{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:W2V5UEGARBZU4ZKKUZDZFGE2O2","short_pith_number":"pith:W2V5UEGA","canonical_record":{"source":{"id":"1102.4695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-23T09:27:26Z","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"title_canon_sha256":"e2ecbf967b340c399d4c5918849a2e8b5984e4f458016e9cc2c8b913bf7fe95c","abstract_canon_sha256":"dba415c9f11e94208323900045fe062663539fb59fa0d52cfaea58954c4a21b1"},"schema_version":"1.0"},"canonical_sha256":"b6abda10c088734e654aa64792989a768ead4c2f96ebe39d485f833db2cc4ea0","source":{"kind":"arxiv","id":"1102.4695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4695","created_at":"2026-05-18T04:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4695v1","created_at":"2026-05-18T04:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4695","created_at":"2026-05-18T04:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"W2V5UEGARBZU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"W2V5UEGARBZU4ZKK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"W2V5UEGA","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:W2V5UEGARBZU4ZKKUZDZFGE2O2","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-23T09:27:26Z","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"title_canon_sha256":"e2ecbf967b340c399d4c5918849a2e8b5984e4f458016e9cc2c8b913bf7fe95c","abstract_canon_sha256":"dba415c9f11e94208323900045fe062663539fb59fa0d52cfaea58954c4a21b1"},"schema_version":"1.0"},"canonical_sha256":"b6abda10c088734e654aa64792989a768ead4c2f96ebe39d485f833db2cc4ea0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:56.859827Z","signature_b64":"dtZ6r2qhw7nTotK1XHE08+91Wx2ek9LQYQobVwxsPXh2GQwqpvWsqZnBYxoitKc0Sw2w2PE4Gv6COsQpAY3GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6abda10c088734e654aa64792989a768ead4c2f96ebe39d485f833db2cc4ea0","last_reissued_at":"2026-05-18T04:10:56.859130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:56.859130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4695","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":"2026-05-18T04:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03VoDlhN+olfuTP1QOHBamzY4uTd2RpBWFtyZfHzFanBsZVtdJqMOJhxvPcnKr48GnhEZ3vL6sujyjW0jWjLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:57:27.270165Z"},"content_sha256":"72ae05361e48c3f072cb94479e75b110f72c548f2873a4502840562482f8dffe","schema_version":"1.0","event_id":"sha256:72ae05361e48c3f072cb94479e75b110f72c548f2873a4502840562482f8dffe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:W2V5UEGARBZU4ZKKUZDZFGE2O2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optical Spectral Singularities as Threshold Resonances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","quant-ph"],"primary_cat":"physics.optics","authors_text":"Ali Mostafazadeh","submitted_at":"2011-02-23T09:27:26Z","abstract_excerpt":"Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral singularity appears whenever the gain coefficient coincides with its threshold value and other parameters of the system are selected properly. We explore a concrete realization of spectral singularities for a typical semiconductor gain medium and propose a method of constructing a tunable laser that operates at threshold gain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4695","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":"2026-05-18T04:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7UmOMd1wh+eSMEo4YSyUGp/8D/zAf9r2uzK9c1ofKVEOhUrv0aJCtuALkRa2vEcjemawlCSpHh0qQhway8zqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:57:27.270532Z"},"content_sha256":"f717a956c3157c904b01a0ab9ca08f0350da579db093b0bfc3aeaa8c21f38140","schema_version":"1.0","event_id":"sha256:f717a956c3157c904b01a0ab9ca08f0350da579db093b0bfc3aeaa8c21f38140"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2/bundle.json","state_url":"https://pith.science/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2/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":"2026-05-28T04:57:27Z","links":{"resolver":"https://pith.science/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2","bundle":"https://pith.science/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2/bundle.json","state":"https://pith.science/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2V5UEGARBZU4ZKKUZDZFGE2O2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:W2V5UEGARBZU4ZKKUZDZFGE2O2","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":"dba415c9f11e94208323900045fe062663539fb59fa0d52cfaea58954c4a21b1","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-23T09:27:26Z","title_canon_sha256":"e2ecbf967b340c399d4c5918849a2e8b5984e4f458016e9cc2c8b913bf7fe95c"},"schema_version":"1.0","source":{"id":"1102.4695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4695","created_at":"2026-05-18T04:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4695v1","created_at":"2026-05-18T04:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4695","created_at":"2026-05-18T04:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"W2V5UEGARBZU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"W2V5UEGARBZU4ZKK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"W2V5UEGA","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:f717a956c3157c904b01a0ab9ca08f0350da579db093b0bfc3aeaa8c21f38140","target":"graph","created_at":"2026-05-18T04:10:56Z","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":"Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral singularity appears whenever the gain coefficient coincides with its threshold value and other parameters of the system are selected properly. We explore a concrete realization of spectral singularities for a typical semiconductor gain medium and propose a method of constructing a tunable laser that operates at threshold gain.","authors_text":"Ali Mostafazadeh","cross_cats":["hep-th","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-23T09:27:26Z","title":"Optical Spectral Singularities as Threshold Resonances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4695","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":"sha256:72ae05361e48c3f072cb94479e75b110f72c548f2873a4502840562482f8dffe","target":"record","created_at":"2026-05-18T04:10:56Z","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":"dba415c9f11e94208323900045fe062663539fb59fa0d52cfaea58954c4a21b1","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-23T09:27:26Z","title_canon_sha256":"e2ecbf967b340c399d4c5918849a2e8b5984e4f458016e9cc2c8b913bf7fe95c"},"schema_version":"1.0","source":{"id":"1102.4695","kind":"arxiv","version":1}},"canonical_sha256":"b6abda10c088734e654aa64792989a768ead4c2f96ebe39d485f833db2cc4ea0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6abda10c088734e654aa64792989a768ead4c2f96ebe39d485f833db2cc4ea0","first_computed_at":"2026-05-18T04:10:56.859130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:56.859130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dtZ6r2qhw7nTotK1XHE08+91Wx2ek9LQYQobVwxsPXh2GQwqpvWsqZnBYxoitKc0Sw2w2PE4Gv6COsQpAY3GAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:56.859827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72ae05361e48c3f072cb94479e75b110f72c548f2873a4502840562482f8dffe","sha256:f717a956c3157c904b01a0ab9ca08f0350da579db093b0bfc3aeaa8c21f38140"],"state_sha256":"46d642a8b1f2112de00880b5690ece12a42e6ee97e6be77e558a311a7a0ddf75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"POUnXrgfnevnd1RypWfht9+kK0Rw5/2qlzjaDm3851Bo/yXsVlP0LeiZ0x6tlXcpn99q3eaEtYolYfWbit5DCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:57:27.274061Z","bundle_sha256":"fac03e124ab5fe7a1acaa70d52a45749e5aa0adf107f09fb85844cbd10f5ef85"}}