{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VF2ULDKGP75JSCJUXM26BAVZBN","short_pith_number":"pith:VF2ULDKG","canonical_record":{"source":{"id":"2606.28806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-27T08:19:04Z","cross_cats_sorted":[],"title_canon_sha256":"f43c0a0bfff98a37e7a2fd993d0a835e9197ab0444adc96c42c439dce0a7dab7","abstract_canon_sha256":"eae6631f0b08c0c1b4cde767dbe88e7bfa68b900c4b059ba66f88b51f96f760d"},"schema_version":"1.0"},"canonical_sha256":"a975458d467ffa990934bb35e082b90b58aad7a820e3ed8dab80d1eb2dc06d56","source":{"kind":"arxiv","id":"2606.28806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28806","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28806v1","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28806","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"pith_short_12","alias_value":"VF2ULDKGP75J","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"pith_short_16","alias_value":"VF2ULDKGP75JSCJU","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"pith_short_8","alias_value":"VF2ULDKG","created_at":"2026-06-30T01:16:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VF2ULDKGP75JSCJUXM26BAVZBN","target":"record","payload":{"canonical_record":{"source":{"id":"2606.28806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-27T08:19:04Z","cross_cats_sorted":[],"title_canon_sha256":"f43c0a0bfff98a37e7a2fd993d0a835e9197ab0444adc96c42c439dce0a7dab7","abstract_canon_sha256":"eae6631f0b08c0c1b4cde767dbe88e7bfa68b900c4b059ba66f88b51f96f760d"},"schema_version":"1.0"},"canonical_sha256":"a975458d467ffa990934bb35e082b90b58aad7a820e3ed8dab80d1eb2dc06d56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:16:52.752964Z","signature_b64":"ceEXSco15Nmr8i4mnZTbCPwn7hEyc/TvWIBhiCl+n0YYMNAbzKzokfiaObxDvrgIDhS86kKxrtnlkvkKyh96CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a975458d467ffa990934bb35e082b90b58aad7a820e3ed8dab80d1eb2dc06d56","last_reissued_at":"2026-06-30T01:16:52.752486Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:16:52.752486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.28806","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":"2026-06-30T01:16:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mVLI+xpNF7+7FYN2Cg2SUPffKc33tk3ETZbrvsJ1OxAGrjfwkIqrAxHkqPz62ImF65X16ru2k5QXfj6J5qVpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:48:15.984068Z"},"content_sha256":"37553fd0cc29c0b92bc42e2dbcddb88d8d82c72bc1228072770d44bc630cf264","schema_version":"1.0","event_id":"sha256:37553fd0cc29c0b92bc42e2dbcddb88d8d82c72bc1228072770d44bc630cf264"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VF2ULDKGP75JSCJUXM26BAVZBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normalized solutions of quasilinear Schr\\\"odinger equations in the general $L^2$-supercritical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiang Gao, Xiaoyan Zhang","submitted_at":"2026-06-27T08:19:04Z","abstract_excerpt":"This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schr\\\"odinger equation \\begin{equation*} \\begin{aligned}\n  -\\Delta u-u\\Delta u^2 +\\lambda u=h(u) \\quad\\mathrm{in}\\ \\mathbb{R}^{3}, \\end{aligned} \\end{equation*} where $\\lambda$ appears as a Lagrange multiplier, $h$ is a $L^2$-supercritical and Sobolev subcritical nonlinearity. The solutions correspond to critical points of the energy functional subject to the $L^2$-norm constraint $\\int_{\\mathbb{R}^3}|u|^2dx=a^2>0$. Taking into account the Pohozaev manifold and perturbation method, we obtain t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28806","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28806/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":"2026-06-30T01:16:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTTWoEZSeOQy9rJ8WvjqtZ7dY8tLECJG0Qch9CUi0P6KwIeBSYYQRHJEh01UI3FjHHlTYxcJa409zGdXSokxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:48:15.984587Z"},"content_sha256":"66e1eb87e27cf689bf16ba120dad9bd65cf7d21f58cfad9a8027b52fd0765a22","schema_version":"1.0","event_id":"sha256:66e1eb87e27cf689bf16ba120dad9bd65cf7d21f58cfad9a8027b52fd0765a22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VF2ULDKGP75