{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TL2ENKW2CBIEWE5LFNF3JYK4FJ","short_pith_number":"pith:TL2ENKW2","canonical_record":{"source":{"id":"1510.07792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-27T07:12:15Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"18ca8b98644da5bb33e1a0511ca4c435d6df3cb9733dd8c558fab7f1179be58b","abstract_canon_sha256":"80b0b8711644131ee13e3d505e7cf42a27c30c4583c23bcf7847e1210523834b"},"schema_version":"1.0"},"canonical_sha256":"9af446aada10504b13ab2b4bb4e15c2a52bfcc82824f1fc87397abf34e53666f","source":{"kind":"arxiv","id":"1510.07792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07792","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07792v1","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07792","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"TL2ENKW2CBIE","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TL2ENKW2CBIEWE5L","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TL2ENKW2","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TL2ENKW2CBIEWE5LFNF3JYK4FJ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-27T07:12:15Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"18ca8b98644da5bb33e1a0511ca4c435d6df3cb9733dd8c558fab7f1179be58b","abstract_canon_sha256":"80b0b8711644131ee13e3d505e7cf42a27c30c4583c23bcf7847e1210523834b"},"schema_version":"1.0"},"canonical_sha256":"9af446aada10504b13ab2b4bb4e15c2a52bfcc82824f1fc87397abf34e53666f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:12.578423Z","signature_b64":"TK15qG2M7ofXqbhkVpfU+IMLbIZoa7hkNowunh4rti9LzTcrkSj2L1iumkknujGtJYnt0RTbApdkZpCQA+hJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9af446aada10504b13ab2b4bb4e15c2a52bfcc82824f1fc87397abf34e53666f","last_reissued_at":"2026-05-18T01:29:12.577713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:12.577713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07792","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":"2026-05-18T01:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LnK9A3cncjhtRWheg/YCtU+qWqNto0j0qXd5hzzEhCzzovDA1wR5qQAFWptYDU8jcXch5rRDDUdX4ZnQWyB2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:32:58.326953Z"},"content_sha256":"4f533760743d085b8f4a1605753cf0560bf0bf649cfe808671ff678bf92348a9","schema_version":"1.0","event_id":"sha256:4f533760743d085b8f4a1605753cf0560bf0bf649cfe808671ff678bf92348a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TL2ENKW2CBIEWE5LFNF3JYK4FJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"De Branges functions of Schroedinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CV","authors_text":"Alexei Poltoratski, Anton Baranov, Yurii Belov","submitted_at":"2015-10-27T07:12:15Z","abstract_excerpt":"We characterize the Hermite-Biehler (de Branges) functions $E$ which correspond to Shroedinger operators with $L^2$ potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07792","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":"2026-05-18T01:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEe2ClMPZ076Xb3QyC8u2HRjX0bYymxgicoTfIV+GtqOCFuwaeD3Prlbo23AHM77wsPw8CEJ7hHlJKdH1wceAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:32:58.327295Z"},"content_sha256":"c535d54b1f890b0fabd00b31110f12b9c1b772b6462730f8ec394756c3308cd5","schema_version":"1.0","event_id":"sha256:c535d54b1f890b0fabd00b31110f12b9c1b772b6462730f8ec394756c3308cd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ/bundle.json","state_url":"https://pith.science/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ/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":"2026-06-27T16:32:58Z","links":{"resolver":"https://pith.science/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ","bundle":"https://pith.science/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ/bundle.json","state":"https://pith.science/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TL2ENKW2CBIEWE5LFNF3JYK4FJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TL2ENKW2CBIEWE5LFNF3JYK4FJ","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":"80b0b8711644131ee13e3d505e7cf42a27c30c4583c23bcf7847e1210523834b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-27T07:12:15Z","title_canon_sha256":"18ca8b98644da5bb33e1a0511ca4c435d6df3cb9733dd8c558fab7f1179be58b"},"schema_version":"1.0","source":{"id":"1510.07792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07792","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07792v1","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07792","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"TL2ENKW2CBIE","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TL2ENKW2CBIEWE5L","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TL2ENKW2","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:c535d54b1f890b0fabd00b31110f12b9c1b772b6462730f8ec394756c3308cd5","target":"graph","created_at":"2026-05-18T01:29:12Z","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 characterize the Hermite-Biehler (de Branges) functions $E$ which correspond to Shroedinger operators with $L^2$ potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances.","authors_text":"Alexei Poltoratski, Anton Baranov, Yurii Belov","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-27T07:12:15Z","title":"De Branges functions of Schroedinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07792","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":"sha256:4f533760743d085b8f4a1605753cf0560bf0bf649cfe808671ff678bf92348a9","target":"record","created_at":"2026-05-18T01:29:12Z","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":"80b0b8711644131ee13e3d505e7cf42a27c30c4583c23bcf7847e1210523834b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-10-27T07:12:15Z","title_canon_sha256":"18ca8b98644da5bb33e1a0511ca4c435d6df3cb9733dd8c558fab7f1179be58b"},"schema_version":"1.0","source":{"id":"1510.07792","kind":"arxiv","version":1}},"canonical_sha256":"9af446aada10504b13ab2b4bb4e15c2a52bfcc82824f1fc87397abf34e53666f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9af446aada10504b13ab2b4bb4e15c2a52bfcc82824f1fc87397abf34e53666f","first_computed_at":"2026-05-18T01:29:12.577713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:12.577713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TK15qG2M7ofXqbhkVpfU+IMLbIZoa7hkNowunh4rti9LzTcrkSj2L1iumkknujGtJYnt0RTbApdkZpCQA+hJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:12.578423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f533760743d085b8f4a1605753cf0560bf0bf649cfe808671ff678bf92348a9","sha256:c535d54b1f890b0fabd00b31110f12b9c1b772b6462730f8ec394756c3308cd5"],"state_sha256":"5b3a77e17c4544e29a058d9a06bd0f6c9f59c322877d1f8c91e571afd48fd266"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKwsSvPGO0vmaUniJsUvaLdb2P219RcSYVUai/a/iyo0bdkctXx7G/V/1zsOhrR5asGzRplXPQ93/28PdS8mBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:32:58.329103Z","bundle_sha256":"2c9446b6e60d431fee2391f073c54bd4d605c146be5ed4edba648fb357fc62fe"}}