{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UKCZMJFAFSIBFLW5ZYUICUVR66","short_pith_number":"pith:UKCZMJFA","canonical_record":{"source":{"id":"1404.0792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-03T07:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"b434ef5717aaf275d191947ced4e2b96f4afe12677a83382708d69a3c525dad2","abstract_canon_sha256":"9354302f172a1ecf738d2afb54ffa1cfa870736612909a1bcc86665f65e1f28f"},"schema_version":"1.0"},"canonical_sha256":"a2859624a02c9012aeddce288152b1f78a48413210b5fc50ece986a02e1109c3","source":{"kind":"arxiv","id":"1404.0792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0792","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0792v1","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0792","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"pith_short_12","alias_value":"UKCZMJFAFSIB","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UKCZMJFAFSIBFLW5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UKCZMJFA","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UKCZMJFAFSIBFLW5ZYUICUVR66","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-03T07:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"b434ef5717aaf275d191947ced4e2b96f4afe12677a83382708d69a3c525dad2","abstract_canon_sha256":"9354302f172a1ecf738d2afb54ffa1cfa870736612909a1bcc86665f65e1f28f"},"schema_version":"1.0"},"canonical_sha256":"a2859624a02c9012aeddce288152b1f78a48413210b5fc50ece986a02e1109c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:55.506365Z","signature_b64":"2x8JK89I43zdvbECiZf3qcpsOzQV81MD4FaMLEx+XLjMr2GioykBPf2J/l/dAv7N9xxfnvfUNoyOFXN5KGKrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2859624a02c9012aeddce288152b1f78a48413210b5fc50ece986a02e1109c3","last_reissued_at":"2026-05-18T02:54:55.505828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:55.505828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0792","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":"2026-05-18T02:54:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIKWed2fRkH671o3AE0m2t0rbocuRuzRYi7MDlWiMutpAZo5l1YFAcyvX5Us7faGMkpab5erzQzChSEXRtY2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:16:24.510799Z"},"content_sha256":"9c79f043e295d9d28669b2dd9c3ebdddf5a0390beaa050bcf48bfd9fd8c236ae","schema_version":"1.0","event_id":"sha256:9c79f043e295d9d28669b2dd9c3ebdddf5a0390beaa050bcf48bfd9fd8c236ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UKCZMJFAFSIBFLW5ZYUICUVR66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non radial solutions for non homogeneous H\\'enon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gianluca Cappa, Marino Badiale","submitted_at":"2014-04-03T07:52:06Z","abstract_excerpt":"In this paper we study a H\\'enon-like equation (see equations (1) below), where the nonlinearity f(t) is not homogeneous (i.e., it is not a power). By minimization on the Nehari manifold, we prove that for large values of the parameter $\\alpha$ there is a breaking of symmetry and non radial solutions appears. This holds for sub- and super-critical growth of the nonlinearity f."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0792","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":"2026-05-18T02:54:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0isyvBP06IesvW4XY7FND2s9irsuK2nja/YqF+L5MHI53qkGifHgZQumYLjTX6TXozyrhAQh5WHpOTzsT0ZGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:16:24.511193Z"},"content_sha256":"ff2128c79bd8f55bb540af24f46a04eb3149bcc94cb901edb2611e9c8ad00b87","schema_version":"1.0","event_id":"sha256:ff2128c79bd8f55bb540af24f46a04eb3149bcc94cb901edb2611e9c8ad00b87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKCZMJFAFSIBFLW5ZYUICUVR66/bundle.json","state_url":"https://pith.science/pith/UKCZMJFAFSIBFLW5ZYUICUVR66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKCZMJFAFSIBFLW5ZYUICUVR66/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":"2026-06-26T11:16:24Z","links":{"resolver":"https://pith.science/pith/UKCZMJFAFSIBFLW5ZYUICUVR66","bundle":"https://pith.science/pith/UKCZMJFAFSIBFLW5ZYUICUVR66/bundle.json","state":"https://pith.science/pith/UKCZMJFAFSIBFLW5ZYUICUVR66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKCZMJFAFSIBFLW5ZYUICUVR66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UKCZMJFAFSIBFLW5ZYUICUVR66","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":"9354302f172a1ecf738d2afb54ffa1cfa870736612909a1bcc86665f65e1f28f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-03T07:52:06Z","title_canon_sha256":"b434ef5717aaf275d191947ced4e2b96f4afe12677a83382708d69a3c525dad2"},"schema_version":"1.0","source":{"id":"1404.0792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0792","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0792v1","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0792","created_at":"2026-05-18T02:54:55Z"},{"alias_kind":"pith_short_12","alias_value":"UKCZMJFAFSIB","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UKCZMJFAFSIBFLW5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UKCZMJFA","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:ff2128c79bd8f55bb540af24f46a04eb3149bcc94cb901edb2611e9c8ad00b87","target":"graph","created_at":"2026-05-18T02:54:55Z","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 study a H\\'enon-like equation (see equations (1) below), where the nonlinearity f(t) is not homogeneous (i.e., it is not a power). By minimization on the Nehari manifold, we prove that for large values of the parameter $\\alpha$ there is a breaking of symmetry and non radial solutions appears. This holds for sub- and super-critical growth of the nonlinearity f.","authors_text":"Gianluca Cappa, Marino Badiale","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-03T07:52:06Z","title":"Non radial solutions for non homogeneous H\\'enon equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0792","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":"sha256:9c79f043e295d9d28669b2dd9c3ebdddf5a0390beaa050bcf48bfd9fd8c236ae","target":"record","created_at":"2026-05-18T02:54:55Z","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":"9354302f172a1ecf738d2afb54ffa1cfa870736612909a1bcc86665f65e1f28f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-03T07:52:06Z","title_canon_sha256":"b434ef5717aaf275d191947ced4e2b96f4afe12677a83382708d69a3c525dad2"},"schema_version":"1.0","source":{"id":"1404.0792","kind":"arxiv","version":1}},"canonical_sha256":"a2859624a02c9012aeddce288152b1f78a48413210b5fc50ece986a02e1109c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2859624a02c9012aeddce288152b1f78a48413210b5fc50ece986a02e1109c3","first_computed_at":"2026-05-18T02:54:55.505828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:55.505828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2x8JK89I43zdvbECiZf3qcpsOzQV81MD4FaMLEx+XLjMr2GioykBPf2J/l/dAv7N9xxfnvfUNoyOFXN5KGKrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:55.506365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c79f043e295d9d28669b2dd9c3ebdddf5a0390beaa050bcf48bfd9fd8c236ae","sha256:ff2128c79bd8f55bb540af24f46a04eb3149bcc94cb901edb2611e9c8ad00b87"],"state_sha256":"a84716f24c14f449cd0c9c5101b13162bfb880642f116342464ce5c30d66ecd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wyMXjIvB+gkygvcL84V3U59+ZLFKAouhcv1lUGcuRyTw5bbaNmHx3edRCC6u3NIRb28cSYJs9XeCCrAilFeCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:16:24.513079Z","bundle_sha256":"8d37af0dd0947467235d186d2a38e3a08b692813b9b515231636ffaf3cc3117a"}}