JSCJUXM26BAVZBN/bundle.json","state_url":"https://pith.science/pith/VF2ULDKGP75JSCJUXM26BAVZBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VF2ULDKGP75JSCJUXM26BAVZBN/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":"2026-08-06T13:48:15Z","links":{"resolver":"https://pith.science/pith/VF2ULDKGP75JSCJUXM26BAVZBN","bundle":"https://pith.science/pith/VF2ULDKGP75JSCJUXM26BAVZBN/bundle.json","state":"https://pith.science/pith/VF2ULDKGP75JSCJUXM26BAVZBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VF2ULDKGP75JSCJUXM26BAVZBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VF2ULDKGP75JSCJUXM26BAVZBN","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":"eae6631f0b08c0c1b4cde767dbe88e7bfa68b900c4b059ba66f88b51f96f760d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-27T08:19:04Z","title_canon_sha256":"f43c0a0bfff98a37e7a2fd993d0a835e9197ab0444adc96c42c439dce0a7dab7"},"schema_version":"1.0","source":{"id":"2606.28806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28806","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28806v1","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28806","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"pith_short_12","alias_value":"VF2ULDKGP75J","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"pith_short_16","alias_value":"VF2ULDKGP75JSCJU","created_at":"2026-06-30T01:16:52Z"},{"alias_kind":"pith_short_8","alias_value":"VF2ULDKG","created_at":"2026-06-30T01:16:52Z"}],"graph_snapshots":[{"event_id":"sha256:66e1eb87e27cf689bf16ba120dad9bd65cf7d21f58cfad9a8027b52fd0765a22","target":"graph","created_at":"2026-06-30T01:16:52Z","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/2606.28806/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schr\\\"odinger equation \\begin{equation*} \\begin{aligned}\n  -\\Delta u-u\\Delta u^2 +\\lambda u=h(u) \\quad\\mathrm{in}\\ \\mathbb{R}^{3}, \\end{aligned} \\end{equation*} where $\\lambda$ appears as a Lagrange multiplier, $h$ is a $L^2$-supercritical and Sobolev subcritical nonlinearity. The solutions correspond to critical points of the energy functional subject to the $L^2$-norm constraint $\\int_{\\mathbb{R}^3}|u|^2dx=a^2>0$. Taking into account the Pohozaev manifold and perturbation method, we obtain t","authors_text":"Qiang Gao, Xiaoyan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-27T08:19:04Z","title":"Normalized solutions of quasilinear Schr\\\"odinger equations in the general $L^2$-supercritical case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28806","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":"sha256:37553fd0cc29c0b92bc42e2dbcddb88d8d82c72bc1228072770d44bc630cf264","target":"record","created_at":"2026-06-30T01:16:52Z","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":"eae6631f0b08c0c1b4cde767dbe88e7bfa68b900c4b059ba66f88b51f96f760d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-27T08:19:04Z","title_canon_sha256":"f43c0a0bfff98a37e7a2fd993d0a835e9197ab0444adc96c42c439dce0a7dab7"},"schema_version":"1.0","source":{"id":"2606.28806","kind":"arxiv","version":1}},"canonical_sha256":"a975458d467ffa990934bb35e082b90b58aad7a820e3ed8dab80d1eb2dc06d56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a975458d467ffa990934bb35e082b90b58aad7a820e3ed8dab80d1eb2dc06d56","first_computed_at":"2026-06-30T01:16:52.752486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:16:52.752486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ceEXSco15Nmr8i4mnZTbCPwn7hEyc/TvWIBhiCl+n0YYMNAbzKzokfiaObxDvrgIDhS86kKxrtnlkvkKyh96CQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:16:52.752964Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37553fd0cc29c0b92bc42e2dbcddb88d8d82c72bc1228072770d44bc630cf264","sha256:66e1eb87e27cf689bf16ba120dad9bd65cf7d21f58cfad9a8027b52fd0765a22"],"state_sha256":"2da35ac0edb79193258cf3f6acca00a16b110eba794b3a3e0122f64b45dd32f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NiwPyZixN9PVPAd4h1jCO1oTQnVwwJYXDKee+qqnwfgeicwWASKLINkAxhkb0WE3A9lWyo/7u4bMWZ/YMVEsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:48:16.001460Z","bundle_sha256":"d1f1487c19ff8b404d52cb66f4535d2d9ed648d5e822d9d999873fdf903bf06d"}}