{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:EQ3K74SBOA743MOXEAIY3J6CST","short_pith_number":"pith:EQ3K74SB","canonical_record":{"source":{"id":"2212.14873","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-30T18:39:51Z","cross_cats_sorted":[],"title_canon_sha256":"3018e61f5d81a38b01f2bc11db56382b43237fd09a884091d7ecc78eeda3d174","abstract_canon_sha256":"a571d335f9a0758eee4b5dd57e52fa464bd889b955f41d9c3fbcbdf4f5f674dd"},"schema_version":"1.0"},"canonical_sha256":"2436aff241703fcdb1d720118da7c294e2970ff4575edcc8abf4c7960a7c4629","source":{"kind":"arxiv","id":"2212.14873","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.14873","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"2212.14873v3","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.14873","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"EQ3K74SBOA74","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"pith_short_16","alias_value":"EQ3K74SBOA743MOX","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"pith_short_8","alias_value":"EQ3K74SB","created_at":"2026-07-05T05:38:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:EQ3K74SBOA743MOXEAIY3J6CST","target":"record","payload":{"canonical_record":{"source":{"id":"2212.14873","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-30T18:39:51Z","cross_cats_sorted":[],"title_canon_sha256":"3018e61f5d81a38b01f2bc11db56382b43237fd09a884091d7ecc78eeda3d174","abstract_canon_sha256":"a571d335f9a0758eee4b5dd57e52fa464bd889b955f41d9c3fbcbdf4f5f674dd"},"schema_version":"1.0"},"canonical_sha256":"2436aff241703fcdb1d720118da7c294e2970ff4575edcc8abf4c7960a7c4629","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:30.518068Z","signature_b64":"NSU5s4HWmns+2Is3q2TaeKFW3M2IrBy3dwRkRUkJPYu1t/GZ2WQh+JPh6t4s6c6xdf9og3nz8SpFGlEkThDqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2436aff241703fcdb1d720118da7c294e2970ff4575edcc8abf4c7960a7c4629","last_reissued_at":"2026-07-05T05:38:30.517641Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:30.517641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.14873","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qklKtFqjutlmkFF0FdyJJFtERxXFu1/vfmJFLmJ+ZIzC7itj9vf21316wA1MJkgpaKrDQDg4XWPi40Slzra6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T09:18:45.842819Z"},"content_sha256":"a4f9fe683d1e6be04ca249242cef35d0b864d95f8d969e0db4c3367061c3b921","schema_version":"1.0","event_id":"sha256:a4f9fe683d1e6be04ca249242cef35d0b864d95f8d969e0db4c3367061c3b921"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:EQ3K74SBOA743MOXEAIY3J6CST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normalized solutions to a class of $(2,q)$-Laplacian equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laura Baldelli, Tao Yang","submitted_at":"2022-12-30T18:39:51Z","abstract_excerpt":"This paper concerns the existence of normalized solutions to a class of $(2,q)$-Laplacian equations in all the possible cases according to the value of $p$ with respect to the critical exponent $2(1+2/N)$. In the $L^2$-subcritical case, we study a global minimization problem and obtain a ground state solution. While in the $L^2$-critical case, we prove several nonexistence results, extended also in the $L^q$-critical case. At last, we derive a ground state and infinitely many radial solutions in the $L^2$-supercritical case. Compared with the classical Schr\\\"{o}dinger equation, the $(2,q)$-Lap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14873","kind":"arxiv","version":3},"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/2212.14873/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":"2026-07-05T05:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/F3r6cxiXJdyDp3YOTcd9JhUqMfwa3Y0+JOjvKihoGJPuige4p2CXjDL3JssmC2EwHZbht9HgGSHE6TA2JJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T09:18:45.843184Z"},"content_sha256":"fd15c25611acb64ab7a2ec70f94ab64778e2d40923e4c23fdef7dcc90db72475","schema_version":"1.0","event_id":"sha256:fd15c25611acb64ab7a2ec70f94ab64778e2d40923e4c23fdef7dcc90db72475"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQ3K74SBOA743MOXEAIY3J6CST/bundle.json","state_url":"https://pith.science/pith/EQ3K74SBOA743