{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P77LCHT6MG2VIWSSDDA6BOSU5L","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":"f17537fc2aeee1531f5c0198a99ddd04b0bea70d0766ab3e58efec839943c6d3","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T10:05:42Z","title_canon_sha256":"23c93b1572f035b2a6f59f00206e0b67eb17458a47e50da7b7bcd5f15fbdb9c0"},"schema_version":"1.0","source":{"id":"1607.00187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00187","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00187v1","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00187","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"pith_short_12","alias_value":"P77LCHT6MG2V","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"P77LCHT6MG2VIWSS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"P77LCHT6","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:8a360b33562c2d76b7e4132652552a59ae38f590d4188f68c8bb574c3c491af6","target":"graph","created_at":"2026-05-18T00:34:23Z","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 Landau Hamiltonians with a weak coupling random electric potential of breather type.\n  Under appropriate assumptions we prove a Wegner estimate.\n  It implies the Hoelder continuity of the integrated density of states.\n  The main challenge is the problem how to deal with non-linear dependence on the random parameters.","authors_text":"Ivan Veselic, Matthias T\\\"aufer","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T10:05:42Z","title":"Wegner estimate for Landau-breather Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00187","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":"sha256:03b2840af8e23f615c437c7d1bf12ed08766eda547db52e20b7790b8a3e0f46e","target":"record","created_at":"2026-05-18T00:34:23Z","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":"f17537fc2aeee1531f5c0198a99ddd04b0bea70d0766ab3e58efec839943c6d3","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T10:05:42Z","title_canon_sha256":"23c93b1572f035b2a6f59f00206e0b67eb17458a47e50da7b7bcd5f15fbdb9c0"},"schema_version":"1.0","source":{"id":"1607.00187","kind":"arxiv","version":1}},"canonical_sha256":"7ffeb11e7e61b5545a5218c1e0ba54ead39d7ad0b5ad2b3c3331dd1c5c18ef72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ffeb11e7e61b5545a5218c1e0ba54ead39d7ad0b5ad2b3c3331dd1c5c18ef72","first_computed_at":"2026-05-18T00:34:23.181690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:23.181690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nc39egCsGvRH9DeyEzsWwCsXBHKUZ0BjGnsOsysDyBSneGbIpNbLS462Ya6X8wbRJvXfkdEfezcszmH9fPGMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:23.182149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03b2840af8e23f615c437c7d1bf12ed08766eda547db52e20b7790b8a3e0f46e","sha256:8a360b33562c2d76b7e4132652552a59ae38f590d4188f68c8bb574c3c491af6"],"state_sha256":"7015da1b8ed57f7ed16817b6909ec4c22570a2377f99a27b05da76cf0927aba8"}