{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YTRJ5QQQYTYNA6SETLVFDOM44Y","short_pith_number":"pith:YTRJ5QQQ","canonical_record":{"source":{"id":"1504.05205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-04-20T20:03:13Z","cross_cats_sorted":["cond-mat.quant-gas"],"title_canon_sha256":"5f0cbf5461be08c2365ccef8577dc4d5a0c28d823bc08e9cb0612e16e992e10f","abstract_canon_sha256":"f9f684d91e3ee2487e1b6cb73cbd21b61f9ec598af0e770a9888e688d81f05a8"},"schema_version":"1.0"},"canonical_sha256":"c4e29ec210c4f0d07a449aea51b99ce6229da11664b9a7baed918712a01266f9","source":{"kind":"arxiv","id":"1504.05205","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05205","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05205v2","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05205","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"YTRJ5QQQYTYN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YTRJ5QQQYTYNA6SE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YTRJ5QQQ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YTRJ5QQQYTYNA6SETLVFDOM44Y","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-04-20T20:03:13Z","cross_cats_sorted":["cond-mat.quant-gas"],"title_canon_sha256":"5f0cbf5461be08c2365ccef8577dc4d5a0c28d823bc08e9cb0612e16e992e10f","abstract_canon_sha256":"f9f684d91e3ee2487e1b6cb73cbd21b61f9ec598af0e770a9888e688d81f05a8"},"schema_version":"1.0"},"canonical_sha256":"c4e29ec210c4f0d07a449aea51b99ce6229da11664b9a7baed918712a01266f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:48.868708Z","signature_b64":"BQW+WbcnfLyAIoPE9U2MzFp+tV6L/sxTc6qvjVM/s4LRH6t/L8U+ee0bwEwn3uDSFk7WVphpM23643bGH6LcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4e29ec210c4f0d07a449aea51b99ce6229da11664b9a7baed918712a01266f9","last_reissued_at":"2026-05-18T01:37:48.868278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:48.868278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05205","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":"2026-05-18T01:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ooggJi2r3dBRDz5zgr7ViEqbhbFv2UE7MW7U99iFevNi3uCQHWDm7UxCfqrCgHubMm6WctKeLl0VSPSE286TCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:13:16.982661Z"},"content_sha256":"778b4460e8b11b4d6a44affc8daa2a70ffd5a9b22a2d5e75cab2b903c34cd089","schema_version":"1.0","event_id":"sha256:778b4460e8b11b4d6a44affc8daa2a70ffd5a9b22a2d5e75cab2b903c34cd089"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YTRJ5QQQYTYNA6SETLVFDOM44Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The almost mobility edge in the almost Mathieu equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas"],"primary_cat":"cond-mat.mes-hall","authors_text":"Akash V. Maharaj, Chao-Ming Jian, Daniel Bulmash, Steven A. Kivelson, Yi Zhang","submitted_at":"2015-04-20T20:03:13Z","abstract_excerpt":"Harper's equation (aka the \"almost Mathieu\" equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V<V_c$ there is an abrupt crossover akin to a mobility edge at an energy $E_c$; states with energy $|E|<E_c$ are robustly delocal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05205","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":"2026-05-18T01:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dW0QFd6MZA1pwKNa7Fus1c0ULtEgHl8d5ySLJSc888T71QCB/EC1HQJmyqSAydXSFEPtRQvq5lysZzONv8N3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:13:16.983057Z"},"content_sha256":"0f14051d07db7e325d4e8cd78bef0d69896a447172612801f7148c519f299297","schema_version":"1.0","event_id":"sha256:0f14051d07db7e325d4e8cd78bef0d69896a447172612801f7148c519f299297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y/bundle.json","state_url":"https://pith.science/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y/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":"2026-05-27T22:13:16Z","links":{"resolver":"https://pith.science/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y","bundle":"https://pith.science/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y/bundle.json","state":"https://pith.science/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTRJ5QQQYTYNA6SETLVFDOM44Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YTRJ5QQQYTYNA6SETLVFDOM44Y","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":"f9f684d91e3ee2487e1b6cb73cbd21b61f9ec598af0e770a9888e688d81f05a8","cross_cats_sorted":["cond-mat.quant-gas"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-04-20T20:03:13Z","title_canon_sha256":"5f0cbf5461be08c2365ccef8577dc4d5a0c28d823bc08e9cb0612e16e992e10f"},"schema_version":"1.0","source":{"id":"1504.05205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05205","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05205v2","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05205","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"YTRJ5QQQYTYN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YTRJ5QQQYTYNA6SE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YTRJ5QQQ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:0f14051d07db7e325d4e8cd78bef0d69896a447172612801f7148c519f299297","target":"graph","created_at":"2026-05-18T01:37:48Z","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":"Harper's equation (aka the \"almost Mathieu\" equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V<V_c$ there is an abrupt crossover akin to a mobility edge at an energy $E_c$; states with energy $|E|<E_c$ are robustly delocal","authors_text":"Akash V. Maharaj, Chao-Ming Jian, Daniel Bulmash, Steven A. Kivelson, Yi Zhang","cross_cats":["cond-mat.quant-gas"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-04-20T20:03:13Z","title":"The almost mobility edge in the almost Mathieu equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05205","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":"sha256:778b4460e8b11b4d6a44affc8daa2a70ffd5a9b22a2d5e75cab2b903c34cd089","target":"record","created_at":"2026-05-18T01:37:48Z","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":"f9f684d91e3ee2487e1b6cb73cbd21b61f9ec598af0e770a9888e688d81f05a8","cross_cats_sorted":["cond-mat.quant-gas"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-04-20T20:03:13Z","title_canon_sha256":"5f0cbf5461be08c2365ccef8577dc4d5a0c28d823bc08e9cb0612e16e992e10f"},"schema_version":"1.0","source":{"id":"1504.05205","kind":"arxiv","version":2}},"canonical_sha256":"c4e29ec210c4f0d07a449aea51b99ce6229da11664b9a7baed918712a01266f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4e29ec210c4f0d07a449aea51b99ce6229da11664b9a7baed918712a01266f9","first_computed_at":"2026-05-18T01:37:48.868278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:48.868278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BQW+WbcnfLyAIoPE9U2MzFp+tV6L/sxTc6qvjVM/s4LRH6t/L8U+ee0bwEwn3uDSFk7WVphpM23643bGH6LcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:48.868708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:778b4460e8b11b4d6a44affc8daa2a70ffd5a9b22a2d5e75cab2b903c34cd089","sha256:0f14051d07db7e325d4e8cd78bef0d69896a447172612801f7148c519f299297"],"state_sha256":"bf9828bbb98aca27f5d5dbd9d6885dede7d809c9a5e293fdba01b8b90452d319"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVpcVxe4uv/CxhI79TIMI1MqXKRM6OC+3BveiAPgYAkp/UCMe1yTIaAMug49ySftU7WEQrdRn5lKqNYIR+8NCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:13:16.985345Z","bundle_sha256":"c91034c0773662e999c16d44b63ed43d37d2720a68c7346039442637be8ac453"}}