{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:G6KMCMKXVJWGATLED7TGOH3EQM","short_pith_number":"pith:G6KMCMKX","canonical_record":{"source":{"id":"1506.06692","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-22T17:23:33Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP","math.PR"],"title_canon_sha256":"4fbe362306c3b0f9ed8fbf9143ee5e7dff251be76e798a15bf4e043243443025","abstract_canon_sha256":"113d7c08deefca139f0a9b17aec262f6a4fa18e1c166e0d9b590f6a52bc2b4e2"},"schema_version":"1.0"},"canonical_sha256":"3794c13157aa6c604d641fe6671f6483007b8ec533ef252fd7b808c53c38b8c3","source":{"kind":"arxiv","id":"1506.06692","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06692","created_at":"2026-05-18T01:18:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06692v3","created_at":"2026-05-18T01:18:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06692","created_at":"2026-05-18T01:18:44Z"},{"alias_kind":"pith_short_12","alias_value":"G6KMCMKXVJWG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G6KMCMKXVJWGATLE","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G6KMCMKX","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:G6KMCMKXVJWGATLED7TGOH3EQM","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06692","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-22T17:23:33Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP","math.PR"],"title_canon_sha256":"4fbe362306c3b0f9ed8fbf9143ee5e7dff251be76e798a15bf4e043243443025","abstract_canon_sha256":"113d7c08deefca139f0a9b17aec262f6a4fa18e1c166e0d9b590f6a52bc2b4e2"},"schema_version":"1.0"},"canonical_sha256":"3794c13157aa6c604d641fe6671f6483007b8ec533ef252fd7b808c53c38b8c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:44.548919Z","signature_b64":"4kmZh1hOsbJF+lqMU1r9Ncvrs2oHr5ig8/eJ0ZSnVfL4qHnoZQwMvkTsTRtm869dW1J+cM8L7kM7LCQl2uJpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3794c13157aa6c604d641fe6671f6483007b8ec533ef252fd7b808c53c38b8c3","last_reissued_at":"2026-05-18T01:18:44.548280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:44.548280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06692","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wftdZ5pdrbVx8H/iE2QKC+nsRt7D4wTaUi6uutxAWqqwYcZw9jwbLDDMrF1Zbg1/BTWD1l6ugZYnGsemFU45CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:24:59.864997Z"},"content_sha256":"29e001ea8f1f577d1c9baba18c3a2de5853fcf20e2f6e6895b9da4947907f774","schema_version":"1.0","event_id":"sha256:29e001ea8f1f577d1c9baba18c3a2de5853fcf20e2f6e6895b9da4947907f774"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:G6KMCMKXVJWGATLED7TGOH3EQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Level Spacing for Non-Monotone Anderson Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"John Z. Imbrie, Rajinder Mavi","submitted_at":"2015-06-22T17:23:33Z","abstract_excerpt":"We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed probabilistic information about the microscopic structure of energy levels of the Hamiltonian, as well as the support and decay of eigenfunctions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06692","kind":"arxiv","version":3},"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":"2026-05-18T01:18:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2jLdZT3NvOOv7yC+ufi9Slqq4Ktgwmsq6xrzDcz4m/SZtY60zRZP+/3Uo/ORp9WFnO4Svh4DdCIfN4whSoTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:24:59.865617Z"},"content_sha256":"54456af0b132f08dd2aa73f4995ef2ab327fa1797e5863cf137b7ba048c1ab5f","schema_version":"1.0","event_id":"sha256:54456af0b132f08dd2aa73f4995ef2ab327fa1797e5863cf137b7ba048c1ab5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6KMCMKXVJWGATLED7TGOH3EQM/bundle.json","state_url":"https://pith.science/pith/G6KMCMKXVJWGATLED7TGOH3EQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6KMCMKXVJWGATLED7TGOH3EQM/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":"2026-06-02T05:24:59Z","links":{"resolver":"https://pith.science/pith/G6KMCMKXVJWGATLED7TGOH3EQM","bundle":"https://pith.science/pith/G6KMCMKXVJWGATLED7TGOH3EQM/bundle.json","state":"https://pith.science/pith/G6KMCMKXVJWGATLED7TGOH3EQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6KMCMKXVJWGATLED7TGOH3EQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G6KMCMKXVJWGATLED7TGOH3EQM","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":"113d7c08deefca139f0a9b17aec262f6a4fa18e1c166e0d9b590f6a52bc2b4e2","cross_cats_sorted":["cond-mat.dis-nn","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-22T17:23:33Z","title_canon_sha256":"4fbe362306c3b0f9ed8fbf9143ee5e7dff251be76e798a15bf4e043243443025"},"schema_version":"1.0","source":{"id":"1506.06692","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06692","created_at":"2026-05-18T01:18:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06692v3","created_at":"2026-05-18T01:18:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06692","created_at":"2026-05-18T01:18:44Z"},{"alias_kind":"pith_short_12","alias_value":"G6KMCMKXVJWG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G6KMCMKXVJWGATLE","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G6KMCMKX","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:54456af0b132f08dd2aa73f4995ef2ab327fa1797e5863cf137b7ba048c1ab5f","target":"graph","created_at":"2026-05-18T01:18:44Z","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 prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed probabilistic information about the microscopic structure of energy levels of the Hamiltonian, as well as the support and decay of eigenfunctions.","authors_text":"John Z. Imbrie, Rajinder Mavi","cross_cats":["cond-mat.dis-nn","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-22T17:23:33Z","title":"Level Spacing for Non-Monotone Anderson Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06692","kind":"arxiv","version":3},"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":"sha256:29e001ea8f1f577d1c9baba18c3a2de5853fcf20e2f6e6895b9da4947907f774","target":"record","created_at":"2026-05-18T01:18:44Z","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":"113d7c08deefca139f0a9b17aec262f6a4fa18e1c166e0d9b590f6a52bc2b4e2","cross_cats_sorted":["cond-mat.dis-nn","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-22T17:23:33Z","title_canon_sha256":"4fbe362306c3b0f9ed8fbf9143ee5e7dff251be76e798a15bf4e043243443025"},"schema_version":"1.0","source":{"id":"1506.06692","kind":"arxiv","version":3}},"canonical_sha256":"3794c13157aa6c604d641fe6671f6483007b8ec533ef252fd7b808c53c38b8c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3794c13157aa6c604d641fe6671f6483007b8ec533ef252fd7b808c53c38b8c3","first_computed_at":"2026-05-18T01:18:44.548280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:44.548280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4kmZh1hOsbJF+lqMU1r9Ncvrs2oHr5ig8/eJ0ZSnVfL4qHnoZQwMvkTsTRtm869dW1J+cM8L7kM7LCQl2uJpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:44.548919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06692","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29e001ea8f1f577d1c9baba18c3a2de5853fcf20e2f6e6895b9da4947907f774","sha256:54456af0b132f08dd2aa73f4995ef2ab327fa1797e5863cf137b7ba048c1ab5f"],"state_sha256":"295d42a3152b6b32bbb414fb7e54565d2e30713e79867487e396ac3249809a59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OjNWOA1vv/W9vZsfwI85sjlCczSaebzQ7p/56mgaaYPdVzuDldRq89RdwhOXGWlf5iu0rC/yR9UwOHF5xq2aBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:24:59.868614Z","bundle_sha256":"d8eeff46dcbe1935e026380c24156e1e400c3db16a7e8e5b70e4d761676ed940"}}