{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2FHZUHAIVPXEK4W7WNHLFVAOVM","short_pith_number":"pith:2FHZUHAI","canonical_record":{"source":{"id":"1607.05026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-07-18T11:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"a125492373549ba95c90e94ef1695d0c7791ee7739d2b78c53ee4b8360c185ff","abstract_canon_sha256":"8d6bfde740ba5e494f7c3e5ad62ec904a768a95a86b9674f3260c5427ea12d6b"},"schema_version":"1.0"},"canonical_sha256":"d14f9a1c08abee4572dfb34eb2d40eab1aa81adc20957229e6760c9f215d6902","source":{"kind":"arxiv","id":"1607.05026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05026","created_at":"2026-05-18T00:27:02Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05026v1","created_at":"2026-05-18T00:27:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05026","created_at":"2026-05-18T00:27:02Z"},{"alias_kind":"pith_short_12","alias_value":"2FHZUHAIVPXE","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FHZUHAIVPXEK4W7","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FHZUHAI","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2FHZUHAIVPXEK4W7WNHLFVAOVM","target":"record","payload":{"canonical_record":{"source":{"id":"1607.05026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-07-18T11:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"a125492373549ba95c90e94ef1695d0c7791ee7739d2b78c53ee4b8360c185ff","abstract_canon_sha256":"8d6bfde740ba5e494f7c3e5ad62ec904a768a95a86b9674f3260c5427ea12d6b"},"schema_version":"1.0"},"canonical_sha256":"d14f9a1c08abee4572dfb34eb2d40eab1aa81adc20957229e6760c9f215d6902","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:02.951972Z","signature_b64":"SNez/IDlgrJ7l4xNtzFC2s3VFl/3MnZEUvxwpOrh7614XQkA2/eR5ZwrL0fZxFI9aFH7xWHFAFEx+MVOLe0hDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d14f9a1c08abee4572dfb34eb2d40eab1aa81adc20957229e6760c9f215d6902","last_reissued_at":"2026-05-18T00:27:02.951468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:02.951468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.05026","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":"2026-05-18T00:27:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yizQyy8K36ExX/r8nyDv+fP28kNwmp/uXw+vJrf95Zjw3SXWkyKNUsNmVRAXjCtDYzfsRxs87787k4EcJEweDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:39:39.005728Z"},"content_sha256":"e3d1abb2f922da8de1f68156ed2d81ef545e65c048a166c979fc686d978cad36","schema_version":"1.0","event_id":"sha256:e3d1abb2f922da8de1f68156ed2d81ef545e65c048a166c979fc686d978cad36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2FHZUHAIVPXEK4W7WNHLFVAOVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Gao Xianlong, Shu Chen, Yucheng Wang","submitted_at":"2016-07-18T11:41:45Z","abstract_excerpt":"We study a one-dimensional quasiperiodic system described by the Aubry-Andr\\'e model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-Andr\\'e model are either extended or localized depending on the strength of incommensurate potential $V$ being less or bigger than a critical value $V_c$, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector $\\alpha$ of the incommensurate potential is small, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05026","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":"2026-05-18T00:27:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1w7mpiCZN027b7yU5SipaerID7DUCczYNpmnfAmbBHb3kFyvqLbbF7ScPQklcG2F/csQ4uoS+5bUqXy4JptAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:39:39.006390Z"},"content_sha256":"4a7058802571516c62ce62dcca14f2ce81856ea299e2a02251da20c934fe9109","schema_version":"1.0","event_id":"sha256:4a7058802571516c62ce62dcca14f2ce81856ea299e2a02251da20c934fe9109"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM/bundle.json","state_url":"https://pith.science/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM/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":"2026-05-27T11:39:39Z","links":{"resolver":"https://pith.science/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM","bundle":"https://pith.science/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM/bundle.json","state":"https://pith.science/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FHZUHAIVPXEK4W7WNHLFVAOVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2FHZUHAIVPXEK4W7WNHLFVAOVM","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":"8d6bfde740ba5e494f7c3e5ad62ec904a768a95a86b9674f3260c5427ea12d6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-07-18T11:41:45Z","title_canon_sha256":"a125492373549ba95c90e94ef1695d0c7791ee7739d2b78c53ee4b8360c185ff"},"schema_version":"1.0","source":{"id":"1607.05026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05026","created_at":"2026-05-18T00:27:02Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05026v1","created_at":"2026-05-18T00:27:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05026","created_at":"2026-05-18T00:27:02Z"},{"alias_kind":"pith_short_12","alias_value":"2FHZUHAIVPXE","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FHZUHAIVPXEK4W7","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FHZUHAI","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:4a7058802571516c62ce62dcca14f2ce81856ea299e2a02251da20c934fe9109","target":"graph","created_at":"2026-05-18T00:27:02Z","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 study a one-dimensional quasiperiodic system described by the Aubry-Andr\\'e model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-Andr\\'e model are either extended or localized depending on the strength of incommensurate potential $V$ being less or bigger than a critical value $V_c$, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector $\\alpha$ of the incommensurate potential is small, an","authors_text":"Gao Xianlong, Shu Chen, Yucheng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-07-18T11:41:45Z","title":"Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05026","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:e3d1abb2f922da8de1f68156ed2d81ef545e65c048a166c979fc686d978cad36","target":"record","created_at":"2026-05-18T00:27:02Z","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":"8d6bfde740ba5e494f7c3e5ad62ec904a768a95a86b9674f3260c5427ea12d6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-07-18T11:41:45Z","title_canon_sha256":"a125492373549ba95c90e94ef1695d0c7791ee7739d2b78c53ee4b8360c185ff"},"schema_version":"1.0","source":{"id":"1607.05026","kind":"arxiv","version":1}},"canonical_sha256":"d14f9a1c08abee4572dfb34eb2d40eab1aa81adc20957229e6760c9f215d6902","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d14f9a1c08abee4572dfb34eb2d40eab1aa81adc20957229e6760c9f215d6902","first_computed_at":"2026-05-18T00:27:02.951468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:02.951468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SNez/IDlgrJ7l4xNtzFC2s3VFl/3MnZEUvxwpOrh7614XQkA2/eR5ZwrL0fZxFI9aFH7xWHFAFEx+MVOLe0hDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:02.951972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3d1abb2f922da8de1f68156ed2d81ef545e65c048a166c979fc686d978cad36","sha256:4a7058802571516c62ce62dcca14f2ce81856ea299e2a02251da20c934fe9109"],"state_sha256":"788c59cdcc1c0af607d6449527190c6d1978cea50d8a3e92ba3bf9d9fa5f2e26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRrc+XjERt3uauZ0Oq8PUaY9UutqM3WLd8Zq+HaJFdj0+QxXGOCVTZTv7IW8hoU1yQurBtWD/94rRikaVGsUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:39:39.010268Z","bundle_sha256":"fe5143930308ff306f1a20c686f20f9384e7670058b419421353dc4d553f44de"}}