{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3SOMF6UP5HWF4MJSH27OAIY3F3","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":"8d02446807027606803e0fb275a0024ea055032c4f15fcad3c163d386e9c4dea","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T15:02:54Z","title_canon_sha256":"a0958d6935b03281155c21bb690ffab96601481c951f67af86917adc73aa1eda"},"schema_version":"1.0","source":{"id":"2605.19946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19946","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19946v1","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19946","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"3SOMF6UP5HWF","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_16","alias_value":"3SOMF6UP5HWF4MJS","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_8","alias_value":"3SOMF6UP","created_at":"2026-05-20T02:05:56Z"}],"graph_snapshots":[{"event_id":"sha256:9b2b8f320327dfff0c6f0081a4ec30f590ba08bc3918ec45855decd43f457821","target":"graph","created_at":"2026-05-20T02:05:56Z","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/2605.19946/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate normalized groundstates for mixed $(p,2)$-Laplacian equations \\begin{align*}\n  \\begin{cases}\n  -\\Delta_p u-\\Delta u+\\lambda u=f(u) & \\text{in } \\mathbb{R}^2,\n  \\displaystyle \\int_{\\mathbb{R}^2}|u|^2\\,\\mathrm{d}x=m,\n  u\\in H^1(\\mathbb{R}^2)\\cap D^{1,p}(\\mathbb{R}^2),\n  \\end{cases} \\end{align*} where $\\Delta_p$ denotes the $p$-Laplacian with $1<p<2$, $\\lambda\\in\\mathbb{R}$ represents a Lagrange multiplier and the nonlinerity $f$ exhibits exponential critical growth. Compared to the single-Laplacian case, the lack of regularity here precludes the Pohozaev identity, and the exponent","authors_text":"Chao Zhong, Jiankang Xia","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T15:02:54Z","title":"Normalized groundstates for mixed $(p,2)$-Laplacian equations in $\\mathbb R^2$ with exponential critical growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19946","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":"sha256:958a3634ca2524adcfe5d40b3baa10f2a8b3e11d2f38ac08ca3337997deb2510","target":"record","created_at":"2026-05-20T02:05:56Z","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":"8d02446807027606803e0fb275a0024ea055032c4f15fcad3c163d386e9c4dea","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T15:02:54Z","title_canon_sha256":"a0958d6935b03281155c21bb690ffab96601481c951f67af86917adc73aa1eda"},"schema_version":"1.0","source":{"id":"2605.19946","kind":"arxiv","version":1}},"canonical_sha256":"dc9cc2fa8fe9ec5e31323ebee0231b2ecac71c861e3264b5418008b8f429dd58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc9cc2fa8fe9ec5e31323ebee0231b2ecac71c861e3264b5418008b8f429dd58","first_computed_at":"2026-05-20T02:05:56.480779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T02:05:56.480779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"98ebYHZ7h9Ir65+KNr7L69ksThxO8G7H9j95R4uUSeSMGpHtHwfrdbObw2KR9CGmnVh3CmAMF5ohBompccbkDQ==","signature_status":"signed_v1","signed_at":"2026-05-20T02:05:56.481502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:958a3634ca2524adcfe5d40b3baa10f2a8b3e11d2f38ac08ca3337997deb2510","sha256:9b2b8f320327dfff0c6f0081a4ec30f590ba08bc3918ec45855decd43f457821"],"state_sha256":"c4df3be68435c180f8efb655b3ac02e7131c8607bdeba86b370ed2b1bf4677a1"}