{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TVAFUHQ2LJ2INMAA5TTINJTPVV","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":"bbfd963531bd650e1d740871101276d4c24594aae75537a6542720b126be8a71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-11T16:10:21Z","title_canon_sha256":"cb7da487de78b1ab9507eae800a7b69d65593eb4f7f38ff32e58f0b82e9e8c9b"},"schema_version":"1.0","source":{"id":"2105.05154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.05154","created_at":"2026-07-05T02:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"2105.05154v1","created_at":"2026-07-05T02:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.05154","created_at":"2026-07-05T02:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"TVAFUHQ2LJ2I","created_at":"2026-07-05T02:39:28Z"},{"alias_kind":"pith_short_16","alias_value":"TVAFUHQ2LJ2INMAA","created_at":"2026-07-05T02:39:28Z"},{"alias_kind":"pith_short_8","alias_value":"TVAFUHQ2","created_at":"2026-07-05T02:39:28Z"}],"graph_snapshots":[{"event_id":"sha256:4ea4a457093bdefe87663ae65295c2845e1af2f29ad6107a5dac86603a48ea21","target":"graph","created_at":"2026-07-05T02:39:28Z","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/2105.05154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the 2D delta-Bose gas by a smooth mollification of the delta potential, where the coupling constant is in the critical window. The main result proves that for two particles, the approximate semigroups on $\\mathscr B_b(\\Bbb R^2)$ for the Schr\\\"odinger operator with singular interaction at the origin converge pointwise in the initial condition. This convergence extends earlier functional analytic results for the convergence in the $L_2$-norm resolvent sense. The central methods introduced here apply the excursion theory of the 2D Bessel process and the ergodicity of the winding numbe","authors_text":"Yu-Ting Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-11T16:10:21Z","title":"The critical 2D delta-Bose gas as mixed-order asymptotics of planar Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.05154","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":"sha256:4cd3f044b5470cf20bb6a82767cd7d7a39fbd75ea46fafdb42b6d890f86e5238","target":"record","created_at":"2026-07-05T02:39:28Z","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":"bbfd963531bd650e1d740871101276d4c24594aae75537a6542720b126be8a71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-11T16:10:21Z","title_canon_sha256":"cb7da487de78b1ab9507eae800a7b69d65593eb4f7f38ff32e58f0b82e9e8c9b"},"schema_version":"1.0","source":{"id":"2105.05154","kind":"arxiv","version":1}},"canonical_sha256":"9d405a1e1a5a7486b000ece686a66fad737e1cd44bdd87075fadaeba88e17aae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d405a1e1a5a7486b000ece686a66fad737e1cd44bdd87075fadaeba88e17aae","first_computed_at":"2026-07-05T02:39:28.772374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:39:28.772374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NTLfPxHBgtDeE4C2kB8Iayw3mkv95ZZaKVdX2NE2hlGknjrgWTHW2ujtlkzey9AeFJ9/0jhDOsygaiwpraClDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:39:28.772877Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.05154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cd3f044b5470cf20bb6a82767cd7d7a39fbd75ea46fafdb42b6d890f86e5238","sha256:4ea4a457093bdefe87663ae65295c2845e1af2f29ad6107a5dac86603a48ea21"],"state_sha256":"6e2516c1e1c9dc0380bb0b3b3c6acc030a7686e190a28b6604095efb54870a1d"}