{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QD57MUA54ZHUOHUCCKM7GFMDFM","short_pith_number":"pith:QD57MUA5","canonical_record":{"source":{"id":"2506.22152","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-27T12:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"0ae5429138ee766ab9f45fc8369c52c585524089571da08439d4b70460f52a38","abstract_canon_sha256":"ba436155e511f1d7c59c12ff6c72bd6ed6baf6c5713e4b3cae4f4385d2794695"},"schema_version":"1.0"},"canonical_sha256":"80fbf6501de64f471e821299f315832b2462ac1a8ecee8f25df3b6cda1001318","source":{"kind":"arxiv","id":"2506.22152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.22152","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"2506.22152v1","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.22152","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"QD57MUA54ZHU","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"QD57MUA54ZHUOHUC","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"QD57MUA5","created_at":"2026-07-05T11:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QD57MUA54ZHUOHUCCKM7GFMDFM","target":"record","payload":{"canonical_record":{"source":{"id":"2506.22152","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-27T12:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"0ae5429138ee766ab9f45fc8369c52c585524089571da08439d4b70460f52a38","abstract_canon_sha256":"ba436155e511f1d7c59c12ff6c72bd6ed6baf6c5713e4b3cae4f4385d2794695"},"schema_version":"1.0"},"canonical_sha256":"80fbf6501de64f471e821299f315832b2462ac1a8ecee8f25df3b6cda1001318","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:22.732236Z","signature_b64":"JDnsEYQbvORDqSQkUmoVYRECf+buvslPo4QyXmrTzS7/MVy3Fy0yiqEjjhB1xB9PERPuFAKH44Z0XGb2f3k+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80fbf6501de64f471e821299f315832b2462ac1a8ecee8f25df3b6cda1001318","last_reissued_at":"2026-07-05T11:28:22.731724Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:22.731724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.22152","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":"2026-07-05T11:28:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQuJJiNfJvTASmFKV4cgnMsQU8JjfcKqv3w8swUSHrcQ4odHgKRv+xNF0v5nBx65fMce1/iNIsQGdNoNBEg3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:50:41.261735Z"},"content_sha256":"84fa24ce2b272f58888535a3785823c703f60cd63c9af85833e7df152de3c7de","schema_version":"1.0","event_id":"sha256:84fa24ce2b272f58888535a3785823c703f60cd63c9af85833e7df152de3c7de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QD57MUA54ZHUOHUCCKM7GFMDFM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domain: the $L^2$-supercritical case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Linjie Song, Qiaoran Wu, Tianhao Liu, Wenming Zou","submitted_at":"2025-06-27T12:05:27Z","abstract_excerpt":"In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an $m$-coupled elliptic system of the Gross-Pitaevskii type:\n  \\begin{equation}\n  \\left\\{\n  \\begin{aligned}\n  &-\\Delta u_j + \\lambda_j u_j = \\sum_{k=1 }^m\\beta_{kj} u_k^2 u_j, \\quad u_j \\in H_0^1(\\Omega),\n  &\\int_\\Omega u_j^2dx = c_j, \\quad j = 1,2,\\cdots,m.\n  \\end{aligned}\n  \\right.\n  \\end{equation}\n  Here, $\\Omega \\subset \\mathbb{R}^N$ ($N = 3,4$) is a bounded domain. The constants $\\beta_{kj} \\neq 0$ and $c_j > 0$ are prescribed constants, while $\\lambda_1, \\cdots, \\lambda_m$ are unk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22152","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/2506.22152/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":"2026-07-05T11:28:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HJ5OossovqeQMnf+TJxI40+/PBDk3Dc+Gc44dpPGFniOxtC7/toECkRldUX/xn7hjt6LWx5f+/uHi+qL1It6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:50:41.262120Z"},"content_sha256":"363d436e486d0cb353e9b3ed5c42864c8c46ad03856b5a2f6e8a427f3c1191d1","schema_version":"1.0","event_id":"sha256:363d436e486d0cb353e9b3ed5c42864c8c46ad03856b5a2f6e8a427f3c1191d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QD57MUA54ZHUOHUCCKM7GFMDFM/bundle.json","state_url":"https://pith.science/pith/QD57MUA54