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We prove that under an appropriate dynamical hypothesis on the Hamilton flow corresponding to $H$, the eigenvalues of the scattering matrix $S_{h}(V)$ define a measure on $\\mathbb{S}^{1}$ that converges to Lebesgue measure away from $1 \\in \\mathbb{S}^{1}$ as $h \\to 0$."},"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":"1311.2353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-11-11T04:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"7adc989182db403e1677926ee9d3fe3f6a53033063be2abb485022ae19044413","abstract_canon_sha256":"a9ffc6713d88363b028434b6f67728edce01010f908c371b6a226961dbec7cba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:09.643574Z","signature_b64":"+6rf0jba0WglEoOPNasPWCn/I4pk86bgegX1KUmxt2ew6Nk82bBbaCS8xeFjh7DOXgQSdqyZYx7VNXHtz874CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50dc13e9fdf59c38c4ca6933303b8182b9167158ddfaf93d8e3453fb9162f91b","last_reissued_at":"2026-05-18T01:53:09.642952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:09.642952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equidistribution of phase shifts in semiclassical potential scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Andrew Hassell, Jesse Gell-Redman, Steve Zelditch","submitted_at":"2013-11-11T04:49:29Z","abstract_excerpt":"Consider a semiclassical Hamiltonian $H := h^{2} \\Delta + V - E$ where $\\Delta$ is the positive Laplacian on $\\mathbb{R}^{d}$, $V \\in C^{\\infty}_{0}(\\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that under an appropriate dynamical hypothesis on the Hamilton flow corresponding to $H$, the eigenvalues of the scattering matrix $S_{h}(V)$ define a measure on $\\mathbb{S}^{1}$ that converges to Lebesgue measure away from $1 \\in \\mathbb{S}^{1}$ as $h \\to 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2353","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":"1311.2353","created_at":"2026-05-18T01:53:09.643050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.2353v1","created_at":"2026-05-18T01:53:09.643050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2353","created_at":"2026-05-18T01:53:09.643050+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDOBH2P56WOD","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDOBH2P56WODRRGK","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDOBH2P5","created_at":"2026-05-18T12:27:49.015174+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/KDOBH2P56WODRRGKNEZTAO4BQK","json":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK.json","graph_json":"https://pith.science/api/pith-number/KDOBH2P56WODRRGKNEZTAO4BQK/graph.json","events_json":"https://pith.science/api/pith-number/KDOBH2P56WODRRGKNEZTAO4BQK/events.json","paper":"https://pith.science/paper/KDOBH2P5"},"agent_actions":{"view_html":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK","download_json":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK.json","view_paper":"https://pith.science/paper/KDOBH2P5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.2353&json=true","fetch_graph":"https://pith.science/api/pith-number/KDOBH2P56WODRRGKNEZTAO4BQK/graph.json","fetch_events":"https://pith.science/api/pith-number/KDOBH2P56WODRRGKNEZTAO4BQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK/action/storage_attestation","attest_author":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK/action/author_attestation","sign_citation":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK/action/citation_signature","submit_replication":"https://pith.science/pith/KDOBH2P56WODRRGKNEZTAO4BQK/action/replication_record"}},"created_at":"2026-05-18T01:53:09.643050+00:00","updated_at":"2026-05-18T01:53:09.643050+00:00"}