{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GZO7BUR7PNXC6CJ6ZEJAPAHGQC","short_pith_number":"pith:GZO7BUR7","canonical_record":{"source":{"id":"1306.5712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-24T19:18:39Z","cross_cats_sorted":[],"title_canon_sha256":"1fa3614a9c0453470b757b16cc54ce015e8f146b6df200c12dafb46e27d27ae3","abstract_canon_sha256":"44718029ed1d5e6037b45b8195106cd4109fa2853e6a29d6d73be777ea830d54"},"schema_version":"1.0"},"canonical_sha256":"365df0d23f7b6e2f093ec9120780e6808b5bffd27086eb86edd641e7a131c62f","source":{"kind":"arxiv","id":"1306.5712","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5712","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5712v2","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5712","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"GZO7BUR7PNXC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"GZO7BUR7PNXC6CJ6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"GZO7BUR7","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GZO7BUR7PNXC6CJ6ZEJAPAHGQC","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-24T19:18:39Z","cross_cats_sorted":[],"title_canon_sha256":"1fa3614a9c0453470b757b16cc54ce015e8f146b6df200c12dafb46e27d27ae3","abstract_canon_sha256":"44718029ed1d5e6037b45b8195106cd4109fa2853e6a29d6d73be777ea830d54"},"schema_version":"1.0"},"canonical_sha256":"365df0d23f7b6e2f093ec9120780e6808b5bffd27086eb86edd641e7a131c62f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:20.337548Z","signature_b64":"Ym7AKN3Pz0c48e94e/0+MdUqG7m9pic2TthwpvtOmhng6i2rwZTZxHcDfJDLqytHwNFFzLR/+fMJ7Sln7PKLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"365df0d23f7b6e2f093ec9120780e6808b5bffd27086eb86edd641e7a131c62f","last_reissued_at":"2026-05-18T02:49:20.336931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:20.336931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5712","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":"2026-05-18T02:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hfQFHK56da7FAIWdUbNHDX7owJmK2qH8oK2g1Xv8SqANZfUu1mBNIArGvFIDTmUipcJhqYg+KCapAa01JRCzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:17:36.521698Z"},"content_sha256":"c7ade4413f77fc997d007eff305c0c45229b6eaafaeda55509ebb5ec066efbd0","schema_version":"1.0","event_id":"sha256:c7ade4413f77fc997d007eff305c0c45229b6eaafaeda55509ebb5ec066efbd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GZO7BUR7PNXC6CJ6ZEJAPAHGQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective Cluster Typical Medium Theory for Diagonal Anderson Disorder Model in One- and Two-Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Chinedu E. Ekuma, Hanna Terletska, Juana Moreno, Mark Jarrell, Samiyeh Mahmoudian, Vladimir Dobrosavljevic, Zi Yang Meng","submitted_at":"2013-06-24T19:18:39Z","abstract_excerpt":"We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power-law, $W_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5712","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":"2026-05-18T02:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YahAjZsIodH6sUyLoKH6GRtSg0InQWuz7wmgHu3uRch7MbQ+JZ9Lpr7NAZz85Eeb2QqPh1R9J7/rT67zRYzzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:17:36.522348Z"},"content_sha256":"2fcd9a581baea8ec23fec92101c5dc0e7d6177eac4a9ca97035cb312894edba3","schema_version":"1.0","event_id":"sha256:2fcd9a581baea8ec23fec92101c5dc0e7d6177eac4a9ca97035cb312894edba3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC/bundle.json","state_url":"https://pith.science/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC/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":"2026-05-27T20:17:36Z","links":{"resolver":"https://pith.science/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC","bundle":"https://pith.science/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC/bundle.json","state":"https://pith.science/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZO7BUR7PNXC6CJ6ZEJAPAHGQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GZO7BUR7PNXC6CJ6ZEJAPAHGQC","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":"44718029ed1d5e6037b45b8195106cd4109fa2853e6a29d6d73be777ea830d54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-24T19:18:39Z","title_canon_sha256":"1fa3614a9c0453470b757b16cc54ce015e8f146b6df200c12dafb46e27d27ae3"},"schema_version":"1.0","source":{"id":"1306.5712","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5712","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5712v2","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5712","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"GZO7BUR7PNXC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"GZO7BUR7PNXC6CJ6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"GZO7BUR7","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:2fcd9a581baea8ec23fec92101c5dc0e7d6177eac4a9ca97035cb312894edba3","target":"graph","created_at":"2026-05-18T02:49:20Z","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 develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power-law, $W_","authors_text":"Chinedu E. Ekuma, Hanna Terletska, Juana Moreno, Mark Jarrell, Samiyeh Mahmoudian, Vladimir Dobrosavljevic, Zi Yang Meng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-24T19:18:39Z","title":"Effective Cluster Typical Medium Theory for Diagonal Anderson Disorder Model in One- and Two-Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5712","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:c7ade4413f77fc997d007eff305c0c45229b6eaafaeda55509ebb5ec066efbd0","target":"record","created_at":"2026-05-18T02:49:20Z","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":"44718029ed1d5e6037b45b8195106cd4109fa2853e6a29d6d73be777ea830d54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-24T19:18:39Z","title_canon_sha256":"1fa3614a9c0453470b757b16cc54ce015e8f146b6df200c12dafb46e27d27ae3"},"schema_version":"1.0","source":{"id":"1306.5712","kind":"arxiv","version":2}},"canonical_sha256":"365df0d23f7b6e2f093ec9120780e6808b5bffd27086eb86edd641e7a131c62f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"365df0d23f7b6e2f093ec9120780e6808b5bffd27086eb86edd641e7a131c62f","first_computed_at":"2026-05-18T02:49:20.336931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:20.336931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ym7AKN3Pz0c48e94e/0+MdUqG7m9pic2TthwpvtOmhng6i2rwZTZxHcDfJDLqytHwNFFzLR/+fMJ7Sln7PKLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:20.337548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5712","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7ade4413f77fc997d007eff305c0c45229b6eaafaeda55509ebb5ec066efbd0","sha256:2fcd9a581baea8ec23fec92101c5dc0e7d6177eac4a9ca97035cb312894edba3"],"state_sha256":"8b169a1f3ed4e9e6e413e969f35028cf1047c6f505220f0d968575866aaa9a03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sazwSHSF6let3sGdeZY0Ex+mWCU4QBhRq/9j//o9tvVtU7pQCz4N0t4qWnN5ZH6CALza3l0V8Ufc9FVoevH5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:17:36.525944Z","bundle_sha256":"659fb45ca43a51ef2132d578c34181092c4ac2f9eac6d4e078d410789ee1bc5c"}}