MOXEAIY3J6CST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQ3K74SBOA743MOXEAIY3J6CST/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":"2026-08-20T09:18:45Z","links":{"resolver":"https://pith.science/pith/EQ3K74SBOA743MOXEAIY3J6CST","bundle":"https://pith.science/pith/EQ3K74SBOA743MOXEAIY3J6CST/bundle.json","state":"https://pith.science/pith/EQ3K74SBOA743MOXEAIY3J6CST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQ3K74SBOA743MOXEAIY3J6CST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EQ3K74SBOA743MOXEAIY3J6CST","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":"a571d335f9a0758eee4b5dd57e52fa464bd889b955f41d9c3fbcbdf4f5f674dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-30T18:39:51Z","title_canon_sha256":"3018e61f5d81a38b01f2bc11db56382b43237fd09a884091d7ecc78eeda3d174"},"schema_version":"1.0","source":{"id":"2212.14873","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.14873","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"2212.14873v3","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.14873","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"EQ3K74SBOA74","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"pith_short_16","alias_value":"EQ3K74SBOA743MOX","created_at":"2026-07-05T05:38:30Z"},{"alias_kind":"pith_short_8","alias_value":"EQ3K74SB","created_at":"2026-07-05T05:38:30Z"}],"graph_snapshots":[{"event_id":"sha256:fd15c25611acb64ab7a2ec70f94ab64778e2d40923e4c23fdef7dcc90db72475","target":"graph","created_at":"2026-07-05T05:38:30Z","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/2212.14873/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper concerns the existence of normalized solutions to a class of $(2,q)$-Laplacian equations in all the possible cases according to the value of $p$ with respect to the critical exponent $2(1+2/N)$. In the $L^2$-subcritical case, we study a global minimization problem and obtain a ground state solution. While in the $L^2$-critical case, we prove several nonexistence results, extended also in the $L^q$-critical case. At last, we derive a ground state and infinitely many radial solutions in the $L^2$-supercritical case. Compared with the classical Schr\\\"{o}dinger equation, the $(2,q)$-Lap","authors_text":"Laura Baldelli, Tao Yang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-30T18:39:51Z","title":"Normalized solutions to a class of $(2,q)$-Laplacian equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14873","kind":"arxiv","version":3},"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:a4f9fe683d1e6be04ca249242cef35d0b864d95f8d969e0db4c3367061c3b921","target":"record","created_at":"2026-07-05T05:38:30Z","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":"a571d335f9a0758eee4b5dd57e52fa464bd889b955f41d9c3fbcbdf4f5f674dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-30T18:39:51Z","title_canon_sha256":"3018e61f5d81a38b01f2bc11db56382b43237fd09a884091d7ecc78eeda3d174"},"schema_version":"1.0","source":{"id":"2212.14873","kind":"arxiv","version":3}},"canonical_sha256":"2436aff241703fcdb1d720118da7c294e2970ff4575edcc8abf4c7960a7c4629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2436aff241703fcdb1d720118da7c294e2970ff4575edcc8abf4c7960a7c4629","first_computed_at":"2026-07-05T05:38:30.517641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:38:30.517641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NSU5s4HWmns+2Is3q2TaeKFW3M2IrBy3dwRkRUkJPYu1t/GZ2WQh+JPh6t4s6c6xdf9og3nz8SpFGlEkThDqDA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:38:30.518068Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.14873","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f9fe683d1e6be04ca249242cef35d0b864d95f8d969e0db4c3367061c3b921","sha256:fd15c25611acb64ab7a2ec70f94ab64778e2d40923e4c23fdef7dcc90db72475"],"state_sha256":"85e6add5156cffe25ed0976656e9dc1181987b0bc4431de4695684a20b1dbf42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqQM7dY5pUfWxYFjL3WPPSK8JEM+mfy71xq6p5NErdbeba+SMBsJ8dslQUPUNe5BZNFGQPujLnTVwhBOlKE+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T09:18:45.846276Z","bundle_sha256":"f87dd15c11980925529539e429f15b9b69c8e7b966cd44078e0be207348e14bf"}}