{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SQ7TTL472BSRZK6VDLDA322GSV","short_pith_number":"pith:SQ7TTL47","canonical_record":{"source":{"id":"1507.08850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-31T12:18:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6a493cb173291a8a1ed150460da10eef7a67ea5555cab67a7a9173f3dc4c1f7a","abstract_canon_sha256":"c4d6db0b223f27736f1daf1a7a25c68ed49d94c5d5248c0daebc51d85eabc61c"},"schema_version":"1.0"},"canonical_sha256":"943f39af9fd0651cabd51ac60deb46955eff227a8a3611049d60d0bec7218fc9","source":{"kind":"arxiv","id":"1507.08850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08850","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08850v2","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08850","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"SQ7TTL472BSR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SQ7TTL472BSRZK6V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SQ7TTL47","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SQ7TTL472BSRZK6VDLDA322GSV","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-31T12:18:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6a493cb173291a8a1ed150460da10eef7a67ea5555cab67a7a9173f3dc4c1f7a","abstract_canon_sha256":"c4d6db0b223f27736f1daf1a7a25c68ed49d94c5d5248c0daebc51d85eabc61c"},"schema_version":"1.0"},"canonical_sha256":"943f39af9fd0651cabd51ac60deb46955eff227a8a3611049d60d0bec7218fc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:58.397890Z","signature_b64":"XpNxkRkBl8TsjR0Bir/lLCnHyrmAS/rqOVoOxarodl2h14mbqmn9wQmZ95t3QyaVoAFwkrOr+s0zXyLVyc9jBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"943f39af9fd0651cabd51ac60deb46955eff227a8a3611049d60d0bec7218fc9","last_reissued_at":"2026-05-18T01:15:58.397255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:58.397255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08850","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":"2026-05-18T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qt4AkzUzoFdt64iIoH/7LTUqv0HiUXh8Bcl2BELYpqpXqq3nQ/D3GwPLSyZbNiaepMPpFkd+oKnluu9XBUumDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:44:50.086271Z"},"content_sha256":"6317d12db6a02bb3b4c5ed9e3434cac7c0f47c3930d20cfd6447efc1e2c9ab0e","schema_version":"1.0","event_id":"sha256:6317d12db6a02bb3b4c5ed9e3434cac7c0f47c3930d20cfd6447efc1e2c9ab0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SQ7TTL472BSRZK6VDLDA322GSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization of parity-time and partial parity-time symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Francisco M. Fern\\'andez","submitted_at":"2015-07-31T12:18:22Z","abstract_excerpt":"We show that parity-time and partial parity-time symmetries are particular cases of antiunitary symmetry. This point is illustrated by means of a recently discussed system of non-Hermitian coupled harmonic oscillators that also exhibits other types of antiunitary symmetries. We also show that a combination of group and perturbation theory is a useful tool for predicting broken antiunitary symmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08850","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":"2026-05-18T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Kovc18VFITkxQ2dNN04B3+gYi++inQjAQMieqkpUIFHcSvqXtKXCGpxhlnO6u9pb5OmRxo3c3ehwHChKeCYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:44:50.086995Z"},"content_sha256":"05087e74f0dbfb522a56e425a6ba8b8f6f96de85661814e095ab90691d77d3c6","schema_version":"1.0","event_id":"sha256:05087e74f0dbfb522a56e425a6ba8b8f6f96de85661814e095ab90691d77d3c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQ7TTL472BSRZK6VDLDA322GSV/bundle.json","state_url":"https://pith.science/pith/SQ7TTL472BSRZK6VDLDA322GSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQ7TTL472BSRZK6VDLDA322GSV/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":"2026-05-26T08:44:50Z","links":{"resolver":"https://pith.science/pith/SQ7TTL472BSRZK6VDLDA322GSV","bundle":"https://pith.science/pith/SQ7TTL472BSRZK6VDLDA322GSV/bundle.json","state":"https://pith.science/pith/SQ7TTL472BSRZK6VDLDA322GSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQ7TTL472BSRZK6VDLDA322GSV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SQ7TTL472BSRZK6VDLDA322GSV","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":"c4d6db0b223f27736f1daf1a7a25c68ed49d94c5d5248c0daebc51d85eabc61c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-31T12:18:22Z","title_canon_sha256":"6a493cb173291a8a1ed150460da10eef7a67ea5555cab67a7a9173f3dc4c1f7a"},"schema_version":"1.0","source":{"id":"1507.08850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08850","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08850v2","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08850","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"SQ7TTL472BSR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SQ7TTL472BSRZK6V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SQ7TTL47","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:05087e74f0dbfb522a56e425a6ba8b8f6f96de85661814e095ab90691d77d3c6","target":"graph","created_at":"2026-05-18T01:15:58Z","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 show that parity-time and partial parity-time symmetries are particular cases of antiunitary symmetry. This point is illustrated by means of a recently discussed system of non-Hermitian coupled harmonic oscillators that also exhibits other types of antiunitary symmetries. We also show that a combination of group and perturbation theory is a useful tool for predicting broken antiunitary symmetry.","authors_text":"Francisco M. Fern\\'andez","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-31T12:18:22Z","title":"Generalization of parity-time and partial parity-time symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08850","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":"sha256:6317d12db6a02bb3b4c5ed9e3434cac7c0f47c3930d20cfd6447efc1e2c9ab0e","target":"record","created_at":"2026-05-18T01:15:58Z","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":"c4d6db0b223f27736f1daf1a7a25c68ed49d94c5d5248c0daebc51d85eabc61c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-31T12:18:22Z","title_canon_sha256":"6a493cb173291a8a1ed150460da10eef7a67ea5555cab67a7a9173f3dc4c1f7a"},"schema_version":"1.0","source":{"id":"1507.08850","kind":"arxiv","version":2}},"canonical_sha256":"943f39af9fd0651cabd51ac60deb46955eff227a8a3611049d60d0bec7218fc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"943f39af9fd0651cabd51ac60deb46955eff227a8a3611049d60d0bec7218fc9","first_computed_at":"2026-05-18T01:15:58.397255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:58.397255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XpNxkRkBl8TsjR0Bir/lLCnHyrmAS/rqOVoOxarodl2h14mbqmn9wQmZ95t3QyaVoAFwkrOr+s0zXyLVyc9jBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:58.397890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6317d12db6a02bb3b4c5ed9e3434cac7c0f47c3930d20cfd6447efc1e2c9ab0e","sha256:05087e74f0dbfb522a56e425a6ba8b8f6f96de85661814e095ab90691d77d3c6"],"state_sha256":"4e48f98757c6a75d7a7a750ae0f4d2cbc2ea5a89545d8a58b577669163154ad3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGk4G8ioPH6HTwx47CANNIwWoYKPnex2yfoVMY4+y9x9v1w4Xj52cVYWin5tJN4H2Dh9F4D+zC/O0Iu5pCqXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:44:50.090968Z","bundle_sha256":"c383979aa7439b3a334e25ec9cdd60d00469e6556513fd63bf07a72dcd129727"}}