{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FZI53AFCSX4SCS4G6NL7PRT7ZC","short_pith_number":"pith:FZI53AFC","canonical_record":{"source":{"id":"1005.2789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-05-17T00:46:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52a6c41213566abbcb277e56313e325301fcc5dabbef7f4bb46a1b8e02c0a75d","abstract_canon_sha256":"3fcbf70ca0818059f95089a0f67bd039386f776f31dda86bb715d987e294f7e4"},"schema_version":"1.0"},"canonical_sha256":"2e51dd80a295f9214b86f357f7c67fc8a9dc91945dc25ac6896a15f9d6634c48","source":{"kind":"arxiv","id":"1005.2789","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2789","created_at":"2026-05-18T02:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2789v2","created_at":"2026-05-18T02:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2789","created_at":"2026-05-18T02:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"FZI53AFCSX4S","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FZI53AFCSX4SCS4G","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FZI53AFC","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FZI53AFCSX4SCS4G6NL7PRT7ZC","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-05-17T00:46:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52a6c41213566abbcb277e56313e325301fcc5dabbef7f4bb46a1b8e02c0a75d","abstract_canon_sha256":"3fcbf70ca0818059f95089a0f67bd039386f776f31dda86bb715d987e294f7e4"},"schema_version":"1.0"},"canonical_sha256":"2e51dd80a295f9214b86f357f7c67fc8a9dc91945dc25ac6896a15f9d6634c48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:18.467509Z","signature_b64":"o1NbM+uxb71vekPZdI7RN62JsWsyx7BzBedOCxMA9CQzh73XdYo8pH14epQENlJVGK/Ht/8x6QmHQCxW25eAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e51dd80a295f9214b86f357f7c67fc8a9dc91945dc25ac6896a15f9d6634c48","last_reissued_at":"2026-05-18T02:07:18.466899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:18.466899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2789","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLKzrroMi6II67zBY6zTUGi6oZX/VkFrUZvTfLogB1NTUmysuhuUf7NaHfvWjLy8hsmrcInPas/N+7WJgMsMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:57:52.059408Z"},"content_sha256":"6aca70bfa11e81f38bbb5b7bc7310bc27732fa515163ff6594475cba5a9b4ed3","schema_version":"1.0","event_id":"sha256:6aca70bfa11e81f38bbb5b7bc7310bc27732fa515163ff6594475cba5a9b4ed3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FZI53AFCSX4SCS4G6NL7PRT7ZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"F. Germinet, G. D. Raikov, N. Dombrowski","submitted_at":"2010-05-17T00:46:00Z","abstract_excerpt":"In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the bands in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic perturbations that split the Landau levels into full intervals of spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2789","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVoIkof7jw6bSdRsSAGYPaZI/sSD6yN1JvBwp1BzZPrAdE91D0DCBN4YkCeDcU7LQed7gBPZa5umF1b+A63lCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:57:52.059839Z"},"content_sha256":"64bff9b4281991b8617316d100d2d23f15b9cb650d5db43dd763831082189f8a","schema_version":"1.0","event_id":"sha256:64bff9b4281991b8617316d100d2d23f15b9cb650d5db43dd763831082189f8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC/bundle.json","state_url":"https://pith.science/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T22:57:52Z","links":{"resolver":"https://pith.science/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC","bundle":"https://pith.science/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC/bundle.json","state":"https://pith.science/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZI53AFCSX4SCS4G6NL7PRT7ZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FZI53AFCSX4SCS4G6NL7PRT7ZC","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":"3fcbf70ca0818059f95089a0f67bd039386f776f31dda86bb715d987e294f7e4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-05-17T00:46:00Z","title_canon_sha256":"52a6c41213566abbcb277e56313e325301fcc5dabbef7f4bb46a1b8e02c0a75d"},"schema_version":"1.0","source":{"id":"1005.2789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2789","created_at":"2026-05-18T02:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2789v2","created_at":"2026-05-18T02:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2789","created_at":"2026-05-18T02:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"FZI53AFCSX4S","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FZI53AFCSX4SCS4G","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FZI53AFC","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:64bff9b4281991b8617316d100d2d23f15b9cb650d5db43dd763831082189f8a","target":"graph","created_at":"2026-05-18T02:07:18Z","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 this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the bands in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic perturbations that split the Landau levels into full intervals of spectrum.","authors_text":"F. Germinet, G. D. Raikov, N. Dombrowski","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-05-17T00:46:00Z","title":"Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2789","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":"sha256:6aca70bfa11e81f38bbb5b7bc7310bc27732fa515163ff6594475cba5a9b4ed3","target":"record","created_at":"2026-05-18T02:07:18Z","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":"3fcbf70ca0818059f95089a0f67bd039386f776f31dda86bb715d987e294f7e4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-05-17T00:46:00Z","title_canon_sha256":"52a6c41213566abbcb277e56313e325301fcc5dabbef7f4bb46a1b8e02c0a75d"},"schema_version":"1.0","source":{"id":"1005.2789","kind":"arxiv","version":2}},"canonical_sha256":"2e51dd80a295f9214b86f357f7c67fc8a9dc91945dc25ac6896a15f9d6634c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e51dd80a295f9214b86f357f7c67fc8a9dc91945dc25ac6896a15f9d6634c48","first_computed_at":"2026-05-18T02:07:18.466899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:18.466899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o1NbM+uxb71vekPZdI7RN62JsWsyx7BzBedOCxMA9CQzh73XdYo8pH14epQENlJVGK/Ht/8x6QmHQCxW25eAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:18.467509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aca70bfa11e81f38bbb5b7bc7310bc27732fa515163ff6594475cba5a9b4ed3","sha256:64bff9b4281991b8617316d100d2d23f15b9cb650d5db43dd763831082189f8a"],"state_sha256":"7d545834d2f26e0ce015cc6a4f1977dcf21866c6c3cd833c13253681c455a398"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmb47sWEOCwy3p6zVAN34v5PnwynJAi4rZLkfRb0L9EB9YcWQM8oNeAJKRXSmHlmgnJPo34D+UyqIbWnUBPkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:57:52.061817Z","bundle_sha256":"692b926aa481242b6b9b50af0eeef3ef9f52f07696ed24769e2dfc5449649e9d"}}