{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:PSWOUUKGUOJ5U7RHKWATGRYNI5","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":"e491855e5d66f23dec347c9eaa5eeed82091a7acb04864db42522f957499089d","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-09-12T15:22:18Z","title_canon_sha256":"acd5f2875935bbad7060fb98a8a8319ed731795dd4897a41e690dadd1cacfa32"},"schema_version":"1.0","source":{"id":"math-ph/0509022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0509022","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0509022v1","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0509022","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"PSWOUUKGUOJ5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"PSWOUUKGUOJ5U7RH","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"PSWOUUKG","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:bf021513fb71e5561b623cec5eb5fecdbe3f2dd0e05592a32351821e284197ec","target":"graph","created_at":"2026-05-18T01:08:51Z","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 consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a the","authors_text":"Fr\\'ed\\'eric Klopp (LAGA), Georgi Raikov","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-09-12T15:22:18Z","title":"Lifshitz Tails in Constant Magnetic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0509022","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":"sha256:434cfa2b8856d1ee29f4a65721b790a4a6eabf97bf359f475bdf32aabed610eb","target":"record","created_at":"2026-05-18T01:08:51Z","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":"e491855e5d66f23dec347c9eaa5eeed82091a7acb04864db42522f957499089d","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-09-12T15:22:18Z","title_canon_sha256":"acd5f2875935bbad7060fb98a8a8319ed731795dd4897a41e690dadd1cacfa32"},"schema_version":"1.0","source":{"id":"math-ph/0509022","kind":"arxiv","version":1}},"canonical_sha256":"7cacea5146a393da7e27558133470d4772d8e8ee6f1d00fba7b0b31a347bd188","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cacea5146a393da7e27558133470d4772d8e8ee6f1d00fba7b0b31a347bd188","first_computed_at":"2026-05-18T01:08:51.742202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:51.742202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1v4qyNiY3GtRnIuoAxbebg++OlzpSMI48xPESSGoDdnGCfrh1y4goWxgVyGRgqNkzjR2futTy59P6XzfVf1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:51.742764Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0509022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:434cfa2b8856d1ee29f4a65721b790a4a6eabf97bf359f475bdf32aabed610eb","sha256:bf021513fb71e5561b623cec5eb5fecdbe3f2dd0e05592a32351821e284197ec"],"state_sha256":"aae3fc1cc59c3a2546bc7b15209a5ba805d39b1d9254f49bf5b0e0907e64e306"}