{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ODPVB6VWEKBPL5ABRNQTZMRYMD","short_pith_number":"pith:ODPVB6VW","canonical_record":{"source":{"id":"math-ph/0701042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2007-01-14T10:00:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b85902d6669ed1379c0fb6ec6eb7a5fcaa332a063fa42c04e0d0acf5f8148146","abstract_canon_sha256":"69b5505b11a983e2d1b132c59e73f00da08857033d0f50979a035c08b998cbe0"},"schema_version":"1.0"},"canonical_sha256":"70df50fab62282f5f4018b613cb23860f62a644485ec32512f1578533c5e884c","source":{"kind":"arxiv","id":"math-ph/0701042","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0701042","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0701042v2","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0701042","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"ODPVB6VWEKBP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ODPVB6VWEKBPL5AB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ODPVB6VW","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ODPVB6VWEKBPL5ABRNQTZMRYMD","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0701042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2007-01-14T10:00:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b85902d6669ed1379c0fb6ec6eb7a5fcaa332a063fa42c04e0d0acf5f8148146","abstract_canon_sha256":"69b5505b11a983e2d1b132c59e73f00da08857033d0f50979a035c08b998cbe0"},"schema_version":"1.0"},"canonical_sha256":"70df50fab62282f5f4018b613cb23860f62a644485ec32512f1578533c5e884c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:05.614576Z","signature_b64":"/PpdgyYdn64gfBd1RQq2PKzhcPBqg7nBg0qj3hqkMlW42C1657U6CXi/CwCaTUtVvhfaodKUNgf2fN08J0XCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70df50fab62282f5f4018b613cb23860f62a644485ec32512f1578533c5e884c","last_reissued_at":"2026-05-18T03:43:05.613957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:05.613957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0701042","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":"2026-05-18T03:43:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Zhrldp/LKkwcR28y5qn09QV0e+is/Gh919mhd8csV1acKmEVWEMBbllNX5iFv0uFpTBzBwNf2Pq1H1nVopVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:51:01.328361Z"},"content_sha256":"ff59fbf349471f4678bf9d32e88523dd43e6e81c4474d0856074fc18f2dcea4d","schema_version":"1.0","event_id":"sha256:ff59fbf349471f4678bf9d32e88523dd43e6e81c4474d0856074fc18f2dcea4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ODPVB6VWEKBPL5ABRNQTZMRYMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of localization centers in some discrete random systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fumihiko Nakano","submitted_at":"2007-01-14T10:00:12Z","abstract_excerpt":"As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the Anderson model, we show that, this point process in the natural scaling limit converges in distribution to the Poisson process on the product space of energy and space. In other models with suitable Wegner-type bounds, we can at least show that any limiting point processes are infinitely divisible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0701042","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":"2026-05-18T03:43:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KXkCQU7vNLw3Kus1sZrWF//xnV+P4kzI7mAGfYCIRJDn+42SIMfxKy5wmSZNPlCUTyO/GIxQMrMsxQA6johnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:51:01.328722Z"},"content_sha256":"2099efd713a75c347d8b3b36f9d7390003e64cbbdb2e0d32e109901f0ff4fb57","schema_version":"1.0","event_id":"sha256:2099efd713a75c347d8b3b36f9d7390003e64cbbdb2e0d32e109901f0ff4fb57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD/bundle.json","state_url":"https://pith.science/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD/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":"2026-06-27T06:51:01Z","links":{"resolver":"https://pith.science/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD","bundle":"https://pith.science/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD/bundle.json","state":"https://pith.science/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODPVB6VWEKBPL5ABRNQTZMRYMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ODPVB6VWEKBPL5ABRNQTZMRYMD","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":"69b5505b11a983e2d1b132c59e73f00da08857033d0f50979a035c08b998cbe0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2007-01-14T10:00:12Z","title_canon_sha256":"b85902d6669ed1379c0fb6ec6eb7a5fcaa332a063fa42c04e0d0acf5f8148146"},"schema_version":"1.0","source":{"id":"math-ph/0701042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0701042","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0701042v2","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0701042","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"ODPVB6VWEKBP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ODPVB6VWEKBPL5AB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ODPVB6VW","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:2099efd713a75c347d8b3b36f9d7390003e64cbbdb2e0d32e109901f0ff4fb57","target":"graph","created_at":"2026-05-18T03:43:05Z","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":"As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the Anderson model, we show that, this point process in the natural scaling limit converges in distribution to the Poisson process on the product space of energy and space. In other models with suitable Wegner-type bounds, we can at least show that any limiting point processes are infinitely divisible.","authors_text":"Fumihiko Nakano","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2007-01-14T10:00:12Z","title":"The distribution of localization centers in some discrete random systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0701042","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:ff59fbf349471f4678bf9d32e88523dd43e6e81c4474d0856074fc18f2dcea4d","target":"record","created_at":"2026-05-18T03:43:05Z","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":"69b5505b11a983e2d1b132c59e73f00da08857033d0f50979a035c08b998cbe0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2007-01-14T10:00:12Z","title_canon_sha256":"b85902d6669ed1379c0fb6ec6eb7a5fcaa332a063fa42c04e0d0acf5f8148146"},"schema_version":"1.0","source":{"id":"math-ph/0701042","kind":"arxiv","version":2}},"canonical_sha256":"70df50fab62282f5f4018b613cb23860f62a644485ec32512f1578533c5e884c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70df50fab62282f5f4018b613cb23860f62a644485ec32512f1578533c5e884c","first_computed_at":"2026-05-18T03:43:05.613957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:05.613957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/PpdgyYdn64gfBd1RQq2PKzhcPBqg7nBg0qj3hqkMlW42C1657U6CXi/CwCaTUtVvhfaodKUNgf2fN08J0XCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:05.614576Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0701042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff59fbf349471f4678bf9d32e88523dd43e6e81c4474d0856074fc18f2dcea4d","sha256:2099efd713a75c347d8b3b36f9d7390003e64cbbdb2e0d32e109901f0ff4fb57"],"state_sha256":"05aec9ec67469c6dc28cc4ccae5a4f2a80eb6b5849091e5910c3d687d957a7de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0C0v1mHurPIzJ+9JgHpbKUVhSpK6biF7UrK/cjs9clxqhecysk3JfCsNRPI7CGMbeFwlx2ZFdHG1CcrxHuMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:51:01.330665Z","bundle_sha256":"b8126c72761f0e534531f7000f803705405aa4b66efcd7fbbaa458552a5fb68a"}}