{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:V4FPLWEDN776CBSYESROUOIJD6","short_pith_number":"pith:V4FPLWED","canonical_record":{"source":{"id":"1910.13177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-29T10:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"bdae5fd04d3fd0c151dd5aa0d4157a12b92619bdfb3e7540ad0d17b65e40dcd1","abstract_canon_sha256":"36320dd3609709630a1275cbc90e6fa18a79f2f7f555bef3472a0e2f6560d4b3"},"schema_version":"1.0"},"canonical_sha256":"af0af5d8836fffe1065824a2ea39091fb7fbc0fe7f77a3425cddf1901c8da25e","source":{"kind":"arxiv","id":"1910.13177","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.13177","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1910.13177v2","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.13177","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"V4FPLWEDN776","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"pith_short_16","alias_value":"V4FPLWEDN776CBSY","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"pith_short_8","alias_value":"V4FPLWED","created_at":"2026-07-05T01:59:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:V4FPLWEDN776CBSYESROUOIJD6","target":"record","payload":{"canonical_record":{"source":{"id":"1910.13177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-29T10:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"bdae5fd04d3fd0c151dd5aa0d4157a12b92619bdfb3e7540ad0d17b65e40dcd1","abstract_canon_sha256":"36320dd3609709630a1275cbc90e6fa18a79f2f7f555bef3472a0e2f6560d4b3"},"schema_version":"1.0"},"canonical_sha256":"af0af5d8836fffe1065824a2ea39091fb7fbc0fe7f77a3425cddf1901c8da25e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:59:26.882125Z","signature_b64":"HYeFuNZhfz8RhddS2iAx+pYw79iLVUdeivn8xqKE9f3nDCmOwO7QgKtzgM1l1bcEd8zN9KeHln3l7gTEldkVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af0af5d8836fffe1065824a2ea39091fb7fbc0fe7f77a3425cddf1901c8da25e","last_reissued_at":"2026-07-05T01:59:26.881664Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:59:26.881664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.13177","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":"2026-07-05T01:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gnMi8kEIGZwSAyuRq7NW+TnE9gwjYMtPxMC0SaoFJnjk5/7l+S/uTvKKIdKAXpVEwwW7xW6+TP1/5UbHoY9OCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:29:53.401551Z"},"content_sha256":"d24bbf142751ee74fe5d25314a2f65a43f4d07e7d792f325c0ffc8a4475b6456","schema_version":"1.0","event_id":"sha256:d24bbf142751ee74fe5d25314a2f65a43f4d07e7d792f325c0ffc8a4475b6456"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:V4FPLWEDN776CBSYESROUOIJD6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some remarks on a minimization problem associated to a fourth order nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio J. Fern\\'andez, Louis Jeanjean, Nabile Boussa\\\"id","submitted_at":"2019-10-29T10:29:23Z","abstract_excerpt":"Let $\\gamma > 0\\,$, $\\beta > 0\\,$, $\\alpha > 0$ and $0 < \\sigma N < 4$. In the present paper, we study, for $c > 0$ given, the constrained minimization problem \\begin{equation*} \\label{MinL2fixed} m(c):=\\inf_{u\\in S (c) }E(u), \\end{equation*} where \\begin{equation*} E (u):=\\frac{\\gamma}{2}\\int_{\\mathbb{R}^N}|\\Delta u|^2\\, dx -\\frac{\\beta}{2}\\int_{\\mathbb{R}^N}|\\nabla u|^2\\, dx-\\frac{\\alpha}{2\\sigma+2}\\int_{\\mathbb{R}^N}|u|^{2\\sigma+2}\\, dx, \\end{equation*} and \\begin{equation*} S(c):=\\left\\{u\\in H^2(\\mathbb{R}^N):\\int_{\\mathbb{R}^N}|u|^{2}\\, dx=c\\right\\}. \\end{equation*} The aim of our study i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.13177","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.13177/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F7dymJbQ68kjdtb6MWatTQ7Hj4+o+BMUzBlVhkjh2/Rz7XScycSM6CiNcgBPHlzhHLQRYpNS4QWX9P+b3Og3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:29:53.401901Z"},"content_sha256":"bda09dd582a5d29cbb4a8e8290ab8b62b7ea8a0ab90d1b828506ef5752cfa758","schema_version":"1.0","event_id":"sha256:bda09dd582a5d29cbb4a8e8290ab8b62b7ea8a0ab90d1b828506ef5752cfa758"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4FPLWEDN776CBSYESROUOIJD6/bundle.json","state_url":"https://pith.science/pith/V4FPLWEDN776CBSYESROUOIJD6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4FPLWEDN776CBSYESROUOIJD6/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":"2026-08-19T10:29:53Z","links":{"resolver":"https://pith.science/pith/V4FPLWEDN776CBSYESROUOIJD6","bundle":"https://pith.science/pith/V4FPLWEDN776CBSYESROUOIJD6/bundle.json","state":"https://pith.science/pith/V4FPLWEDN776CBSYESROUOIJD6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4FPLWEDN776CBSYESROUOIJD6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:V4FPLWEDN776CBSYESROUOIJD6","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":"36320dd3609709630a1275cbc90e6fa18a79f2f7f555bef3472a0e2f6560d4b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-29T10:29:23Z","title_canon_sha256":"bdae5fd04d3fd0c151dd5aa0d4157a12b92619bdfb3e7540ad0d17b65e40dcd1"},"schema_version":"1.0","source":{"id":"1910.13177","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.13177","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1910.13177v2","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.13177","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"V4FPLWEDN776","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"pith_short_16","alias_value":"V4FPLWEDN776CBSY","created_at":"2026-07-05T01:59:26Z"},{"alias_kind":"pith_short_8","alias_value":"V4FPLWED","created_at":"2026-07-05T01:59:26Z"}],"graph_snapshots":[{"event_id":"sha256:bda09dd582a5d29cbb4a8e8290ab8b62b7ea8a0ab90d1b828506ef5752cfa758","target":"graph","created_at":"2026-07-05T01:59:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.13177/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\gamma > 0\\,$, $\\beta > 0\\,$, $\\alpha > 0$ and $0 < \\sigma N < 4$. In the present paper, we study, for $c > 0$ given, the constrained minimization problem \\begin{equation*} \\label{MinL2fixed} m(c):=\\inf_{u\\in S (c) }E(u), \\end{equation*} where \\begin{equation*} E (u):=\\frac{\\gamma}{2}\\int_{\\mathbb{R}^N}|\\Delta u|^2\\, dx -\\frac{\\beta}{2}\\int_{\\mathbb{R}^N}|\\nabla u|^2\\, dx-\\frac{\\alpha}{2\\sigma+2}\\int_{\\mathbb{R}^N}|u|^{2\\sigma+2}\\, dx, \\end{equation*} and \\begin{equation*} S(c):=\\left\\{u\\in H^2(\\mathbb{R}^N):\\int_{\\mathbb{R}^N}|u|^{2}\\, dx=c\\right\\}. \\end{equation*} The aim of our study i","authors_text":"Antonio J. Fern\\'andez, Louis Jeanjean, Nabile Boussa\\\"id","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-29T10:29:23Z","title":"Some remarks on a minimization problem associated to a fourth order nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.13177","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:d24bbf142751ee74fe5d25314a2f65a43f4d07e7d792f325c0ffc8a4475b6456","target":"record","created_at":"2026-07-05T01:59:26Z","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":"36320dd3609709630a1275cbc90e6fa18a79f2f7f555bef3472a0e2f6560d4b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-29T10:29:23Z","title_canon_sha256":"bdae5fd04d3fd0c151dd5aa0d4157a12b92619bdfb3e7540ad0d17b65e40dcd1"},"schema_version":"1.0","source":{"id":"1910.13177","kind":"arxiv","version":2}},"canonical_sha256":"af0af5d8836fffe1065824a2ea39091fb7fbc0fe7f77a3425cddf1901c8da25e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af0af5d8836fffe1065824a2ea39091fb7fbc0fe7f77a3425cddf1901c8da25e","first_computed_at":"2026-07-05T01:59:26.881664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:59:26.881664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYeFuNZhfz8RhddS2iAx+pYw79iLVUdeivn8xqKE9f3nDCmOwO7QgKtzgM1l1bcEd8zN9KeHln3l7gTEldkVCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:59:26.882125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.13177","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d24bbf142751ee74fe5d25314a2f65a43f4d07e7d792f325c0ffc8a4475b6456","sha256:bda09dd582a5d29cbb4a8e8290ab8b62b7ea8a0ab90d1b828506ef5752cfa758"],"state_sha256":"20f564ba0cd4afe210248f250bbf586943230d553d951f29736d789622f93513"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99woAziiMvcY/xLYskhQiF9I+I3uDb43cTEJeIQsAz3LVoAFVkUCJAtmUa9t6Qhxo5TR6HVD31dG9B2fGJYaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T10:29:53.405044Z","bundle_sha256":"8afeb9916ca207e7f18de772410d4239fcc7ccad049ab8d8d03a1a7ffde62fdf"}}