{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:U6JSNWSSEW73WGIELKN2THWTZI","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":"3701e632a22d600584fdeba418d7ff887bf8bd77b4210c853795ec1915f3723d","cross_cats_sorted":["cs.NA","math.MP","math.NA","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-08-05T18:54:46Z","title_canon_sha256":"dbbc39edf181d0654818e108acdfb0eea83bff6f92add5cf8025e0b4d8680f85"},"schema_version":"1.0","source":{"id":"2608.05338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05338","created_at":"2026-08-07T00:47:02Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05338v1","created_at":"2026-08-07T00:47:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05338","created_at":"2026-08-07T00:47:02Z"},{"alias_kind":"pith_short_12","alias_value":"U6JSNWSSEW73","created_at":"2026-08-07T00:47:02Z"},{"alias_kind":"pith_short_16","alias_value":"U6JSNWSSEW73WGIE","created_at":"2026-08-07T00:47:02Z"},{"alias_kind":"pith_short_8","alias_value":"U6JSNWSS","created_at":"2026-08-07T00:47:02Z"}],"graph_snapshots":[{"event_id":"sha256:7f7e9881d5304138c34075a7035500c1e45bd9ecfd63d8bb1b9e6ac679c408cb","target":"graph","created_at":"2026-08-07T00:47:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.05338/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct exact transparent boundary conditions (TBCs) for a time-continuous, spatially discrete Schr\\\"odinger equation that models a one-dimensional quantum lattice. Using a recently developed exact solution for the discrete system, we derive the Dirichlet-to-Neumann maps analytically via Laplace transforms. This yields a convolution-type boundary condition governed by Bessel functions. We rigorously demonstrate the consistency of this discrete formulation with its continuous counterpart in the continuum limit. Additionally, we present an efficient time-discretization scheme based on the t","authors_text":"Davron U. Matrasulov, Jambul R. Yusupov, Mashrab E. Akramov, Matthias Ehrhardt","cross_cats":["cs.NA","math.MP","math.NA","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-08-05T18:54:46Z","title":"Transparent boundary conditions for the spatially discrete Schr\\\"odinger equation: Reflectionless quantum transport in 1D lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05338","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":"sha256:71457fb0bba39610d4c07d9ab5b279b46baac28ef5fb831a5e4af3db41f29ed1","target":"record","created_at":"2026-08-07T00:47:02Z","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":"3701e632a22d600584fdeba418d7ff887bf8bd77b4210c853795ec1915f3723d","cross_cats_sorted":["cs.NA","math.MP","math.NA","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-08-05T18:54:46Z","title_canon_sha256":"dbbc39edf181d0654818e108acdfb0eea83bff6f92add5cf8025e0b4d8680f85"},"schema_version":"1.0","source":{"id":"2608.05338","kind":"arxiv","version":1}},"canonical_sha256":"a79326da5225bfbb19045a9ba99ed3ca05a44c2aa68f73d52ae5dbf30df59cb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a79326da5225bfbb19045a9ba99ed3ca05a44c2aa68f73d52ae5dbf30df59cb7","first_computed_at":"2026-08-07T00:47:02.249727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T00:47:02.249727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VcLHtyjelZgoykPcmPCZh7D1Ep49rxmSmKcpHzePhOm/LAnGwRSqG4ppthHAWz7FlG9plspojtAi6Sqs0c4tCw==","signature_status":"signed_v1","signed_at":"2026-08-07T00:47:02.251160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.05338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71457fb0bba39610d4c07d9ab5b279b46baac28ef5fb831a5e4af3db41f29ed1","sha256:7f7e9881d5304138c34075a7035500c1e45bd9ecfd63d8bb1b9e6ac679c408cb"],"state_sha256":"0569b70214c6e79e0cfc205ee493e4646e4c4dcaed21a3be39645d5841f4cd99"}