{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SWBMHUQA5ODIVLBQBIXX4YWDUN","short_pith_number":"pith:SWBMHUQA","canonical_record":{"source":{"id":"1208.2575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-13T13:11:32Z","cross_cats_sorted":["cond-mat.dis-nn","physics.optics"],"title_canon_sha256":"ead7c45162cf4fcb65adc4522747c6fb630434edd61ccc562184d964e4f71484","abstract_canon_sha256":"f3f3be30e4203e85766c36924a5e1c71c34aba5c8f55b9ff5570fe74b2848453"},"schema_version":"1.0"},"canonical_sha256":"9582c3d200eb868aac300a2f7e62c3a34c8a40e719be99c3d23c024334391438","source":{"kind":"arxiv","id":"1208.2575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2575","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2575v1","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2575","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"SWBMHUQA5ODI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SWBMHUQA5ODIVLBQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SWBMHUQA","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SWBMHUQA5ODIVLBQBIXX4YWDUN","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-13T13:11:32Z","cross_cats_sorted":["cond-mat.dis-nn","physics.optics"],"title_canon_sha256":"ead7c45162cf4fcb65adc4522747c6fb630434edd61ccc562184d964e4f71484","abstract_canon_sha256":"f3f3be30e4203e85766c36924a5e1c71c34aba5c8f55b9ff5570fe74b2848453"},"schema_version":"1.0"},"canonical_sha256":"9582c3d200eb868aac300a2f7e62c3a34c8a40e719be99c3d23c024334391438","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:04.863228Z","signature_b64":"TLibBufAdlFtwRqUocWd6xv35v5LuJDIqKnga9j3re52mYKp7Q03DK86GuOn/aaL92SRlTlPv3goD4l3/VIcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9582c3d200eb868aac300a2f7e62c3a34c8a40e719be99c3d23c024334391438","last_reissued_at":"2026-05-18T03:38:04.862795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:04.862795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2575","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":"2026-05-18T03:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3Vxyghdxi9T5mDNyMer9bPVQJ2+3irTC7Ll6X4aZIFRRkW4ynvQOB+KkqdeObYaSc24F0LMNq+WqjFYyOxZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:09:11.156956Z"},"content_sha256":"932cc49afdbbd801a185d32a7efda2e28cff8f0ff1b81fa9c1b59835bdef9127","schema_version":"1.0","event_id":"sha256:932cc49afdbbd801a185d32a7efda2e28cff8f0ff1b81fa9c1b59835bdef9127"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SWBMHUQA5ODIVLBQBIXX4YWDUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","physics.optics"],"primary_cat":"quant-ph","authors_text":"Christopher Birchall, Henning Schomerus","submitted_at":"2012-08-13T13:11:32Z","abstract_excerpt":"We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a PT or a PTT' time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2575","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":"2026-05-18T03:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPUNQn+LokIDo+8nS/4rp/K28bBcyqIILEsNNL+s1+d6WHMWBeJQ1VYUyRb6Qtb25aIZGPp74OWHFeHgV90fCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:09:11.157711Z"},"content_sha256":"b5f471d5de8d831b61904e1d4f8ea1d797a39c8206a5c46b9e1ec3b4a09814e4","schema_version":"1.0","event_id":"sha256:b5f471d5de8d831b61904e1d4f8ea1d797a39c8206a5c46b9e1ec3b4a09814e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN/bundle.json","state_url":"https://pith.science/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN/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":"2026-05-28T22:09:11Z","links":{"resolver":"https://pith.science/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN","bundle":"https://pith.science/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN/bundle.json","state":"https://pith.science/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWBMHUQA5ODIVLBQBIXX4YWDUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SWBMHUQA5ODIVLBQBIXX4YWDUN","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":"f3f3be30e4203e85766c36924a5e1c71c34aba5c8f55b9ff5570fe74b2848453","cross_cats_sorted":["cond-mat.dis-nn","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-13T13:11:32Z","title_canon_sha256":"ead7c45162cf4fcb65adc4522747c6fb630434edd61ccc562184d964e4f71484"},"schema_version":"1.0","source":{"id":"1208.2575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2575","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2575v1","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2575","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"SWBMHUQA5ODI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SWBMHUQA5ODIVLBQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SWBMHUQA","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:b5f471d5de8d831b61904e1d4f8ea1d797a39c8206a5c46b9e1ec3b4a09814e4","target":"graph","created_at":"2026-05-18T03:38:04Z","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 formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a PT or a PTT' time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues ","authors_text":"Christopher Birchall, Henning Schomerus","cross_cats":["cond-mat.dis-nn","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-13T13:11:32Z","title":"Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2575","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":"sha256:932cc49afdbbd801a185d32a7efda2e28cff8f0ff1b81fa9c1b59835bdef9127","target":"record","created_at":"2026-05-18T03:38:04Z","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":"f3f3be30e4203e85766c36924a5e1c71c34aba5c8f55b9ff5570fe74b2848453","cross_cats_sorted":["cond-mat.dis-nn","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-08-13T13:11:32Z","title_canon_sha256":"ead7c45162cf4fcb65adc4522747c6fb630434edd61ccc562184d964e4f71484"},"schema_version":"1.0","source":{"id":"1208.2575","kind":"arxiv","version":1}},"canonical_sha256":"9582c3d200eb868aac300a2f7e62c3a34c8a40e719be99c3d23c024334391438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9582c3d200eb868aac300a2f7e62c3a34c8a40e719be99c3d23c024334391438","first_computed_at":"2026-05-18T03:38:04.862795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:04.862795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TLibBufAdlFtwRqUocWd6xv35v5LuJDIqKnga9j3re52mYKp7Q03DK86GuOn/aaL92SRlTlPv3goD4l3/VIcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:04.863228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:932cc49afdbbd801a185d32a7efda2e28cff8f0ff1b81fa9c1b59835bdef9127","sha256:b5f471d5de8d831b61904e1d4f8ea1d797a39c8206a5c46b9e1ec3b4a09814e4"],"state_sha256":"5b4b63d2fd007962278539b9af2f1525fcb33dc96b3174d6cddb28555e1a2d5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZwMCFiZeEBXKLyA+uH2ch0/nuePTvGDNKX5JtIQ+lXOKQruww1hSFEzgpshQNffJew7Y4DQHAftuTAVMdypAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:09:11.161779Z","bundle_sha256":"2010ee9dcbd1f1a534f4615b1a80c2bb425b29ad2f29ceeddc3d07c9b9137dc3"}}