ZHUOHUCCKM7GFMDFM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QD57MUA54ZHUOHUCCKM7GFMDFM/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":"2026-08-13T14:50:41Z","links":{"resolver":"https://pith.science/pith/QD57MUA54ZHUOHUCCKM7GFMDFM","bundle":"https://pith.science/pith/QD57MUA54ZHUOHUCCKM7GFMDFM/bundle.json","state":"https://pith.science/pith/QD57MUA54ZHUOHUCCKM7GFMDFM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QD57MUA54ZHUOHUCCKM7GFMDFM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QD57MUA54ZHUOHUCCKM7GFMDFM","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":"ba436155e511f1d7c59c12ff6c72bd6ed6baf6c5713e4b3cae4f4385d2794695","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-27T12:05:27Z","title_canon_sha256":"0ae5429138ee766ab9f45fc8369c52c585524089571da08439d4b70460f52a38"},"schema_version":"1.0","source":{"id":"2506.22152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.22152","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"2506.22152v1","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.22152","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"QD57MUA54ZHU","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"QD57MUA54ZHUOHUC","created_at":"2026-07-05T11:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"QD57MUA5","created_at":"2026-07-05T11:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:363d436e486d0cb353e9b3ed5c42864c8c46ad03856b5a2f6e8a427f3c1191d1","target":"graph","created_at":"2026-07-05T11:28:22Z","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/2506.22152/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an $m$-coupled elliptic system of the Gross-Pitaevskii type:\n  \\begin{equation}\n  \\left\\{\n  \\begin{aligned}\n  &-\\Delta u_j + \\lambda_j u_j = \\sum_{k=1 }^m\\beta_{kj} u_k^2 u_j, \\quad u_j \\in H_0^1(\\Omega),\n  &\\int_\\Omega u_j^2dx = c_j, \\quad j = 1,2,\\cdots,m.\n  \\end{aligned}\n  \\right.\n  \\end{equation}\n  Here, $\\Omega \\subset \\mathbb{R}^N$ ($N = 3,4$) is a bounded domain. The constants $\\beta_{kj} \\neq 0$ and $c_j > 0$ are prescribed constants, while $\\lambda_1, \\cdots, \\lambda_m$ are unk","authors_text":"Linjie Song, Qiaoran Wu, Tianhao Liu, Wenming Zou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-27T12:05:27Z","title":"Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domain: the $L^2$-supercritical case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22152","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":"sha256:84fa24ce2b272f58888535a3785823c703f60cd63c9af85833e7df152de3c7de","target":"record","created_at":"2026-07-05T11:28:22Z","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":"ba436155e511f1d7c59c12ff6c72bd6ed6baf6c5713e4b3cae4f4385d2794695","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-27T12:05:27Z","title_canon_sha256":"0ae5429138ee766ab9f45fc8369c52c585524089571da08439d4b70460f52a38"},"schema_version":"1.0","source":{"id":"2506.22152","kind":"arxiv","version":1}},"canonical_sha256":"80fbf6501de64f471e821299f315832b2462ac1a8ecee8f25df3b6cda1001318","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80fbf6501de64f471e821299f315832b2462ac1a8ecee8f25df3b6cda1001318","first_computed_at":"2026-07-05T11:28:22.731724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:22.731724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JDnsEYQbvORDqSQkUmoVYRECf+buvslPo4QyXmrTzS7/MVy3Fy0yiqEjjhB1xB9PERPuFAKH44Z0XGb2f3k+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:22.732236Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.22152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84fa24ce2b272f58888535a3785823c703f60cd63c9af85833e7df152de3c7de","sha256:363d436e486d0cb353e9b3ed5c42864c8c46ad03856b5a2f6e8a427f3c1191d1"],"state_sha256":"408be7d90ede3c10e27e5064580770a014f768b7d3db4a436b7709ed4b39f63c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tULOPVEEUvNhgvYrGBwTpPwd/O5W54RkQ+jnJbIaWwONN6gVpogReUBqdlapRjBVDX1IPol+8NEBvgWUI357DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T14:50:41.264668Z","bundle_sha256":"a40b5bc523fc31d5f956d74f23e3c11be5a5255d98163406e1289a75b69137af"}}