{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:CKZ4OQZVBWT6LEYIOGJ53VWV6O","short_pith_number":"pith:CKZ4OQZV","canonical_record":{"source":{"id":"cond-mat/0209058","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2002-09-03T13:55:20Z","cross_cats_sorted":[],"title_canon_sha256":"c8cee7f5067914a6849d91804693955d7760115b4783cecee4a049a9fc850f63","abstract_canon_sha256":"cbbf502967268d59fc21bdab622b2f12f96637f282991afc10b4722b298092b3"},"schema_version":"1.0"},"canonical_sha256":"12b3c743350da7e593087193ddd6d5f3ab876e7ef4d868e03df4a5ab6b057bf5","source":{"kind":"arxiv","id":"cond-mat/0209058","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0209058","created_at":"2026-05-18T01:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0209058v1","created_at":"2026-05-18T01:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0209058","created_at":"2026-05-18T01:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"CKZ4OQZVBWT6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CKZ4OQZVBWT6LEYI","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CKZ4OQZV","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:CKZ4OQZVBWT6LEYIOGJ53VWV6O","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0209058","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2002-09-03T13:55:20Z","cross_cats_sorted":[],"title_canon_sha256":"c8cee7f5067914a6849d91804693955d7760115b4783cecee4a049a9fc850f63","abstract_canon_sha256":"cbbf502967268d59fc21bdab622b2f12f96637f282991afc10b4722b298092b3"},"schema_version":"1.0"},"canonical_sha256":"12b3c743350da7e593087193ddd6d5f3ab876e7ef4d868e03df4a5ab6b057bf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:03.024673Z","signature_b64":"RS51tYVMvQDs7ERJYFow0Kq2SPaSPJ6wZmBE2JgR+snmG8lThYRpYma5Rd3C67VXgZ5ccKai/Xiuy4SPKz7IBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b3c743350da7e593087193ddd6d5f3ab876e7ef4d868e03df4a5ab6b057bf5","last_reissued_at":"2026-05-18T01:40:03.024018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:03.024018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0209058","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R+6wrqnSVFztVapIKDqNWkexzkSHn/hRjA1H8J1RaFFQeY1LNeHq9jJg4VO7F739/OaQGf5AnB5zu6EQ/ybzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:14:52.719813Z"},"content_sha256":"0170c6d2694d8f731e656da762c80ffd3ab879645d1ad0254b7242d0f81a846d","schema_version":"1.0","event_id":"sha256:0170c6d2694d8f731e656da762c80ffd3ab879645d1ad0254b7242d0f81a846d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:CKZ4OQZVBWT6LEYIOGJ53VWV6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divergences of the localization lengths in the two- dimensional, off-diagonal Anderson model on bipartite lattices","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Andrzej Eilmes, Rudolf A. Roemer","submitted_at":"2002-09-03T13:55:20Z","abstract_excerpt":"We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). Using the transfer-matrix method and finite-size scaling we compute the infinite-size localization lengths for bipartite square and hexagonal 2D lattices, non-bipartite triangular lattices and different distribution functions for the hopping elements. We show that for small energies the localization lengths in the bipartite case diverge with a power-law behavior. The corresponding exponents are in the range $0.2 - 0.6$ and seem to depend on the ty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0209058","kind":"arxiv","version":1},"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":"2026-05-18T01:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djZkT7VfJGAm5HE0s+8Sxx9bvZBCe/L/BSI/ct5gCM7DlMb7vWK+EyeWNLE9SdO9o5mzX1qAVOAqlsJV9UP2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:14:52.720162Z"},"content_sha256":"1d7928157b921705df50b4f43cb500dd29e5be91eac24e5fda24b3ea72ad108a","schema_version":"1.0","event_id":"sha256:1d7928157b921705df50b4f43cb500dd29e5be91eac24e5fda24b3ea72ad108a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O/bundle.json","state_url":"https://pith.science/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O/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":"2026-07-02T12:14:52Z","links":{"resolver":"https://pith.science/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O","bundle":"https://pith.science/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O/bundle.json","state":"https://pith.science/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKZ4OQZVBWT6LEYIOGJ53VWV6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:CKZ4OQZVBWT6LEYIOGJ53VWV6O","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":"cbbf502967268d59fc21bdab622b2f12f96637f282991afc10b4722b298092b3","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2002-09-03T13:55:20Z","title_canon_sha256":"c8cee7f5067914a6849d91804693955d7760115b4783cecee4a049a9fc850f63"},"schema_version":"1.0","source":{"id":"cond-mat/0209058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0209058","created_at":"2026-05-18T01:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0209058v1","created_at":"2026-05-18T01:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0209058","created_at":"2026-05-18T01:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"CKZ4OQZVBWT6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CKZ4OQZVBWT6LEYI","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CKZ4OQZV","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:1d7928157b921705df50b4f43cb500dd29e5be91eac24e5fda24b3ea72ad108a","target":"graph","created_at":"2026-05-18T01:40:03Z","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 investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). Using the transfer-matrix method and finite-size scaling we compute the infinite-size localization lengths for bipartite square and hexagonal 2D lattices, non-bipartite triangular lattices and different distribution functions for the hopping elements. We show that for small energies the localization lengths in the bipartite case diverge with a power-law behavior. The corresponding exponents are in the range $0.2 - 0.6$ and seem to depend on the ty","authors_text":"Andrzej Eilmes, Rudolf A. Roemer","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2002-09-03T13:55:20Z","title":"Divergences of the localization lengths in the two- dimensional, off-diagonal Anderson model on bipartite lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0209058","kind":"arxiv","version":1},"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":"sha256:0170c6d2694d8f731e656da762c80ffd3ab879645d1ad0254b7242d0f81a846d","target":"record","created_at":"2026-05-18T01:40:03Z","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":"cbbf502967268d59fc21bdab622b2f12f96637f282991afc10b4722b298092b3","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2002-09-03T13:55:20Z","title_canon_sha256":"c8cee7f5067914a6849d91804693955d7760115b4783cecee4a049a9fc850f63"},"schema_version":"1.0","source":{"id":"cond-mat/0209058","kind":"arxiv","version":1}},"canonical_sha256":"12b3c743350da7e593087193ddd6d5f3ab876e7ef4d868e03df4a5ab6b057bf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12b3c743350da7e593087193ddd6d5f3ab876e7ef4d868e03df4a5ab6b057bf5","first_computed_at":"2026-05-18T01:40:03.024018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:03.024018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RS51tYVMvQDs7ERJYFow0Kq2SPaSPJ6wZmBE2JgR+snmG8lThYRpYma5Rd3C67VXgZ5ccKai/Xiuy4SPKz7IBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:03.024673Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0209058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0170c6d2694d8f731e656da762c80ffd3ab879645d1ad0254b7242d0f81a846d","sha256:1d7928157b921705df50b4f43cb500dd29e5be91eac24e5fda24b3ea72ad108a"],"state_sha256":"c925296290744ef65214a3122d9a2659a2eee00c8b449735813bc1c753676ba6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bioSRvBS8he8NhpbbxodFbzLkAFIqH0tg6Af9lFm8vufTMiRYuzxKirHHrLjEBcCFxuoSfMrRwRu06yUzTV8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:14:52.722116Z","bundle_sha256":"26d34a82a3132c4f1cb67a2ba354be50a241c024b905bc7acd2ed713a72ffac5"}}