{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WYSPW75PWQFRVGBMXJYMTVXWJW","short_pith_number":"pith:WYSPW75P","schema_version":"1.0","canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","source":{"kind":"arxiv","id":"1303.4521","version":1},"attestation_state":"computed","paper":{"title":"Minimal energy solutions for repulsive nonlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2013-03-19T09:21:59Z","abstract_excerpt":"In this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear Schr\\\"odinger system\n  \\begin{align*}\n  \\begin{gathered}\n  -\\Delta u + \\, u = |u|^{2q-2}u + b|u|^{q-2}u|v|^q \\quad\\text{in}\\R^n,\n  -\\Delta v + \\omega^2 v = |v|^{2q-2}v + b|u|^q|v|^{q-2}v\\quad\\text{in}\\R^n.\n  \\end{gathered}\n  \\end{align*}\n  We consider the repulsive case $b<0$ and assume that the exponent $q$ satisfies $1<q<\\frac{n}{n-2}$ in case $n\\geq 3$ and $1<q<\\infty$ in case $n=1$ or $n=2$. For space dimensions $n\\geq 2$ and arbitrary $b<0$ we prove the exist"},"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":"1303.4521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-19T09:21:59Z","cross_cats_sorted":[],"title_canon_sha256":"9b0e3a60544598b799959d562c5234e27472efe0305d5d98a0dcd5ede539751e","abstract_canon_sha256":"e14030d60e27dfe97672d9ff598ff95ff9f38f9e2b318ae08192b95367df6b9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:26.900460Z","signature_b64":"Wxl/WG8H7g+wXfpUXyblbPWyJkhlOnN0U4mtxZMeWlq+gZ/RAhM1cDwwBrGZL08fNueQtPAkCOl0QnGiFrP7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","last_reissued_at":"2026-05-18T03:30:26.899722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:26.899722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal energy solutions for repulsive nonlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2013-03-19T09:21:59Z","abstract_excerpt":"In this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear Schr\\\"odinger system\n  \\begin{align*}\n  \\begin{gathered}\n  -\\Delta u + \\, u = |u|^{2q-2}u + b|u|^{q-2}u|v|^q \\quad\\text{in}\\R^n,\n  -\\Delta v + \\omega^2 v = |v|^{2q-2}v + b|u|^q|v|^{q-2}v\\quad\\text{in}\\R^n.\n  \\end{gathered}\n  \\end{align*}\n  We consider the repulsive case $b<0$ and assume that the exponent $q$ satisfies $1<q<\\frac{n}{n-2}$ in case $n\\geq 3$ and $1<q<\\infty$ in case $n=1$ or $n=2$. For space dimensions $n\\geq 2$ and arbitrary $b<0$ we prove the exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4521","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":""},"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":"1303.4521","created_at":"2026-05-18T03:30:26.899837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4521v1","created_at":"2026-05-18T03:30:26.899837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4521","created_at":"2026-05-18T03:30:26.899837+00:00"},{"alias_kind":"pith_short_12","alias_value":"WYSPW75PWQFR","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"WYSPW75PWQFRVGBM","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"WYSPW75P","created_at":"2026-05-18T12:28:06.772260+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/WYSPW75PWQFRVGBMXJYMTVXWJW","json":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW.json","graph_json":"https://pith.science/api/pith-number/WYSPW75PWQFRVGBMXJYMTVXWJW/graph.json","events_json":"https://pith.science/api/pith-number/WYSPW75PWQFRVGBMXJYMTVXWJW/events.json","paper":"https://pith.science/paper/WYSPW75P"},"agent_actions":{"view_html":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW","download_json":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW.json","view_paper":"https://pith.science/paper/WYSPW75P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4521&json=true","fetch_graph":"https://pith.science/api/pith-number/WYSPW75PWQFRVGBMXJYMTVXWJW/graph.json","fetch_events":"https://pith.science/api/pith-number/WYSPW75PWQFRVGBMXJYMTVXWJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/action/storage_attestation","attest_author":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/action/author_attestation","sign_citation":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/action/citation_signature","submit_replication":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/action/replication_record"}},"created_at":"2026-05-18T03:30:26.899837+00:00","updated_at":"2026-05-18T03:30:26.899837+00:00"}