{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:W2ZQ4KJZSLDMKL5BQMWU3QYLF3","short_pith_number":"pith:W2ZQ4KJZ","canonical_record":{"source":{"id":"1205.5669","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T11:49:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bdfbe5a09ae5c2630a271959ad572bd597cdf32ce012fd51cfdc826677f16110","abstract_canon_sha256":"2615fe3d8da8191135ae08ca2c6057550e9bc394f118dd091f550db49d8904ce"},"schema_version":"1.0"},"canonical_sha256":"b6b30e293992c6c52fa1832d4dc30b2efa3ce0f884327cca9dc02c949de59e84","source":{"kind":"arxiv","id":"1205.5669","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5669","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5669v3","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5669","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"W2ZQ4KJZSLDM","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W2ZQ4KJZSLDMKL5B","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W2ZQ4KJZ","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:W2ZQ4KJZSLDMKL5BQMWU3QYLF3","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5669","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T11:49:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bdfbe5a09ae5c2630a271959ad572bd597cdf32ce012fd51cfdc826677f16110","abstract_canon_sha256":"2615fe3d8da8191135ae08ca2c6057550e9bc394f118dd091f550db49d8904ce"},"schema_version":"1.0"},"canonical_sha256":"b6b30e293992c6c52fa1832d4dc30b2efa3ce0f884327cca9dc02c949de59e84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:17.388461Z","signature_b64":"9JRTrj5sPxwb7bo0B59kXu1ICUk+2gsH6w88MykXn7qLDt7sj2ztnw/s1oTHUPlo5Tkt4IkQYZTtifccOboPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6b30e293992c6c52fa1832d4dc30b2efa3ce0f884327cca9dc02c949de59e84","last_reissued_at":"2026-05-18T01:57:17.387939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:17.387939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5669","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":"2026-05-18T01:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"56ikHEJRmsI9oyv+b6rrzJSM0AgIo0ZlLdzh3UV1BPHVtprsHRhlGmH9yhDERDNl3EaLPIuPNnSNlLcxUCJCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:04:06.193487Z"},"content_sha256":"7d53169f22e07e40b84fdeb3ba9d91d36495e66c51c59ff1538907474e151fbe","schema_version":"1.0","event_id":"sha256:7d53169f22e07e40b84fdeb3ba9d91d36495e66c51c59ff1538907474e151fbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:W2ZQ4KJZSLDMKL5BQMWU3QYLF3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Delocalization and Diffusion Profile for Random Band Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Antti Knowles, Horng-Tzer Yau, Jun Yin, Laszlo Erdos","submitted_at":"2012-05-25T11:49:50Z","abstract_excerpt":"We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \\geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by $x,y \\in (\\bZ/L\\bZ)^d$, are independent, centred random variables with variances $s_{xy} = \\E |h_{xy}|^2$. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\\gg L^{4/5}$. We also show that the magnitude of the matrix entries $\\abs{G_{xy}}^2$ of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute $\\E \\abs{G_{xy}}^2$. We show that, as $L\\to\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5669","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":"2026-05-18T01:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWugsBtXZEdDKpm0cvDGGDnR0Pm8jl1xn4S83EGFFnAdmvohAoBtkkMCdhNQ+eEmJ0svrNQZOALfSbEvQZ8QCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:04:06.194179Z"},"content_sha256":"3ab73a306f8fcfe440595c33660fd1bc2368d1089099b212810ccc60fb596032","schema_version":"1.0","event_id":"sha256:3ab73a306f8fcfe440595c33660fd1bc2368d1089099b212810ccc60fb596032"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3/bundle.json","state_url":"https://pith.science/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3/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":"2026-05-26T23:04:06Z","links":{"resolver":"https://pith.science/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3","bundle":"https://pith.science/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3/bundle.json","state":"https://pith.science/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2ZQ4KJZSLDMKL5BQMWU3QYLF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W2ZQ4KJZSLDMKL5BQMWU3QYLF3","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":"2615fe3d8da8191135ae08ca2c6057550e9bc394f118dd091f550db49d8904ce","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T11:49:50Z","title_canon_sha256":"bdfbe5a09ae5c2630a271959ad572bd597cdf32ce012fd51cfdc826677f16110"},"schema_version":"1.0","source":{"id":"1205.5669","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5669","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5669v3","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5669","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"W2ZQ4KJZSLDM","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W2ZQ4KJZSLDMKL5B","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W2ZQ4KJZ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:3ab73a306f8fcfe440595c33660fd1bc2368d1089099b212810ccc60fb596032","target":"graph","created_at":"2026-05-18T01:57:17Z","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 Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \\geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by $x,y \\in (\\bZ/L\\bZ)^d$, are independent, centred random variables with variances $s_{xy} = \\E |h_{xy}|^2$. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\\gg L^{4/5}$. We also show that the magnitude of the matrix entries $\\abs{G_{xy}}^2$ of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute $\\E \\abs{G_{xy}}^2$. We show that, as $L\\to\\inf","authors_text":"Antti Knowles, Horng-Tzer Yau, Jun Yin, Laszlo Erdos","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T11:49:50Z","title":"Delocalization and Diffusion Profile for Random Band Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5669","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":"sha256:7d53169f22e07e40b84fdeb3ba9d91d36495e66c51c59ff1538907474e151fbe","target":"record","created_at":"2026-05-18T01:57:17Z","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":"2615fe3d8da8191135ae08ca2c6057550e9bc394f118dd091f550db49d8904ce","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T11:49:50Z","title_canon_sha256":"bdfbe5a09ae5c2630a271959ad572bd597cdf32ce012fd51cfdc826677f16110"},"schema_version":"1.0","source":{"id":"1205.5669","kind":"arxiv","version":3}},"canonical_sha256":"b6b30e293992c6c52fa1832d4dc30b2efa3ce0f884327cca9dc02c949de59e84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6b30e293992c6c52fa1832d4dc30b2efa3ce0f884327cca9dc02c949de59e84","first_computed_at":"2026-05-18T01:57:17.387939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:17.387939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9JRTrj5sPxwb7bo0B59kXu1ICUk+2gsH6w88MykXn7qLDt7sj2ztnw/s1oTHUPlo5Tkt4IkQYZTtifccOboPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:17.388461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5669","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d53169f22e07e40b84fdeb3ba9d91d36495e66c51c59ff1538907474e151fbe","sha256:3ab73a306f8fcfe440595c33660fd1bc2368d1089099b212810ccc60fb596032"],"state_sha256":"69100fe60079e616f119c1381ae75f78856a3dbdce737a6e38344ab4f13911af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USuPwjm5S3w9EwYRFu4ONoCH4lp6GYu+whR4bK7uSHl5dJ8IJLMPIP4AKJtTGCTI+TFX0JLVbQMNwxgrE0USAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:04:06.197348Z","bundle_sha256":"0900d61ecf3de06966accd1104228a15e240f7768f95b7c550eab2230ad3e13a"}}