{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:THMLMTYHGFFDHBD4Y36A6ECFEW","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":"284a404c433a2972d620d2a7edfa5a61deb9b132d0455fbae79b3dc2249e1856","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-27T05:56:25Z","title_canon_sha256":"1587cedcfc96a8bf934c2f35d9c3c10a3a14f42acd55d30ff8e4693e413d6871"},"schema_version":"1.0","source":{"id":"1709.09344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09344","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09344v1","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09344","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"pith_short_12","alias_value":"THMLMTYHGFFD","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"THMLMTYHGFFDHBD4","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"THMLMTYH","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:9ea572339f5d0697b18613b00e2bc5b2f2bdae56c0dec08ddbe49b0f7e05513f","target":"graph","created_at":"2026-05-18T00:34:12Z","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":"In a seminal work, S.A.R. Horsley and collaborators [S.A.R. Horsley {\\em et al.}, Nature Photon. {\\bf 9}, 436 (2015)] have shown that, in the framework of non-Hermitian extensions of the Schr\\\"odinger and Helmholtz equations, a localized complex scattering potential with spatial distributions of the real and imaginary parts related to one another by the spatial Kramers-Kronig relations are reflectionless and even invisible under certain conditions. Here we consider the scattering properties of Kramers-Kronig potentials for the discrete version of the Schr\\\"odinger equation, which generally des","authors_text":"Stefano Longhi","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-27T05:56:25Z","title":"Kramers-Kronig potentials for the discrete Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09344","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":"sha256:98d8df3c28932404f5c24126a25d1ce4451b284202748d9b9a610ec42aacbaeb","target":"record","created_at":"2026-05-18T00:34:12Z","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":"284a404c433a2972d620d2a7edfa5a61deb9b132d0455fbae79b3dc2249e1856","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-27T05:56:25Z","title_canon_sha256":"1587cedcfc96a8bf934c2f35d9c3c10a3a14f42acd55d30ff8e4693e413d6871"},"schema_version":"1.0","source":{"id":"1709.09344","kind":"arxiv","version":1}},"canonical_sha256":"99d8b64f07314a33847cc6fc0f104525b9f3ae63fc9eb9751d8132e279ca3ac6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99d8b64f07314a33847cc6fc0f104525b9f3ae63fc9eb9751d8132e279ca3ac6","first_computed_at":"2026-05-18T00:34:12.133889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:12.133889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlkZl6L14JEw3+fqpGV2J2LVAXoWEn5p6t1fPjEqdy2s8XEGxej8xUuKkVSxWw54dhIBGs2e7FQtVUr4WL0MBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:12.134431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98d8df3c28932404f5c24126a25d1ce4451b284202748d9b9a610ec42aacbaeb","sha256:9ea572339f5d0697b18613b00e2bc5b2f2bdae56c0dec08ddbe49b0f7e05513f"],"state_sha256":"f0f7b9bc515ab81ce950d215bd117913e7b112b9c8b10ec91e8746891e935538"}