{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VLRI5NXRSXK22ZQQYIIBSNCRJB","short_pith_number":"pith:VLRI5NXR","canonical_record":{"source":{"id":"1512.09326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-31T17:29:47Z","cross_cats_sorted":[],"title_canon_sha256":"19477f791cd17fb9368d2db29e38692b68e0a6bd6148818ce6dccebeae34b654","abstract_canon_sha256":"45b278e115d322690bca6adef1e801b4602f5e7d0c0c2037bcf11d559a16fca6"},"schema_version":"1.0"},"canonical_sha256":"aae28eb6f195d5ad6610c210193451485db30b615faa8dfe4d8a7c368182c169","source":{"kind":"arxiv","id":"1512.09326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09326","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09326v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09326","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"VLRI5NXRSXK2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VLRI5NXRSXK22ZQQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VLRI5NXR","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VLRI5NXRSXK22ZQQYIIBSNCRJB","target":"record","payload":{"canonical_record":{"source":{"id":"1512.09326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-31T17:29:47Z","cross_cats_sorted":[],"title_canon_sha256":"19477f791cd17fb9368d2db29e38692b68e0a6bd6148818ce6dccebeae34b654","abstract_canon_sha256":"45b278e115d322690bca6adef1e801b4602f5e7d0c0c2037bcf11d559a16fca6"},"schema_version":"1.0"},"canonical_sha256":"aae28eb6f195d5ad6610c210193451485db30b615faa8dfe4d8a7c368182c169","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:32.664617Z","signature_b64":"hCvamDoISl/TfKHCkPnnUKpAbzAeYLQlaxo/28KOpOw/SgYPdWhqkhG9hpbBnN7ipmKMSyVW18m3dA2oM4ySBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aae28eb6f195d5ad6610c210193451485db30b615faa8dfe4d8a7c368182c169","last_reissued_at":"2026-05-18T01:23:32.663943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:32.663943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.09326","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":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCt9ETUlseCyGW5hmAvBBO87Y604qK+mLS8xSLZ8ger07wjpB+DJkTKC1DhQRvvKFPm1/D1tQUGZudSRJpm7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:40:09.525639Z"},"content_sha256":"c5dbef7ceceff463219b4ee18147f6c2818766bb0b198c99b5800cc1841cfbbc","schema_version":"1.0","event_id":"sha256:c5dbef7ceceff463219b4ee18147f6c2818766bb0b198c99b5800cc1841cfbbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VLRI5NXRSXK22ZQQYIIBSNCRJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On two exactly-solvable one-dimensional Hamiltonians with PT symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Francisco M. Fern\\'andez","submitted_at":"2015-12-31T17:29:47Z","abstract_excerpt":"We provide an explanation to the behaviour of the spectra of two exactly-solvable one-dimensional Hamiltonians with PT symmetry proposed earlier. We calculate the branch points at which pairs of eigenvalues coalesce and discuss the perturbation series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09326","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":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zMZ0hV4OkJl9BX5L4YMZyclXNoSukFltjDrW869zSIq8bXgAgNc5jxLgUn5dogk63Eno3/Si9T53xWZZ8z9pBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:40:09.526179Z"},"content_sha256":"1f399af9ab0477702dcd6443fbec89ee4dd46eab0c349ade022ebbb33c3a17db","schema_version":"1.0","event_id":"sha256:1f399af9ab0477702dcd6443fbec89ee4dd46eab0c349ade022ebbb33c3a17db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB/bundle.json","state_url":"https://pith.science/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB/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":"2026-05-26T12:40:09Z","links":{"resolver":"https://pith.science/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB","bundle":"https://pith.science/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB/bundle.json","state":"https://pith.science/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VLRI5NXRSXK22ZQQYIIBSNCRJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VLRI5NXRSXK22ZQQYIIBSNCRJB","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":"45b278e115d322690bca6adef1e801b4602f5e7d0c0c2037bcf11d559a16fca6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-31T17:29:47Z","title_canon_sha256":"19477f791cd17fb9368d2db29e38692b68e0a6bd6148818ce6dccebeae34b654"},"schema_version":"1.0","source":{"id":"1512.09326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09326","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09326v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09326","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"VLRI5NXRSXK2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VLRI5NXRSXK22ZQQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VLRI5NXR","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:1f399af9ab0477702dcd6443fbec89ee4dd46eab0c349ade022ebbb33c3a17db","target":"graph","created_at":"2026-05-18T01:23:32Z","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 provide an explanation to the behaviour of the spectra of two exactly-solvable one-dimensional Hamiltonians with PT symmetry proposed earlier. We calculate the branch points at which pairs of eigenvalues coalesce and discuss the perturbation series.","authors_text":"Francisco M. Fern\\'andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-31T17:29:47Z","title":"On two exactly-solvable one-dimensional Hamiltonians with PT symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09326","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:c5dbef7ceceff463219b4ee18147f6c2818766bb0b198c99b5800cc1841cfbbc","target":"record","created_at":"2026-05-18T01:23:32Z","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":"45b278e115d322690bca6adef1e801b4602f5e7d0c0c2037bcf11d559a16fca6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-31T17:29:47Z","title_canon_sha256":"19477f791cd17fb9368d2db29e38692b68e0a6bd6148818ce6dccebeae34b654"},"schema_version":"1.0","source":{"id":"1512.09326","kind":"arxiv","version":1}},"canonical_sha256":"aae28eb6f195d5ad6610c210193451485db30b615faa8dfe4d8a7c368182c169","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aae28eb6f195d5ad6610c210193451485db30b615faa8dfe4d8a7c368182c169","first_computed_at":"2026-05-18T01:23:32.663943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:32.663943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hCvamDoISl/TfKHCkPnnUKpAbzAeYLQlaxo/28KOpOw/SgYPdWhqkhG9hpbBnN7ipmKMSyVW18m3dA2oM4ySBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:32.664617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5dbef7ceceff463219b4ee18147f6c2818766bb0b198c99b5800cc1841cfbbc","sha256:1f399af9ab0477702dcd6443fbec89ee4dd46eab0c349ade022ebbb33c3a17db"],"state_sha256":"6783650dfd1a5d5531d6753a13a70e5ef083eb3be90173e7d6ed65a94fbb31ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5xvvPbCFtCgH1fmO8DVEI1iECbHNcfVmef8u2LiQeQ4j12sm9XebKEo7MkPQBc3eJGW3zNUnd7ATDa2Kq+uDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:40:09.529586Z","bundle_sha256":"8ff022c6b5f10755b189d7df0a5855b17fbdf7adfe9400c530860e73f0b7e1c4"}}