{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BPTBVWJUQGNUFF6DAN5HDS2LZG","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":"c4fcfea4af4a90c22e93835e1bc0b5ffb3bb1c663e9dc538051e1c6d8e954ded","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-12T04:54:46Z","title_canon_sha256":"1c71e6c3518612d52acd7ff131b90ddd8a8738d7355c457020c14ec5f6b49186"},"schema_version":"1.0","source":{"id":"1909.05453","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.05453","created_at":"2026-07-05T05:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1909.05453v3","created_at":"2026-07-05T05:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.05453","created_at":"2026-07-05T05:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"BPTBVWJUQGNU","created_at":"2026-07-05T05:28:40Z"},{"alias_kind":"pith_short_16","alias_value":"BPTBVWJUQGNUFF6D","created_at":"2026-07-05T05:28:40Z"},{"alias_kind":"pith_short_8","alias_value":"BPTBVWJU","created_at":"2026-07-05T05:28:40Z"}],"graph_snapshots":[{"event_id":"sha256:c2171b948e33e2be96df1e6084279569ae5a8e033312271f631d0878c64dd48a","target":"graph","created_at":"2026-07-05T05:28:40Z","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/1909.05453/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Tianxiang Gou, Zhitao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-12T04:54:46Z","title":"Concentration Phenomenon of Semiclassical States to Reaction-Diffusion Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.05453","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":"sha256:45c90b2e09420d4d6ffe41342941adc64d74c1222a8fb64b33c16bd999f38936","target":"record","created_at":"2026-07-05T05:28:40Z","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":"c4fcfea4af4a90c22e93835e1bc0b5ffb3bb1c663e9dc538051e1c6d8e954ded","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-12T04:54:46Z","title_canon_sha256":"1c71e6c3518612d52acd7ff131b90ddd8a8738d7355c457020c14ec5f6b49186"},"schema_version":"1.0","source":{"id":"1909.05453","kind":"arxiv","version":3}},"canonical_sha256":"0be61ad934819b4297c3037a71cb4bc9be5049fa19ac1b20f5bf1a6aad4aff65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0be61ad934819b4297c3037a71cb4bc9be5049fa19ac1b20f5bf1a6aad4aff65","first_computed_at":"2026-07-05T05:28:40.325913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:28:40.325913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERxmDz16gzjfJ+uoyt8roIBF8vzhzNzwA3i7zStBmGOWD0/Oa69rEOtrRx9Tvah2urcdkNh1da/J50zNG3wdBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:28:40.326304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.05453","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45c90b2e09420d4d6ffe41342941adc64d74c1222a8fb64b33c16bd999f38936","sha256:c2171b948e33e2be96df1e6084279569ae5a8e033312271f631d0878c64dd48a"],"state_sha256":"8f7108e78cede5b5e406950c947299365da2052b21c1dd259a8c8d54c372428b"}