{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NDJNOMLWJSNKCVQ6NY7AE4SXIY","short_pith_number":"pith:NDJNOMLW","canonical_record":{"source":{"id":"1505.06267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-23T03:10:55Z","cross_cats_sorted":[],"title_canon_sha256":"f5a1ddb4d2ae33fedb7c9baec2505a625c41a2a034e751575452e68ac3086124","abstract_canon_sha256":"103a4d8286453c52cb00ad3cd2d676b35f7659907d39c0917ea8e126308dbee5"},"schema_version":"1.0"},"canonical_sha256":"68d2d731764c9aa1561e6e3e027257463331123ae46f3b07282c513bb7926160","source":{"kind":"arxiv","id":"1505.06267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06267","created_at":"2026-05-18T02:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06267v1","created_at":"2026-05-18T02:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06267","created_at":"2026-05-18T02:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"NDJNOMLWJSNK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDJNOMLWJSNKCVQ6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDJNOMLW","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NDJNOMLWJSNKCVQ6NY7AE4SXIY","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-23T03:10:55Z","cross_cats_sorted":[],"title_canon_sha256":"f5a1ddb4d2ae33fedb7c9baec2505a625c41a2a034e751575452e68ac3086124","abstract_canon_sha256":"103a4d8286453c52cb00ad3cd2d676b35f7659907d39c0917ea8e126308dbee5"},"schema_version":"1.0"},"canonical_sha256":"68d2d731764c9aa1561e6e3e027257463331123ae46f3b07282c513bb7926160","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:47.727619Z","signature_b64":"gkDyo1LVdA8+a/fgEDh9I0FLt2SjUR4r56MqPkLgPe185xIUC8Ok9P4gr3RiBBdf4Te7W2NTsBfJrsYBSwbfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68d2d731764c9aa1561e6e3e027257463331123ae46f3b07282c513bb7926160","last_reissued_at":"2026-05-18T02:03:47.727026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:47.727026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06267","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkvZAT3pChHlJblNSRw8wktLluhXPr+Om5OuTTVOdApPAZX6USR1yZF5njSZc/pj4zrS/vwkQAbTXl5x1ofdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:45:30.853658Z"},"content_sha256":"813cdbd51cea1eda219ed799eadebd0967d0ea0e4a102341d7980d93d3e2fb8b","schema_version":"1.0","event_id":"sha256:813cdbd51cea1eda219ed799eadebd0967d0ea0e4a102341d7980d93d3e2fb8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NDJNOMLWJSNKCVQ6NY7AE4SXIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions II: applications to Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hayato Chiba","submitted_at":"2015-05-23T03:10:55Z","abstract_excerpt":"A spectral theory of linear operators on a rigged Hilbert space is applied to Schr\\\"odinger operators with exponentially decaying potentials and dilation analytic potentials. The theory of rigged Hilbert spaces provides a unified approach to resonances (generalized eigenvalues) for both classes of potentials without using any spectral deformation techniques. Generalized eigenvalues for one dimensional Schr\\\"odinger operators (ordinary differential operators) are investigated in detail. A certain holomorphic function $\\mathbb{D}(\\lambda)$ is constructed so that $\\mathbb{D}(\\lambda) = 0$ if and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06267","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvteC/frprepj+jKW4lJ2f7UejYD9WHzVwuzeVrprmzjULB4scg3qvYmSXGsvZ6xqq399MmnFbY+1Ub4pwg9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:45:30.854005Z"},"content_sha256":"3c9259121fba9ca678cb0e1626bbf7aba5131aaa4034cffb0d7b53a4c36c4b2a","schema_version":"1.0","event_id":"sha256:3c9259121fba9ca678cb0e1626bbf7aba5131aaa4034cffb0d7b53a4c36c4b2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY/bundle.json","state_url":"https://pith.science/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T19:45:30Z","links":{"resolver":"https://pith.science/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY","bundle":"https://pith.science/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY/bundle.json","state":"https://pith.science/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDJNOMLWJSNKCVQ6NY7AE4SXIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NDJNOMLWJSNKCVQ6NY7AE4SXIY","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":"103a4d8286453c52cb00ad3cd2d676b35f7659907d39c0917ea8e126308dbee5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-23T03:10:55Z","title_canon_sha256":"f5a1ddb4d2ae33fedb7c9baec2505a625c41a2a034e751575452e68ac3086124"},"schema_version":"1.0","source":{"id":"1505.06267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06267","created_at":"2026-05-18T02:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06267v1","created_at":"2026-05-18T02:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06267","created_at":"2026-05-18T02:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"NDJNOMLWJSNK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDJNOMLWJSNKCVQ6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDJNOMLW","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:3c9259121fba9ca678cb0e1626bbf7aba5131aaa4034cffb0d7b53a4c36c4b2a","target":"graph","created_at":"2026-05-18T02:03:47Z","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":"A spectral theory of linear operators on a rigged Hilbert space is applied to Schr\\\"odinger operators with exponentially decaying potentials and dilation analytic potentials. The theory of rigged Hilbert spaces provides a unified approach to resonances (generalized eigenvalues) for both classes of potentials without using any spectral deformation techniques. Generalized eigenvalues for one dimensional Schr\\\"odinger operators (ordinary differential operators) are investigated in detail. A certain holomorphic function $\\mathbb{D}(\\lambda)$ is constructed so that $\\mathbb{D}(\\lambda) = 0$ if and ","authors_text":"Hayato Chiba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-23T03:10:55Z","title":"A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions II: applications to Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06267","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":"sha256:813cdbd51cea1eda219ed799eadebd0967d0ea0e4a102341d7980d93d3e2fb8b","target":"record","created_at":"2026-05-18T02:03:47Z","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":"103a4d8286453c52cb00ad3cd2d676b35f7659907d39c0917ea8e126308dbee5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-23T03:10:55Z","title_canon_sha256":"f5a1ddb4d2ae33fedb7c9baec2505a625c41a2a034e751575452e68ac3086124"},"schema_version":"1.0","source":{"id":"1505.06267","kind":"arxiv","version":1}},"canonical_sha256":"68d2d731764c9aa1561e6e3e027257463331123ae46f3b07282c513bb7926160","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68d2d731764c9aa1561e6e3e027257463331123ae46f3b07282c513bb7926160","first_computed_at":"2026-05-18T02:03:47.727026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:47.727026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gkDyo1LVdA8+a/fgEDh9I0FLt2SjUR4r56MqPkLgPe185xIUC8Ok9P4gr3RiBBdf4Te7W2NTsBfJrsYBSwbfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:47.727619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:813cdbd51cea1eda219ed799eadebd0967d0ea0e4a102341d7980d93d3e2fb8b","sha256:3c9259121fba9ca678cb0e1626bbf7aba5131aaa4034cffb0d7b53a4c36c4b2a"],"state_sha256":"900985752f80b1312b3a05cea0f33ea59be51601a7eea37777a9a33f6a6e4a57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01leaBcrPcYcOvPut7AVonxqdg87XAW6o8/eL91QzrCMrv1M42qmZwQ9gvys0lboBYvBos83+vg+mZj0ZYIbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:45:30.856126Z","bundle_sha256":"ce89baa0454256cb8b31490e4c64b486c81a199927c8f975abe42fb8aef1b8e7"}}