{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IV4N7EDB4YMYBTOWFI2624BVCP","short_pith_number":"pith:IV4N7EDB","schema_version":"1.0","canonical_sha256":"4578df9061e61980cdd62a35ed703513ff00008d15996d6e9a56cd02c8be6200","source":{"kind":"arxiv","id":"2607.28279","version":1},"attestation_state":"computed","paper":{"title":"On Sirakov's equal-frequency uniqueness conjecture","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Hong-Ge Chen, Juncheng Wei, Wen Yang, Yong Liu","submitted_at":"2026-07-30T14:28:43Z","abstract_excerpt":"Let $N\\in\\{2,3\\}$, $0<\\mu _1\\leq\\mu _2$, and $0<\\beta<\\mu _1$. We prove that the equal-frequency two-component cubic Schr\\\"odinger system \\[\n  -\\Delta u+u=\\mu _1u^3+\\beta uv^2,\n  \\qquad\n  -\\Delta v+v=\\mu _2v^3+\\beta u^2v\n  \\quad\\text{in }\\mathbb{R}^N \\] has exactly one positive solution in $H^1(\\mathbb{R}^N)\\times H^1(\\mathbb{R}^N)$ modulo simultaneous translations. More precisely, every positive solution is a simultaneous translate of the synchronized state constructed from the unique positive radial solution of $-\\Delta w+w=w^3$ in $\\mathbb{R}^N$. This settles Sirakov's equal-frequency uniqu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.28279","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-30T14:28:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b94ad3b7a297f524084df4629e8f77964fd7cb4726cfefcaba5327abcb4e7c98","abstract_canon_sha256":"54981d1baa6f9c3a932f61a6b9d3898a9795e278969095d426234a8854f3deec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4578df9061e61980cdd62a35ed703513ff00008d15996d6e9a56cd02c8be6200","last_reissued_at":"2026-07-31T01:37:08.034456Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:37:08.034456Z"},"graph_snapshot":{"paper":{"title":"On Sirakov's equal-frequency uniqueness conjecture","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Hong-Ge Chen, Juncheng Wei, Wen Yang, Yong Liu","submitted_at":"2026-07-30T14:28:43Z","abstract_excerpt":"Let $N\\in\\{2,3\\}$, $0<\\mu _1\\leq\\mu _2$, and $0<\\beta<\\mu _1$. We prove that the equal-frequency two-component cubic Schr\\\"odinger system \\[\n  -\\Delta u+u=\\mu _1u^3+\\beta uv^2,\n  \\qquad\n  -\\Delta v+v=\\mu _2v^3+\\beta u^2v\n  \\quad\\text{in }\\mathbb{R}^N \\] has exactly one positive solution in $H^1(\\mathbb{R}^N)\\times H^1(\\mathbb{R}^N)$ modulo simultaneous translations. More precisely, every positive solution is a simultaneous translate of the synchronized state constructed from the unique positive radial solution of $-\\Delta w+w=w^3$ in $\\mathbb{R}^N$. This settles Sirakov's equal-frequency uniqu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28279","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/2607.28279/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.28279","created_at":"2026-07-31T01:37:08.037590+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.28279v1","created_at":"2026-07-31T01:37:08.037590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28279","created_at":"2026-07-31T01:37:08.037590+00:00"},{"alias_kind":"pith_short_12","alias_value":"IV4N7EDB4YMY","created_at":"2026-07-31T01:37:08.037590+00:00"},{"alias_kind":"pith_short_16","alias_value":"IV4N7EDB4YMYBTOW","created_at":"2026-07-31T01:37:08.037590+00:00"},{"alias_kind":"pith_short_8","alias_value":"IV4N7EDB","created_at":"2026-07-31T01:37:08.037590+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP","json":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP.json","graph_json":"https://pith.science/api/pith-number/IV4N7EDB4YMYBTOWFI2624BVCP/graph.json","events_json":"https://pith.science/api/pith-number/IV4N7EDB4YMYBTOWFI2624BVCP/events.json","paper":"https://pith.science/paper/IV4N7EDB"},"agent_actions":{"view_html":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP","download_json":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP.json","view_paper":"https://pith.science/paper/IV4N7EDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.28279&json=true","fetch_graph":"https://pith.science/api/pith-number/IV4N7EDB4YMYBTOWFI2624BVCP/graph.json","fetch_events":"https://pith.science/api/pith-number/IV4N7EDB4YMYBTOWFI2624BVCP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP/action/storage_attestation","attest_author":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP/action/author_attestation","sign_citation":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP/action/citation_signature","submit_replication":"https://pith.science/pith/IV4N7EDB4YMYBTOWFI2624BVCP/action/replication_record"}},"created_at":"2026-07-31T01:37:08.037590+00:00","updated_at":"2026-07-31T01:37:08.037590+00:00"}