9L//WD0LVpvqje9d2A/WYwV7oqwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:34:46.613853Z"},"content_sha256":"aa25b406bed68d3917ed295fa466e0308f106fa3b3e2034158dcf95178af7458","schema_version":"1.0","event_id":"sha256:aa25b406bed68d3917ed295fa466e0308f106fa3b3e2034158dcf95178af7458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:M33TACLW47IUDDH6F555FMZ44Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A supercritical scalar field equation with a forcing term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Shinya Okabe, Tokushi Sato","submitted_at":"2019-02-05T09:37:06Z","abstract_excerpt":"This paper is concerned with the elliptic problem for a scalar field equation with a forcing term \\begin{equation} \\tag{P}-\\Delta u+u=u^p+ \\kappa \\mu \\quad \\mbox{in} \\quad{\\bf R}^N, \\quad u>0 \\quad \\mbox{in} \\quad {\\bf R}^N, \\quad u(x)\\to 0\\quad \\mbox{as} \\quad |x| \\to \\infty, \\end{equation} where $N\\ge 2$, $p>1$, $\\kappa>0$ and $\\mu$ is a Radon measure in ${\\bf R}^N$ with a compact support. Under a suitable integrability condition on $\\mu$, we give a complete classification of the solvability of problem~(P) with $1<p<p_{JL}$. Here $p_{JL}$ is the Joseph-Lundgren exponent defined by $$\n  p_{JL"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01606","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rESbrAHBCjC4EhEogOcdX5I0KZo8fbx6vAsBzy2BUYAdwcJM2PvrhWoV2UUAyqE+8/5rp2B8IWo1Ee+m+5oDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:34:46.614449Z"},"content_sha256":"f2c4601067dc4595b4e143bf6fd3bb48ac4011bab49e448c7610735f2f812a63","schema_version":"1.0","event_id":"sha256:f2c4601067dc4595b4e143bf6fd3bb48ac4011bab49e448c7610735f2f812a63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M33TACLW47IUDDH6F555FMZ44Z/bundle.json","state_url":"https://pith.science/pith/M33TACLW47IUDDH6F555FMZ44Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M33TACLW47IUDDH6F555FMZ44Z/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":"2026-06-03T15:34:46Z","links":{"resolver":"https://pith.science/pith/M33TACLW47IUDDH6F555FMZ44Z","bundle":"https://pith.science/pith/M33TACLW47IUDDH6F555FMZ44Z/bundle.json","state":"https://pith.science/pith/M33TACLW47IUDDH6F555FMZ44Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M33TACLW47IUDDH6F555FMZ44Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M33TACLW47IUDDH6F555FMZ44Z","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":"e52ce38abad31f780bf7cc551a7633896f35220b67dd4a6ef956b334ca9c95ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-05T09:37:06Z","title_canon_sha256":"d9ef0e193185d1e4e1e43a3029546e1808d80379c423d6518de6cf75d555b2d3"},"schema_version":"1.0","source":{"id":"1902.01606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01606","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01606v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01606","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"M33TACLW47IU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M33TACLW47IUDDH6","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M33TACLW","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:f2c4601067dc4595b4e143bf6fd3bb48ac4011bab49e448c7610735f2f812a63","target":"graph","created_at":"2026-05-17T23:54:47Z","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":"This paper is concerned with the elliptic problem for a scalar field equation with a forcing term \\begin{equation} \\tag{P}-\\Delta u+u=u^p+ \\kappa \\mu \\quad \\mbox{in} \\quad{\\bf R}^N, \\quad u>0 \\quad \\mbox{in} \\quad {\\bf R}^N, \\quad u(x)\\to 0\\quad \\mbox{as} \\quad |x| \\to \\infty, \\end{equation} where $N\\ge 2$, $p>1$, $\\kappa>0$ and $\\mu$ is a Radon measure in ${\\bf R}^N$ with a compact support. Under a suitable integrability condition on $\\mu$, we give a complete classification of the solvability of problem~(P) with $1<p<p_{JL}$. Here $p_{JL}$ is the Joseph-Lundgren exponent defined by $$\n  p_{JL","authors_text":"Kazuhiro Ishige, Shinya Okabe, Tokushi Sato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-05T09:37:06Z","title":"A supercritical scalar field equation with a forcing term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01606","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:aa25b406bed68d3917ed295fa466e0308f106fa3b3e2034158dcf95178af7458","target":"record","created_at":"2026-05-17T23:54:47Z","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":"e52ce38abad31f780bf7cc551a7633896f35220b67dd4a6ef956b334ca9c95ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-05T09:37:06Z","title_canon_sha256":"d9ef0e193185d1e4e1e43a3029546e1808d80379c423d6518de6cf75d555b2d3"},"schema_version":"1.0","source":{"id":"1902.01606","kind":"arxiv","version":1}},"canonical_sha256":"66f7300976e7d1418cfe2f7bd2b33ce67bb180f34ec79493c702f14d2702e117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66f7300976e7d1418cfe2f7bd2b33ce67bb180f34ec79493c702f14d2702e117","first_computed_at":"2026-05-17T23:54:47.166487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:47.166487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QUC7auZnC9BK4M2hFAWUmUCj6j7SUDRmFMFYk1OfvUWFC+0CGZMNbxuV7cHMG+i8Mc0cTGAqqor+2Uqa7zkdBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:47.167218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa25b406bed68d3917ed295fa466e0308f106fa3b3e2034158dcf95178af7458","sha256:f2c4601067dc4595b4e143bf6fd3bb48ac4011bab49e448c7610735f2f812a63"],"state_sha256":"7e6612cb4064a0c3c6c2e187695aaf30d46825d56745052e50621f35150ed986"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUg8cSOuxrTz9afpAygEPgYAftfz3PlCs77tzYH0e4HDLKKXgD5PeEZY0AVw20+4l/aNIeqxPgdKWQOTXb7DBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:34:46.616786Z","bundle_sha256":"ced4bc2e29a11f04ce668a7a0e02ace8186d27bd27a3f25581b9403fcbc0cc1c"}}