{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7RHYCKGTUUFJF7KYRYD52644ZL","short_pith_number":"pith:7RHYCKGT","canonical_record":{"source":{"id":"2104.12048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-25T02:15:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"28303f7ac9d9dd8891b7e498be515287566855bbb453c4aa7074cc78d338b0ee","abstract_canon_sha256":"d85a0b3648ea61f4f03da18acada0579c600f3cdb46e4455659c48ebd0ecbcc2"},"schema_version":"1.0"},"canonical_sha256":"fc4f8128d3a50a92fd588e07dd7b9ccaf731224bb62316a45c45db63483060da","source":{"kind":"arxiv","id":"2104.12048","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12048","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12048v2","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12048","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"7RHYCKGTUUFJ","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"pith_short_16","alias_value":"7RHYCKGTUUFJF7KY","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"pith_short_8","alias_value":"7RHYCKGT","created_at":"2026-07-05T02:57:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7RHYCKGTUUFJF7KYRYD52644ZL","target":"record","payload":{"canonical_record":{"source":{"id":"2104.12048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-25T02:15:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"28303f7ac9d9dd8891b7e498be515287566855bbb453c4aa7074cc78d338b0ee","abstract_canon_sha256":"d85a0b3648ea61f4f03da18acada0579c600f3cdb46e4455659c48ebd0ecbcc2"},"schema_version":"1.0"},"canonical_sha256":"fc4f8128d3a50a92fd588e07dd7b9ccaf731224bb62316a45c45db63483060da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:57:53.912462Z","signature_b64":"wmUtCnBltaNbA5bTpLZNubVpUqK/ufz5oYBw47+hD9TVETY4BR5V8N5lVp1xsZpW6zB07LkA/jKeYmdREf0HDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc4f8128d3a50a92fd588e07dd7b9ccaf731224bb62316a45c45db63483060da","last_reissued_at":"2026-07-05T02:57:53.912039Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:57:53.912039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.12048","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":"2026-07-05T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2gVI9VSIPY49yEBBQ3H7YbQQLAJYBF7ISo9s3QtxkDYOP8ca+1apfO2LvYZgvDhAAVoeIJWz8qtDrrbNFbuGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:19:58.357363Z"},"content_sha256":"8249d3ea6c8b247861ffcda163208258fa6cee5e7119cd84e7c61f88cf852449","schema_version":"1.0","event_id":"sha256:8249d3ea6c8b247861ffcda163208258fa6cee5e7119cd84e7c61f88cf852449"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7RHYCKGTUUFJF7KYRYD52644ZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Delocalization and quantum diffusion of random band matrices in high dimensions I: Self-energy renormalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Fan Yang, Horng-Tzer Yau, Jun Yin","submitted_at":"2021-04-25T02:15:44Z","abstract_excerpt":"We consider Hermitian random band matrices $H=(h_{xy})$ on the $d$-dimensional lattice $(\\mathbb Z/L\\mathbb Z)^d$. The entries $h_{xy}$ are independent (up to Hermitian conditions) centered complex Gaussian random variables with variances $s_{xy}=\\mathbb E|h_{xy}|^2$. The variance matrix $S=(s_{xy})$ has a banded structure so that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In dimensions $d\\ge 8$, we prove that, as long as $W\\ge L^\\epsilon$ for a small constant $\\epsilon>0$, with high probability most bulk eigenvectors of $H$ are delocalized in the sense that their localizati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12048","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.12048/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nQUGVnammdhNpxYrWv/EmtG37yJFk5VMiORl11eIbH49Qp8WNbn3FpHIG96rB/OUXtu8k0gu3/kr9DAOK57CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:19:58.358524Z"},"content_sha256":"6835f6c5e04ccc277a4d6d791e99619e8dd3d84fabfdbeee4a049f2a8416b5ce","schema_version":"1.0","event_id":"sha256:6835f6c5e04ccc277a4d6d791e99619e8dd3d84fabfdbeee4a049f2a8416b5ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RHYCKGTUUFJF7KYRYD52644ZL/bundle.json","state_url":"https://pith.science/pith/7RHYCKGTUUFJF7KYRYD52644ZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RHYCKGTUUFJF7KYRYD52644ZL/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":"2026-08-15T00:19:58Z","links":{"resolver":"https://pith.science/pith/7RHYCKGTUUFJF7KYRYD52644ZL","bundle":"https://pith.science/pith/7RHYCKGTUUFJF7KYRYD52644ZL/bundle.json","state":"https://pith.science/pith/7RHYCKGTUUFJF7KYRYD52644ZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RHYCKGTUUFJF7KYRYD52644ZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7RHYCKGTUUFJF7KYRYD52644ZL","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":"d85a0b3648ea61f4f03da18acada0579c600f3cdb46e4455659c48ebd0ecbcc2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-25T02:15:44Z","title_canon_sha256":"28303f7ac9d9dd8891b7e498be515287566855bbb453c4aa7074cc78d338b0ee"},"schema_version":"1.0","source":{"id":"2104.12048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12048","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12048v2","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12048","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"7RHYCKGTUUFJ","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"pith_short_16","alias_value":"7RHYCKGTUUFJF7KY","created_at":"2026-07-05T02:57:53Z"},{"alias_kind":"pith_short_8","alias_value":"7RHYCKGT","created_at":"2026-07-05T02:57:53Z"}],"graph_snapshots":[{"event_id":"sha256:6835f6c5e04ccc277a4d6d791e99619e8dd3d84fabfdbeee4a049f2a8416b5ce","target":"graph","created_at":"2026-07-05T02:57:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.12048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider Hermitian random band matrices $H=(h_{xy})$ on the $d$-dimensional lattice $(\\mathbb Z/L\\mathbb Z)^d$. The entries $h_{xy}$ are independent (up to Hermitian conditions) centered complex Gaussian random variables with variances $s_{xy}=\\mathbb E|h_{xy}|^2$. The variance matrix $S=(s_{xy})$ has a banded structure so that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In dimensions $d\\ge 8$, we prove that, as long as $W\\ge L^\\epsilon$ for a small constant $\\epsilon>0$, with high probability most bulk eigenvectors of $H$ are delocalized in the sense that their localizati","authors_text":"Fan Yang, Horng-Tzer Yau, Jun Yin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-25T02:15:44Z","title":"Delocalization and quantum diffusion of random band matrices in high dimensions I: Self-energy renormalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12048","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":"sha256:8249d3ea6c8b247861ffcda163208258fa6cee5e7119cd84e7c61f88cf852449","target":"record","created_at":"2026-07-05T02:57:53Z","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":"d85a0b3648ea61f4f03da18acada0579c600f3cdb46e4455659c48ebd0ecbcc2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-25T02:15:44Z","title_canon_sha256":"28303f7ac9d9dd8891b7e498be515287566855bbb453c4aa7074cc78d338b0ee"},"schema_version":"1.0","source":{"id":"2104.12048","kind":"arxiv","version":2}},"canonical_sha256":"fc4f8128d3a50a92fd588e07dd7b9ccaf731224bb62316a45c45db63483060da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4f8128d3a50a92fd588e07dd7b9ccaf731224bb62316a45c45db63483060da","first_computed_at":"2026-07-05T02:57:53.912039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:57:53.912039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wmUtCnBltaNbA5bTpLZNubVpUqK/ufz5oYBw47+hD9TVETY4BR5V8N5lVp1xsZpW6zB07LkA/jKeYmdREf0HDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:57:53.912462Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.12048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8249d3ea6c8b247861ffcda163208258fa6cee5e7119cd84e7c61f88cf852449","sha256:6835f6c5e04ccc277a4d6d791e99619e8dd3d84fabfdbeee4a049f2a8416b5ce"],"state_sha256":"10965d8d0ac590046b281f97fb85a08ec284d9a7496d437d695d9b17b2a41f42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opcMJXo0YETStVIOeE6AWrD/eVkBATa5V0Zc7wbyDgxL7yqlVu4DO3D3vurOJzfKDFGjjcMbJeHcIPwD2kWtAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T00:19:58.366434Z","bundle_sha256":"bb8f4b34ba32ab62eaf0974c3627d911f31fd58bfd2fe28d869f4449719b3b2b"}}