{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BPTBVWJUQGNUFF6DAN5HDS2LZG","short_pith_number":"pith:BPTBVWJU","schema_version":"1.0","canonical_sha256":"0be61ad934819b4297c3037a71cb4bc9be5049fa19ac1b20f5bf1a6aad4aff65","source":{"kind":"arxiv","id":"1909.05453","version":3},"attestation_state":"computed","paper":{"title":"Concentration Phenomenon of Semiclassical States to Reaction-Diffusion Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tianxiang Gou, Zhitao Zhang","submitted_at":"2019-09-12T04:54:46Z","abstract_excerpt":"In this paper, we consider concentration phenomenon of semiclassical states to the following $2M$-component reaction-diffusion system in $\\R \\times \\R^N$, \\begin{align*} \\left\\{ \\begin{aligned} \\partial_t u &=\\eps^2 \\Delta_x u-u-V(x)v + \\partial_v H(u, v),\\\\ \\partial_t v &=-\\eps^2 \\Delta_x v+v + V(x)u - \\partial_u H(u, v), \\end{aligned} \\right. \\end{align*} where $M \\geq 1$, $N \\geq 1$, $\\eps>0$ is a small parameter, $V \\in C^1(\\R^N, \\, \\R)$, $H \\in C^1(\\R^M \\times \\R^M, \\, \\R)$ and $(u, v): \\R \\times \\R^N \\to \\R^M \\times \\R^M$. It is proved that there exist semiclassical states concentrating "},"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":"1909.05453","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-12T04:54:46Z","cross_cats_sorted":[],"title_canon_sha256":"1c71e6c3518612d52acd7ff131b90ddd8a8738d7355c457020c14ec5f6b49186","abstract_canon_sha256":"c4fcfea4af4a90c22e93835e1bc0b5ffb3bb1c663e9dc538051e1c6d8e954ded"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:28:40.326304Z","signature_b64":"ERxmDz16gzjfJ+uoyt8roIBF8vzhzNzwA3i7zStBmGOWD0/Oa69rEOtrRx9Tvah2urcdkNh1da/J50zNG3wdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0be61ad934819b4297c3037a71cb4bc9be5049fa19ac1b20f5bf1a6aad4aff65","last_reissued_at":"2026-07-05T05:28:40.325913Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:28:40.325913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration Phenomenon of Semiclassical States to Reaction-Diffusion Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tianxiang Gou, Zhitao Zhang","submitted_at":"2019-09-12T04:54:46Z","abstract_excerpt":"In this paper, we consider concentration phenomenon of semiclassical states to the following $2M$-component reaction-diffusion system in $\\R \\times \\R^N$, \\begin{align*} \\left\\{ \\begin{aligned} \\partial_t u &=\\eps^2 \\Delta_x u-u-V(x)v + \\partial_v H(u, v),\\\\ \\partial_t v &=-\\eps^2 \\Delta_x v+v + V(x)u - \\partial_u H(u, v), \\end{aligned} \\right. \\end{align*} where $M \\geq 1$, $N \\geq 1$, $\\eps>0$ is a small parameter, $V \\in C^1(\\R^N, \\, \\R)$, $H \\in C^1(\\R^M \\times \\R^M, \\, \\R)$ and $(u, v): \\R \\times \\R^N \\to \\R^M \\times \\R^M$. It is proved that there exist semiclassical states concentrating "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.05453","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/1909.05453/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":"1909.05453","created_at":"2026-07-05T05:28:40.325965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.05453v3","created_at":"2026-07-05T05:28:40.325965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.05453","created_at":"2026-07-05T05:28:40.325965+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPTBVWJUQGNU","created_at":"2026-07-05T05:28:40.325965+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPTBVWJUQGNUFF6D","created_at":"2026-07-05T05:28:40.325965+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPTBVWJU","created_at":"2026-07-05T05:28:40.325965+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/BPTBVWJUQGNUFF6DAN5HDS2LZG","json":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG.json","graph_json":"https://pith.science/api/pith-number/BPTBVWJUQGNUFF6DAN5HDS2LZG/graph.json","events_json":"https://pith.science/api/pith-number/BPTBVWJUQGNUFF6DAN5HDS2LZG/events.json","paper":"https://pith.science/paper/BPTBVWJU"},"agent_actions":{"view_html":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG","download_json":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG.json","view_paper":"https://pith.science/paper/BPTBVWJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.05453&json=true","fetch_graph":"https://pith.science/api/pith-number/BPTBVWJUQGNUFF6DAN5HDS2LZG/graph.json","fetch_events":"https://pith.science/api/pith-number/BPTBVWJUQGNUFF6DAN5HDS2LZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG/action/storage_attestation","attest_author":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG/action/author_attestation","sign_citation":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG/action/citation_signature","submit_replication":"https://pith.science/pith/BPTBVWJUQGNUFF6DAN5HDS2LZG/action/replication_record"}},"created_at":"2026-07-05T05:28:40.325965+00:00","updated_at":"2026-07-05T05:28:40.325965+00:00"}