{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GBXW722PHOYT3EBC6VQFPT6MMX","short_pith_number":"pith:GBXW722P","canonical_record":{"source":{"id":"1503.05725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-19T11:54:53Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"1ad796d1ff392740ad279ba9a72c82e5e72651b7c376b74f2e332ea917f26bf5","abstract_canon_sha256":"f762c4d20dd5690bb01e06211086d698830048fc740ec89ba8126173e7644c2a"},"schema_version":"1.0"},"canonical_sha256":"306f6feb4f3bb13d9022f56057cfcc65f8241b5429258df889de9f9b5043c6f3","source":{"kind":"arxiv","id":"1503.05725","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05725","created_at":"2026-05-18T01:55:41Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05725v1","created_at":"2026-05-18T01:55:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05725","created_at":"2026-05-18T01:55:41Z"},{"alias_kind":"pith_short_12","alias_value":"GBXW722PHOYT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GBXW722PHOYT3EBC","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GBXW722P","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GBXW722PHOYT3EBC6VQFPT6MMX","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-19T11:54:53Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"1ad796d1ff392740ad279ba9a72c82e5e72651b7c376b74f2e332ea917f26bf5","abstract_canon_sha256":"f762c4d20dd5690bb01e06211086d698830048fc740ec89ba8126173e7644c2a"},"schema_version":"1.0"},"canonical_sha256":"306f6feb4f3bb13d9022f56057cfcc65f8241b5429258df889de9f9b5043c6f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:41.800219Z","signature_b64":"wkKZwl5CV/Yydjg7T6gXPC3DBSiwvMe8A3REeeZ5lHZZ2JUFgbL3MRVcwLDQ9kP/Tl4n22pwW/0vPXp9BG9LDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"306f6feb4f3bb13d9022f56057cfcc65f8241b5429258df889de9f9b5043c6f3","last_reissued_at":"2026-05-18T01:55:41.799669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:41.799669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05725","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":"2026-05-18T01:55:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UI+C9VOi8pdkc+v9gOfKCMVGi4KjA//I2kW+C+0K6zzlfts7rOsY6iYdO3ugwO82ylBqvXPLwhHktzRPomjwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T13:38:47.742371Z"},"content_sha256":"f3421022c9b5ab0103278fa37dddd779516f4f3fc929230a8e0387bd3ecbb412","schema_version":"1.0","event_id":"sha256:f3421022c9b5ab0103278fa37dddd779516f4f3fc929230a8e0387bd3ecbb412"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GBXW722PHOYT3EBC6VQFPT6MMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupled Oscillator Systems Having Partial PT Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alireza Beygi, Carl M. Bender, S. P. Klevansky","submitted_at":"2015-03-19T11:54:53Z","abstract_excerpt":"This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\\leq j\\leq N$) has the natural frequency $\\omega_j$ and is described by the Hamiltonian $\\frac{1}{2}p_j^2+\\frac{1}{2}\\omega_j^2x_j^2$. The oscillators are coupled adjacently with coupling constants that are purely imaginary; the coupling of the $j$th oscillator to the $(j+1)$st oscillator has the bilinear form $i\\gamma x_jx_{j+1}$ ($\\gamma$ real). The complex Hamiltonians for these systems exhibit {\\it partial} $\\mathcal{PT}$ symmetry; that is, they are invariant under $i\\to-i$ (time reversal)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05725","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":"2026-05-18T01:55:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkuViBY8gEjqaC6LV38/BoeaIe+/deGn+PnJarI6DFEN4yDd1c8Mp+MivpQ2lShhnyxIYyhhEncyLSbp3hRnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T13:38:47.742721Z"},"content_sha256":"9a54963cc76255167358767b71bb907e44fe601c2ada8119d476a3a3467f57c0","schema_version":"1.0","event_id":"sha256:9a54963cc76255167358767b71bb907e44fe601c2ada8119d476a3a3467f57c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBXW722PHOYT3EBC6VQFPT6MMX/bundle.json","state_url":"https://pith.science