{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KILWQDHHDY24LQGH4ZBFR567YY","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":"f0d1d856c8751bcb95aabbb9cc57a89c58681b224bd7ca62409f340d4488f826","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-09T08:10:32Z","title_canon_sha256":"e103f7dda950c370c8c0663d1bab41edd5d1deaed8b6f12e10703243b2701e89"},"schema_version":"1.0","source":{"id":"1703.03172","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03172","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03172v2","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03172","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"pith_short_12","alias_value":"KILWQDHHDY24","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KILWQDHHDY24LQGH","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KILWQDHH","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:56b76f49438e4a9d7bedafb4efdef8367a5569b0cee845edc07d437a7381fbec","target":"graph","created_at":"2026-05-18T00:33:21Z","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"},"paper":{"abstract_excerpt":"We consider the large $L$ limit of one dimensional Schr\\\"odinger operators $H_L=-d^2/dx^2 + V_1(x) + V_{2,L}(x)$ in two cases: when $V_{2,L}(x)=V_2(x-L)$ and when $V_{2,L}(x)=e^{-cL}\\delta(x-L)$. This is motivated by some recent work of Herbst and Mavi where $V_{2,L}$ is replaced by a Dirichlet boundary condition at $L$. The Hamiltonian $H_L$ converges to $H = -d^2/dx^2 + V_1(x)$ as $L\\to \\infty$ in the strong resolvent sense (and even in the norm resolvent sense for our second case). However, most of the resonances of $H_L$ do not converge to those of $H$. Instead, they crowd together and con","authors_text":"Ira Herbst, Richard Froese","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-09T08:10:32Z","title":"Resonances - lost and found"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03172","kind":"arxiv","version":2},"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":"sha256:456948603d80ca5f68d8c5931880d15279c09a4f1b0795679c67eaf54abcf766","target":"record","created_at":"2026-05-18T00:33:21Z","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":"f0d1d856c8751bcb95aabbb9cc57a89c58681b224bd7ca62409f340d4488f826","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-09T08:10:32Z","title_canon_sha256":"e103f7dda950c370c8c0663d1bab41edd5d1deaed8b6f12e10703243b2701e89"},"schema_version":"1.0","source":{"id":"1703.03172","kind":"arxiv","version":2}},"canonical_sha256":"5217680ce71e35c5c0c7e64258f7dfc63f7f36e96f6162c13bc191d992bd54d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5217680ce71e35c5c0c7e64258f7dfc63f7f36e96f6162c13bc191d992bd54d5","first_computed_at":"2026-05-18T00:33:21.199533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:21.199533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9d13n/V9/jOcy+qboCy6sEbddNRFzZiC+cMqUz7pwvnQQ+CeTUsdPWyW/dZn2f/gkeDl87/ly7WPSg+uLOB5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:21.200192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03172","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:456948603d80ca5f68d8c5931880d15279c09a4f1b0795679c67eaf54abcf766","sha256:56b76f49438e4a9d7bedafb4efdef8367a5569b0cee845edc07d437a7381fbec"],"state_sha256":"2812ca9502ef30e6c5cbbd10d2ed1eebb336aa589fcdad658edcb88c06814dad"}