{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HYEBBAMLELGKSZF65CCFG4IOGC","short_pith_number":"pith:HYEBBAML","canonical_record":{"source":{"id":"1307.1844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-07T10:00:47Z","cross_cats_sorted":["math-ph","math.MP","physics.optics"],"title_canon_sha256":"bd86701d49d41e423a4f9b1829945cf700e36f7fe4815dac0b5256dc8d7fbd19","abstract_canon_sha256":"0f2e1c24930410ebac8273b2ccb481d94e09efb16fbfcef40962b93c5e6918fe"},"schema_version":"1.0"},"canonical_sha256":"3e0810818b22cca964bee88453710e30836bf0af23ea0478388eba636f975420","source":{"kind":"arxiv","id":"1307.1844","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1844","created_at":"2026-05-18T01:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1844v2","created_at":"2026-05-18T01:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1844","created_at":"2026-05-18T01:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"HYEBBAMLELGK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HYEBBAMLELGKSZF6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HYEBBAML","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HYEBBAMLELGKSZF65CCFG4IOGC","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-07T10:00:47Z","cross_cats_sorted":["math-ph","math.MP","physics.optics"],"title_canon_sha256":"bd86701d49d41e423a4f9b1829945cf700e36f7fe4815dac0b5256dc8d7fbd19","abstract_canon_sha256":"0f2e1c24930410ebac8273b2ccb481d94e09efb16fbfcef40962b93c5e6918fe"},"schema_version":"1.0"},"canonical_sha256":"3e0810818b22cca964bee88453710e30836bf0af23ea0478388eba636f975420","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:59.040087Z","signature_b64":"s7hoLtNT+MokM5zN/K0Cis5GQJWgg0yrlxXboUREyQbmMWq8b33bUjWABLPLtdnrFb143BW5AKvdHBwjhV1xCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e0810818b22cca964bee88453710e30836bf0af23ea0478388eba636f975420","last_reissued_at":"2026-05-18T01:48:59.039591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:59.039591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1844","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":"2026-05-18T01:48:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aWdnSSFii7Ab5oxM6xAxFbDvZ/R83KAgBUPHBELNwnAfjSJX9fph1YMD68pT+jZPseAU/3nbmDvWPqojPjOMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:49:58.344235Z"},"content_sha256":"4c3b9d238c8d9a63631326cc8cc734be0e3c532822ac9f49b4e5aa5e6f2545e2","schema_version":"1.0","event_id":"sha256:4c3b9d238c8d9a63631326cc8cc734be0e3c532822ac9f49b4e5aa5e6f2545e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HYEBBAMLELGKSZF65CCFG4IOGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Singularity in confined PT symmetric optical potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"quant-ph","authors_text":"Anjana Sinha, R. Roychoudhury","submitted_at":"2013-07-07T10:00:47Z","abstract_excerpt":"We present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\\cal{PT}}$ symmetric optical potential $ V(x) = \\displaystyle W_0 \\left( \\cos ^2 x + i V_0 \\sin 2x \\right) $ confined within the region $0 \\leq x \\leq L$, embedded in a homogeneous medium having uniform potential $W_0$. The confining length $L$ is considered to be some integral multiple of the period $ \\pi $. We give some new and interesting results. Scattering is observed to be normal ($|T| ^2 \\leq 1, \\ |R|^2 \\leq 1$) for $V_0 \\leq 0.5 $, when the above potential can be ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1844","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":"2026-05-18T01:48:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fk2PgbqvXXZ2JJYwxxPWaCyVSzBoCTChX+Gelb4JtjZDWEPnANyx8cdYWY4u9yRzN7kmMn2cLGRI+6VqQGIUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:49:58.344601Z"},"content_sha256":"1eb681d7925e9ed04ef357a24c7a405f6ec16aea4a4adab853faa128127979da","schema_version":"1.0","event_id":"sha256:1eb681d7925e9ed04ef357a24c7a405f6ec16aea4a4adab853faa128127979da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYEBBAMLELGKSZF65CCFG4IOGC/bundle.json","state_url":"https://pith.science/pith/HYEBBAMLELGKSZF65CCFG4IOGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYEBBAMLELGKSZF65CCFG4IOGC/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":"2026-06-23T13:49:58Z","links":{"resolver":"https://pith.science/pith/HYEBBAMLELGKSZF65CCFG4IOGC","bundle":"https://pith.science/pith/HYEBBAMLELGKSZF65CCFG4IOGC/bundle.json","state":"https://pith.science/pith/HYEBBAMLELGKSZF65CCFG4IOGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYEBBAMLELGKSZF65CCFG4IOGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HYEBBAMLELGKSZF65CCFG4IOGC","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":"0f2e1c24930410ebac8273b2ccb481d94e09efb16fbfcef40962b93c5e6918fe","cross_cats_sorted":["math-ph","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-07T10:00:47Z","title_canon_sha256":"bd86701d49d41e423a4f9b1829945cf700e36f7fe4815dac0b5256dc8d7fbd19"},"schema_version":"1.0","source":{"id":"1307.1844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1844","created_at":"2026-05-18T01:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1844v2","created_at":"2026-05-18T01:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1844","created_at":"2026-05-18T01:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"HYEBBAMLELGK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HYEBBAMLELGKSZF6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HYEBBAML","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:1eb681d7925e9ed04ef357a24c7a405f6ec16aea4a4adab853faa128127979da","target":"graph","created_at":"2026-05-18T01:48:59Z","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 present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\\cal{PT}}$ symmetric optical potential $ V(x) = \\displaystyle W_0 \\left( \\cos ^2 x + i V_0 \\sin 2x \\right) $ confined within the region $0 \\leq x \\leq L$, embedded in a homogeneous medium having uniform potential $W_0$. The confining length $L$ is considered to be some integral multiple of the period $ \\pi $. We give some new and interesting results. Scattering is observed to be normal ($|T| ^2 \\leq 1, \\ |R|^2 \\leq 1$) for $V_0 \\leq 0.5 $, when the above potential can be ma","authors_text":"Anjana Sinha, R. Roychoudhury","cross_cats":["math-ph","math.MP","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-07T10:00:47Z","title":"Spectral Singularity in confined PT symmetric optical potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1844","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":"sha256:4c3b9d238c8d9a63631326cc8cc734be0e3c532822ac9f49b4e5aa5e6f2545e2","target":"record","created_at":"2026-05-18T01:48:59Z","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":"0f2e1c24930410ebac8273b2ccb481d94e09efb16fbfcef40962b93c5e6918fe","cross_cats_sorted":["math-ph","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-07T10:00:47Z","title_canon_sha256":"bd86701d49d41e423a4f9b1829945cf700e36f7fe4815dac0b5256dc8d7fbd19"},"schema_version":"1.0","source":{"id":"1307.1844","kind":"arxiv","version":2}},"canonical_sha256":"3e0810818b22cca964bee88453710e30836bf0af23ea0478388eba636f975420","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0810818b22cca964bee88453710e30836bf0af23ea0478388eba636f975420","first_computed_at":"2026-05-18T01:48:59.039591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:59.039591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s7hoLtNT+MokM5zN/K0Cis5GQJWgg0yrlxXboUREyQbmMWq8b33bUjWABLPLtdnrFb143BW5AKvdHBwjhV1xCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:59.040087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c3b9d238c8d9a63631326cc8cc734be0e3c532822ac9f49b4e5aa5e6f2545e2","sha256:1eb681d7925e9ed04ef357a24c7a405f6ec16aea4a4adab853faa128127979da"],"state_sha256":"37d57bc74111139d2c92b3f65c4958a730f60b2928ab82f6510eb1f3f98602e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fT4hE9nIQxJqnU3xSI1xazId8IT9c3HKNIsO2hNIKcxAw/vqTxWk4XfFvdgCX0wdrGA5Wa/F5aLT1b3lOrplDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:49:58.346635Z","bundle_sha256":"393222e30ec95b5cb29a0efaef50f7efa7e20fc7e0c6c5ab52a3e83dd48603de"}}