{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RGWD3KRDHCXY6Q6L5S47HDXC5N","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":"fe874d8efeafdc858e9e7072c4ae089a0bd8397789909514d9b6c88ae38dc10c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-09T00:18:54Z","title_canon_sha256":"86f936a998e92e2fbb18945f43adf4a498b99379a34e9c7520a355659ca72df8"},"schema_version":"1.0","source":{"id":"1409.3624","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3624","created_at":"2026-05-18T01:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3624v2","created_at":"2026-05-18T01:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3624","created_at":"2026-05-18T01:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"RGWD3KRDHCXY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RGWD3KRDHCXY6Q6L","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RGWD3KRD","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:3bbd10e50a9fb62e4dfc168f764f37079568496f4213552b5753a8ff550c0a70","target":"graph","created_at":"2026-05-18T01:59:38Z","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 analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of weak static field the spectrum is shown to be a superposition of two Wannier-Stark ladders originated from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions which describe the rearrangement employing the analogy between the Wannier-Stark problem and the driven two-level system in the strong-coupling regime.","authors_text":"A.R. Kolovsky, D.N. Maksimov, E.N. Bulgakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-09T00:18:54Z","title":"Wannier-Stark states in double-periodic lattices I: one-dimensional lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3624","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:ac9a4b547aec64c063bb2a34bcd868b30ac137e43139b89eb1e22c765685e436","target":"record","created_at":"2026-05-18T01:59:38Z","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":"fe874d8efeafdc858e9e7072c4ae089a0bd8397789909514d9b6c88ae38dc10c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-09T00:18:54Z","title_canon_sha256":"86f936a998e92e2fbb18945f43adf4a498b99379a34e9c7520a355659ca72df8"},"schema_version":"1.0","source":{"id":"1409.3624","kind":"arxiv","version":2}},"canonical_sha256":"89ac3daa2338af8f43cbecb9f38ee2eb4cac1a6c9584e6aec0637480fef1a4ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89ac3daa2338af8f43cbecb9f38ee2eb4cac1a6c9584e6aec0637480fef1a4ca","first_computed_at":"2026-05-18T01:59:38.544950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:38.544950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6wnOiyZslJh3y0Uwc5sPoDILHB3+yZIfv7aGe+IyEf3gq5n6+hCjLQmOuuTgfRXF+9lbhJz4nIYWkZo1Agu1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:38.545599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3624","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac9a4b547aec64c063bb2a34bcd868b30ac137e43139b89eb1e22c765685e436","sha256:3bbd10e50a9fb62e4dfc168f764f37079568496f4213552b5753a8ff550c0a70"],"state_sha256":"d5db8c79aaf7022196956baf9fc309d51980d3a5fa8dcb08d847b5916598b5e2"}