/pith/GBXW722PHOYT3EBC6VQFPT6MMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBXW722PHOYT3EBC6VQFPT6MMX/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":"2026-05-21T13:38:47Z","links":{"resolver":"https://pith.science/pith/GBXW722PHOYT3EBC6VQFPT6MMX","bundle":"https://pith.science/pith/GBXW722PHOYT3EBC6VQFPT6MMX/bundle.json","state":"https://pith.science/pith/GBXW722PHOYT3EBC6VQFPT6MMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBXW722PHOYT3EBC6VQFPT6MMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GBXW722PHOYT3EBC6VQFPT6MMX","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":"f762c4d20dd5690bb01e06211086d698830048fc740ec89ba8126173e7644c2a","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-19T11:54:53Z","title_canon_sha256":"1ad796d1ff392740ad279ba9a72c82e5e72651b7c376b74f2e332ea917f26bf5"},"schema_version":"1.0","source":{"id":"1503.05725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05725","created_at":"2026-05-18T01:55:41Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05725v1","created_at":"2026-05-18T01:55:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05725","created_at":"2026-05-18T01:55:41Z"},{"alias_kind":"pith_short_12","alias_value":"GBXW722PHOYT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GBXW722PHOYT3EBC","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GBXW722P","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:9a54963cc76255167358767b71bb907e44fe601c2ada8119d476a3a3467f57c0","target":"graph","created_at":"2026-05-18T01:55:41Z","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":"This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\\leq j\\leq N$) has the natural frequency $\\omega_j$ and is described by the Hamiltonian $\\frac{1}{2}p_j^2+\\frac{1}{2}\\omega_j^2x_j^2$. The oscillators are coupled adjacently with coupling constants that are purely imaginary; the coupling of the $j$th oscillator to the $(j+1)$st oscillator has the bilinear form $i\\gamma x_jx_{j+1}$ ($\\gamma$ real). The complex Hamiltonians for these systems exhibit {\\it partial} $\\mathcal{PT}$ symmetry; that is, they are invariant under $i\\to-i$ (time reversal)","authors_text":"Alireza Beygi, Carl M. Bender, S. P. Klevansky","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-19T11:54:53Z","title":"Coupled Oscillator Systems Having Partial PT Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05725","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:f3421022c9b5ab0103278fa37dddd779516f4f3fc929230a8e0387bd3ecbb412","target":"record","created_at":"2026-05-18T01:55:41Z","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":"f762c4d20dd5690bb01e06211086d698830048fc740ec89ba8126173e7644c2a","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-19T11:54:53Z","title_canon_sha256":"1ad796d1ff392740ad279ba9a72c82e5e72651b7c376b74f2e332ea917f26bf5"},"schema_version":"1.0","source":{"id":"1503.05725","kind":"arxiv","version":1}},"canonical_sha256":"306f6feb4f3bb13d9022f56057cfcc65f8241b5429258df889de9f9b5043c6f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"306f6feb4f3bb13d9022f56057cfcc65f8241b5429258df889de9f9b5043c6f3","first_computed_at":"2026-05-18T01:55:41.799669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:41.799669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkKZwl5CV/Yydjg7T6gXPC3DBSiwvMe8A3REeeZ5lHZZ2JUFgbL3MRVcwLDQ9kP/Tl4n22pwW/0vPXp9BG9LDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:41.800219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3421022c9b5ab0103278fa37dddd779516f4f3fc929230a8e0387bd3ecbb412","sha256:9a54963cc76255167358767b71bb907e44fe601c2ada8119d476a3a3467f57c0"],"state_sha256":"d3032866274adbb1daa5fe7ceaa21b03345ee5b989e896a0bc01bb6bac539cc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sk3WsU19Ry3zKwGzuhw00He65ybZswzeUrMdd3/it719bQOCRBNYFvhAm8qCQ8QfJjzb7XACklNui3K5WIRCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T13:38:47.744675Z","bundle_sha256":"caf5cbb2cd6b2f4f1fc48925af1e6decde3c72832db4093915eebc644f031158"}}