{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FGEMUB2YH7SE3PZ6HBAT7A6HEG","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":"5e3e0823bdade04288944f276a11d1506f1ae3cb014153fbd8803f36f004354f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-11T12:00:54Z","title_canon_sha256":"a8b15c0d79a854c92b84427e6eb11ea06b0acd80b8776139b43aa601e3b5e4ab"},"schema_version":"1.0","source":{"id":"1509.03468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03468","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03468v1","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03468","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"FGEMUB2YH7SE","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FGEMUB2YH7SE3PZ6","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FGEMUB2Y","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:343f9307c6240a20777857e9f100af4c221ed4e0c5a70f5d7f181ea6a986fb52","target":"graph","created_at":"2026-05-18T01:33:23Z","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":"This is the third paper in a series analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix, $S_h(E)$, for semiclassical Schr\\\"odinger operators on $\\mathbb{R}^d$ which are perturbations of the free Hamiltonian by a potential $V$ with polynomial decay. Our assumption is that $V(x) \\sim |x|^{-\\alpha} v(\\hat x)$ as $x \\to \\infty$, for some $\\alpha > d$, with corresponding derivative estimates. In the semiclassical limit $h \\to 0$, we show that the atomic measure on the","authors_text":"Andrew Hassell, Jesse Gell-Redman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-11T12:00:54Z","title":"The distribution of phase shifts for semiclassical potentials with polynomial decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03468","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":"sha256:4039c153968d47827306087dc40ccd7ad8de11adb347e8562130c3d54a8da1a8","target":"record","created_at":"2026-05-18T01:33:23Z","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":"5e3e0823bdade04288944f276a11d1506f1ae3cb014153fbd8803f36f004354f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-11T12:00:54Z","title_canon_sha256":"a8b15c0d79a854c92b84427e6eb11ea06b0acd80b8776139b43aa601e3b5e4ab"},"schema_version":"1.0","source":{"id":"1509.03468","kind":"arxiv","version":1}},"canonical_sha256":"2988ca07583fe44dbf3e38413f83c7218fe8b48d7d272fb6b69f6c1b238f0d9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2988ca07583fe44dbf3e38413f83c7218fe8b48d7d272fb6b69f6c1b238f0d9d","first_computed_at":"2026-05-18T01:33:23.128111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:23.128111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zwi8T5HJ4vj1zludrFMBcC4Ra/nV6pV1iFbRji6Tr69A/b189Fgs8e8pM4GG8SpN8AmZviALMJkhEZZd3CqSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:23.128897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4039c153968d47827306087dc40ccd7ad8de11adb347e8562130c3d54a8da1a8","sha256:343f9307c6240a20777857e9f100af4c221ed4e0c5a70f5d7f181ea6a986fb52"],"state_sha256":"d8475684aa5040103a03496c9f3db3c85a3579368bf591e30ae9e660c656f293"}