{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YKDFXTF6X3UI4TDJ3NMVBLEMRT","short_pith_number":"pith:YKDFXTF6","canonical_record":{"source":{"id":"1501.03349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-14T13:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"278dda497095ec89b90bb0cc7b4e3a6ec76ac5efa6d69d28675e7547fdd418ba","abstract_canon_sha256":"f6b799a497d60076a38b6a3308da83c8d6aab41679843edf4ce09669d5827689"},"schema_version":"1.0"},"canonical_sha256":"c2865bccbebee88e4c69db5950ac8c8cfb67dd3127edcc5cbfec16643a73283e","source":{"kind":"arxiv","id":"1501.03349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03349","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03349v1","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03349","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"YKDFXTF6X3UI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YKDFXTF6X3UI4TDJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YKDFXTF6","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YKDFXTF6X3UI4TDJ3NMVBLEMRT","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-14T13:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"278dda497095ec89b90bb0cc7b4e3a6ec76ac5efa6d69d28675e7547fdd418ba","abstract_canon_sha256":"f6b799a497d60076a38b6a3308da83c8d6aab41679843edf4ce09669d5827689"},"schema_version":"1.0"},"canonical_sha256":"c2865bccbebee88e4c69db5950ac8c8cfb67dd3127edcc5cbfec16643a73283e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:24.232384Z","signature_b64":"A6wI+qdeI9PfRR+13fBTleSQAW9T574qLmPZU7C5c1owRp9GWATnmwofB6RoH5rlR59qSIHDYGvNXV27WvpNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2865bccbebee88e4c69db5950ac8c8cfb67dd3127edcc5cbfec16643a73283e","last_reissued_at":"2026-05-18T02:29:24.231964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:24.231964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03349","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":"2026-05-18T02:29:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WYtGZ9JnYuUT7VQLWAf5PqTeHVHlGVYo9GADNLkGPwsYRgNg15h1yYVuHWIJ+LxKxuEH156AxN/Ze5aMux2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:42:35.018074Z"},"content_sha256":"14a906b52d23dbf499c0538899146a8aa98a7833096333017fb37bcf5d744aa1","schema_version":"1.0","event_id":"sha256:14a906b52d23dbf499c0538899146a8aa98a7833096333017fb37bcf5d744aa1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YKDFXTF6X3UI4TDJ3NMVBLEMRT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetries, Hopf fibrations and supercritical elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, M\\'onica Clapp","submitted_at":"2015-01-14T13:59:13Z","abstract_excerpt":"We consider the semilinear elliptic boundary value problem \\[ -\\Delta u=\\left\\vert u\\right\\vert ^{p-2}u\\text{ in }\\Omega,\\text{\\quad }u=0\\text{ on }\\partial\\Omega, \\] in a bounded smooth domain $\\Omega$ of $\\mathbb{R}^{N}$ for supercritical exponents $p>\\frac{2N}{N-2}.$\n  Until recently, only few existence results were known. An approach which has been successfully applied to study this problem, consists in reducing it to a more general critical or subcritical problem, either by considering rotational symmetries, or by means of maps which preserve the Laplace operator, or by a combination of b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03349","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":"2026-05-18T02:29:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AxUYOmwGcKq/iMJJYirvZrCwsZBW7PRRsV+c26TRbawf9cusenlIukkKbIjj53NH7YQJKN0O/Cv7YvbRh916Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:42:35.018427Z"},"content_sha256":"3cd5debca7394d62940a851c1e688a6c0fe12c3a7aa0be71537236011b07cadc","schema_version":"1.0","event_id":"sha256:3cd5debca7394d62940a851c1e688a6c0fe12c3a7aa0be71537236011b07cadc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT/bundle.json","state_url":"https://pith.science/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT/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":"2026-06-02T04:42:35Z","links":{"resolver":"https://pith.science/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT","bundle":"https://pith.science/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT/bundle.json","state":"https://pith.science/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKDFXTF6X3UI4TDJ3NMVBLEMRT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YKDFXTF6X3UI4TDJ3NMVBLEMRT","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":"f6b799a497d60076a38b6a3308da83c8d6aab41679843edf4ce09669d5827689","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-14T13:59:13Z","title_canon_sha256":"278dda497095ec89b90bb0cc7b4e3a6ec76ac5efa6d69d28675e7547fdd418ba"},"schema_version":"1.0","source":{"id":"1501.03349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03349","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03349v1","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03349","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"YKDFXTF6X3UI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YKDFXTF6X3UI4TDJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YKDFXTF6","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:3cd5debca7394d62940a851c1e688a6c0fe12c3a7aa0be71537236011b07cadc","target":"graph","created_at":"2026-05-18T02:29:24Z","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 consider the semilinear elliptic boundary value problem \\[ -\\Delta u=\\left\\vert u\\right\\vert ^{p-2}u\\text{ in }\\Omega,\\text{\\quad }u=0\\text{ on }\\partial\\Omega, \\] in a bounded smooth domain $\\Omega$ of $\\mathbb{R}^{N}$ for supercritical exponents $p>\\frac{2N}{N-2}.$\n  Until recently, only few existence results were known. An approach which has been successfully applied to study this problem, consists in reducing it to a more general critical or subcritical problem, either by considering rotational symmetries, or by means of maps which preserve the Laplace operator, or by a combination of b","authors_text":"Angela Pistoia, M\\'onica Clapp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-14T13:59:13Z","title":"Symmetries, Hopf fibrations and supercritical elliptic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03349","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":"sha256:14a906b52d23dbf499c0538899146a8aa98a7833096333017fb37bcf5d744aa1","target":"record","created_at":"2026-05-18T02:29:24Z","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":"f6b799a497d60076a38b6a3308da83c8d6aab41679843edf4ce09669d5827689","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-14T13:59:13Z","title_canon_sha256":"278dda497095ec89b90bb0cc7b4e3a6ec76ac5efa6d69d28675e7547fdd418ba"},"schema_version":"1.0","source":{"id":"1501.03349","kind":"arxiv","version":1}},"canonical_sha256":"c2865bccbebee88e4c69db5950ac8c8cfb67dd3127edcc5cbfec16643a73283e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2865bccbebee88e4c69db5950ac8c8cfb67dd3127edcc5cbfec16643a73283e","first_computed_at":"2026-05-18T02:29:24.231964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:24.231964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A6wI+qdeI9PfRR+13fBTleSQAW9T574qLmPZU7C5c1owRp9GWATnmwofB6RoH5rlR59qSIHDYGvNXV27WvpNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:24.232384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14a906b52d23dbf499c0538899146a8aa98a7833096333017fb37bcf5d744aa1","sha256:3cd5debca7394d62940a851c1e688a6c0fe12c3a7aa0be71537236011b07cadc"],"state_sha256":"5416df63835c8b7544899c8395ca6c765af43a5ce2d8259700cd66b49ac459ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDNrH2jI4runpF7KzdLCs7wqWKx+aiwZesXvj7F6djiUCwSvxxNZIpD8RdZ7pvXBe9c3pNQZsWAD2jDG6HRsCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:42:35.020369Z","bundle_sha256":"eff97cd7e5ebc9025ddca55c18db6778da15aa77858fcf55fd40ec8a5ebe1844"}}