{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XXUAMYBASXHJKXDZKI4DF7HXS4","short_pith_number":"pith:XXUAMYBA","canonical_record":{"source":{"id":"1001.2964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-18T07:09:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a50e1a916612bf29507f62473412273670a4e8cb1235cf38d2dbedde8a6555a6","abstract_canon_sha256":"ce00ea758c207984c4f3a2c672102ad28c01ff5be07718ad31b93e7cfcf07a06"},"schema_version":"1.0"},"canonical_sha256":"bde806602095ce955c79523832fcf7970ab68ade8d5db506d26f8ffdd2c62958","source":{"kind":"arxiv","id":"1001.2964","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2964","created_at":"2026-05-18T02:09:43Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2964v2","created_at":"2026-05-18T02:09:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2964","created_at":"2026-05-18T02:09:43Z"},{"alias_kind":"pith_short_12","alias_value":"XXUAMYBASXHJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XXUAMYBASXHJKXDZ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XXUAMYBA","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XXUAMYBASXHJKXDZKI4DF7HXS4","target":"record","payload":{"canonical_record":{"source":{"id":"1001.2964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-18T07:09:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a50e1a916612bf29507f62473412273670a4e8cb1235cf38d2dbedde8a6555a6","abstract_canon_sha256":"ce00ea758c207984c4f3a2c672102ad28c01ff5be07718ad31b93e7cfcf07a06"},"schema_version":"1.0"},"canonical_sha256":"bde806602095ce955c79523832fcf7970ab68ade8d5db506d26f8ffdd2c62958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:43.220424Z","signature_b64":"sODLyBbEJLUi93WX+TeIto1RJUIY2Y3WEC2zJxA/64cPdDuVxlJCWVlvOb02hVs/oSgRiX7jyUcz2RqcUbagAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bde806602095ce955c79523832fcf7970ab68ade8d5db506d26f8ffdd2c62958","last_reissued_at":"2026-05-18T02:09:43.219774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:43.219774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.2964","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:09:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4jslH8MS4LpGVg4R1TYk1d4/C82/W8+17Emju8xhuFuSAgvXgSm0MO6wfV9d6hThx8Nl9wU3ypYXfubih8YfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:26:20.204159Z"},"content_sha256":"0af0273d90872858bff3bdcb5d05fff3a96af0674ec5fec68527bc68d093aad3","schema_version":"1.0","event_id":"sha256:0af0273d90872858bff3bdcb5d05fff3a96af0674ec5fec68527bc68d093aad3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XXUAMYBASXHJKXDZKI4DF7HXS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alberto Ventura, Francesco Cannata","submitted_at":"2010-01-18T07:09:37Z","abstract_excerpt":"We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are real and the potentials are reflectionless and conserve unitarity in the scattering process. Absence of reflection makes it meaningful to consider also PT-symmetric potentials that do not vanish asymptotically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2964","kind":"arxiv","version":2},"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":"2026-05-18T02:09:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IyIkMnUQOhBcYBVwze1wp/zhz4/MXmYbkMR8NA9a06j53UBNyLi/xc8u4h+IZ/I+e1knIUUYOCfKBqyS2Ev+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:26:20.204813Z"},"content_sha256":"c19821dfb3c4b545391738d2628df199c12308d1a377db616633187d0f34b579","schema_version":"1.0","event_id":"sha256:c19821dfb3c4b545391738d2628df199c12308d1a377db616633187d0f34b579"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XXUAMYBASXHJKXDZKI4DF7HXS4/bundle.json","state_url":"https://pith.science/pith/XXUAMYBASXHJKXDZKI4DF7HXS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XXUAMYBASXHJKXDZKI4DF7HXS4/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":"2026-05-31T16:26:20Z","links":{"resolver":"https://pith.science/pith/XXUAMYBASXHJKXDZKI4DF7HXS4","bundle":"https://pith.science/pith/XXUAMYBASXHJKXDZKI4DF7HXS4/bundle.json","state":"https://pith.science/pith/XXUAMYBASXHJKXDZKI4DF7HXS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XXUAMYBASXHJKXDZKI4DF7HXS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XXUAMYBASXHJKXDZKI4DF7HXS4","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":"ce00ea758c207984c4f3a2c672102ad28c01ff5be07718ad31b93e7cfcf07a06","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-18T07:09:37Z","title_canon_sha256":"a50e1a916612bf29507f62473412273670a4e8cb1235cf38d2dbedde8a6555a6"},"schema_version":"1.0","source":{"id":"1001.2964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2964","created_at":"2026-05-18T02:09:43Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2964v2","created_at":"2026-05-18T02:09:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2964","created_at":"2026-05-18T02:09:43Z"},{"alias_kind":"pith_short_12","alias_value":"XXUAMYBASXHJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XXUAMYBASXHJKXDZ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XXUAMYBA","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:c19821dfb3c4b545391738d2628df199c12308d1a377db616633187d0f34b579","target":"graph","created_at":"2026-05-18T02:09:43Z","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 study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are real and the potentials are reflectionless and conserve unitarity in the scattering process. Absence of reflection makes it meaningful to consider also PT-symmetric potentials that do not vanish asymptotically.","authors_text":"Alberto Ventura, Francesco Cannata","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-18T07:09:37Z","title":"Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2964","kind":"arxiv","version":2},"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":"sha256:0af0273d90872858bff3bdcb5d05fff3a96af0674ec5fec68527bc68d093aad3","target":"record","created_at":"2026-05-18T02:09:43Z","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":"ce00ea758c207984c4f3a2c672102ad28c01ff5be07718ad31b93e7cfcf07a06","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-18T07:09:37Z","title_canon_sha256":"a50e1a916612bf29507f62473412273670a4e8cb1235cf38d2dbedde8a6555a6"},"schema_version":"1.0","source":{"id":"1001.2964","kind":"arxiv","version":2}},"canonical_sha256":"bde806602095ce955c79523832fcf7970ab68ade8d5db506d26f8ffdd2c62958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bde806602095ce955c79523832fcf7970ab68ade8d5db506d26f8ffdd2c62958","first_computed_at":"2026-05-18T02:09:43.219774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:43.219774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sODLyBbEJLUi93WX+TeIto1RJUIY2Y3WEC2zJxA/64cPdDuVxlJCWVlvOb02hVs/oSgRiX7jyUcz2RqcUbagAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:43.220424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0af0273d90872858bff3bdcb5d05fff3a96af0674ec5fec68527bc68d093aad3","sha256:c19821dfb3c4b545391738d2628df199c12308d1a377db616633187d0f34b579"],"state_sha256":"41d1b378ebeb1f642fabb13842e176de5829496a59dfdc0fcbcd0edf819a458c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Obl0pP9wrOHKf3vKb8T5WNzKzuA+vOG28853HDgDMYJP6T9Rcjp5gYOywwIHGFXQpc7A4ieCUu7Zwv38FnY9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:26:20.208911Z","bundle_sha256":"93907b34af5cb9b9441bf46ef9a1f46adae52a86f3b478e6527de1cb750613f8"}}