{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5R4LOLQTKSYIFWKE4F2ECTXYHF","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":"eb82087455f5cd9481a8cf5a51f04b354c91c7cfb5133cea61718ab32e04fc03","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-11T12:11:38Z","title_canon_sha256":"755e585fcc512853b456f0da278f19146245c49b41f460926b70a31ef84ac5b2"},"schema_version":"1.0","source":{"id":"1903.04242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04242","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04242v1","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04242","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"pith_short_12","alias_value":"5R4LOLQTKSYI","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5R4LOLQTKSYIFWKE","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5R4LOLQT","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:f8a4dcaf537e438a3332a6f5ca9a3a360239b40bc8b53bc57eb9c08adac259e6","target":"graph","created_at":"2026-05-17T23:51:36Z","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 give an explicit formula for the wave operators for Schroedinger operators on the half-line with a potential decaying strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering operator and a function of the generator of the dilation group, and a Hilbert-Schmidt remainder term. Our method is based on the elementary construction of the generalized Fourier transform in terms of the solutions of the Volterra integral equations. As a corollary, a topological interpretation of Levinson's theorem is established via an index theorem appro","authors_text":"Hideki Inoue","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-11T12:11:38Z","title":"Explicit formula for Schroedinger wave operators on the half-line for potentials up to optimal decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04242","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":"sha256:4532448003c31dbd810490589f86e4b9ed50e082931d3b14b86044678b3152a9","target":"record","created_at":"2026-05-17T23:51:36Z","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":"eb82087455f5cd9481a8cf5a51f04b354c91c7cfb5133cea61718ab32e04fc03","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-11T12:11:38Z","title_canon_sha256":"755e585fcc512853b456f0da278f19146245c49b41f460926b70a31ef84ac5b2"},"schema_version":"1.0","source":{"id":"1903.04242","kind":"arxiv","version":1}},"canonical_sha256":"ec78b72e1354b082d944e174414ef8395bea11ab942bb4b12c9d93415d252b03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec78b72e1354b082d944e174414ef8395bea11ab942bb4b12c9d93415d252b03","first_computed_at":"2026-05-17T23:51:36.089757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:36.089757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W7uWHIIpWTOilpxAjwEEhhe29Wjf51YUYhw+MWwQyppcrp1mV+2d9VlHNapL5/s1y+mo3zfkxgaFPZfZ4PeCDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:36.090381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4532448003c31dbd810490589f86e4b9ed50e082931d3b14b86044678b3152a9","sha256:f8a4dcaf537e438a3332a6f5ca9a3a360239b40bc8b53bc57eb9c08adac259e6"],"state_sha256":"a8ab2c2e98a97e2f9d04a21b075a6eb204969f14e607779e828356bde58d1829"}