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We show that such composite systems have an SS at $k_{c}$ if the reflection amplitudes $r^{A}\\left( k_{c}\\right) $ and $r^{B}\\left( k_{c}\\right) $ of the two scattering centers satisfy the condition $r_{\\mathrm{R}% }^{A}\\left( k_{c}\\right) r_{\\mathrm{L}}^{B}\\left( k_{c}\\right) e^{i2k_{c}\\left( x_{B}-x_{A}\\right) }=1$. We also extend the condition to the sy"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.10238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-29T05:01:32Z","cross_cats_sorted":[],"title_canon_sha256":"cbe50892ba3279af893bd771f18b665053165db814e4e4ba3fff87a9eace27f1","abstract_canon_sha256":"f2f63137998a672089cbdedec781210362e36d71377f2fbfb27f6027cfbb5bed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:03.826653Z","signature_b64":"3uO+uYZbwcv/Y0S7Fl10fbyd5ZDDfcTLV9jIIih6H3qyW36CrMuqrRkXTfhL8g5Uo3l05cUqmhSsMX+Z6X7oBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1485bb201e97859ac8192de580cf1293d3f4ed0d9a970be4194699038b4ecb2","last_reissued_at":"2026-05-18T00:34:03.825937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:03.825937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral singularity in composite systems and simulation of a resonant lasing cavity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"G. 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