{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UJ4IXBXJFTQXTDWDHXALY5TCVJ","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":"cedd37a30e231ccd09904b7ff2441af40e7afc49938aa76cb68f47756ce9d27c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-28T22:38:04Z","title_canon_sha256":"0aaa858905f7ab65fac4dbc213e89817ef2e6c23f5cd337be123b2df65d87ab2"},"schema_version":"1.0","source":{"id":"1001.5280","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5280","created_at":"2026-07-04T17:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5280v2","created_at":"2026-07-04T17:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5280","created_at":"2026-07-04T17:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"UJ4IXBXJFTQX","created_at":"2026-07-04T17:20:37Z"},{"alias_kind":"pith_short_16","alias_value":"UJ4IXBXJFTQXTDWD","created_at":"2026-07-04T17:20:37Z"},{"alias_kind":"pith_short_8","alias_value":"UJ4IXBXJ","created_at":"2026-07-04T17:20:37Z"}],"graph_snapshots":[{"event_id":"sha256:406c9bcfaf27ba1763d2bcb12a32c9f9d6e3a31bdb22e5817e62ee80d3edf663","target":"graph","created_at":"2026-07-04T17:20:37Z","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/1001.5280/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a possible definition of a mobility gap for a many-body quantum system, in analogy to definitions of dynamical localization for single particle systems. Using this definition, we construct \"corrected\" quasi-adiabatic continuation operators. Under an appropriate definition of a unique ground state, we show how to introduce virtual fluxes. Armed with these results, we can directly carry over previous results in the case of a spectral gap. We present a proof of decay of correlation functions and we present a proof of Hall conductance quantization under very mild density-of-states assum","authors_text":"M. B. Hastings","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-28T22:38:04Z","title":"Quasi-adiabatic Continuation for Disordered Systems: Applications to Correlations, Lieb-Schultz-Mattis, and Hall Conductance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5280","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":"sha256:55f26a37284123a7f2a54fdd7deff4ea4ec2596fd300b122184861e39661324e","target":"record","created_at":"2026-07-04T17:20:37Z","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":"cedd37a30e231ccd09904b7ff2441af40e7afc49938aa76cb68f47756ce9d27c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-28T22:38:04Z","title_canon_sha256":"0aaa858905f7ab65fac4dbc213e89817ef2e6c23f5cd337be123b2df65d87ab2"},"schema_version":"1.0","source":{"id":"1001.5280","kind":"arxiv","version":2}},"canonical_sha256":"a2788b86e92ce1798ec33dc0bc7662aa72452d85d6bcd8e3553e19bbc154a174","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2788b86e92ce1798ec33dc0bc7662aa72452d85d6bcd8e3553e19bbc154a174","first_computed_at":"2026-07-04T17:20:37.735578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:20:37.735578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86JHJ6/V5ztMjVH5BVv18WmGM1M4wOzrjZcGWdgoxj8sQGnZyAJ8Clix/ROybXp0IrAIp0+RVcHOyAs3n4IbCA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:20:37.735958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5280","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55f26a37284123a7f2a54fdd7deff4ea4ec2596fd300b122184861e39661324e","sha256:406c9bcfaf27ba1763d2bcb12a32c9f9d6e3a31bdb22e5817e62ee80d3edf663"],"state_sha256":"8ef720dab1d7f8265ab49ef0c9f9be1498a10da9c208a2877cbc910fc0473ec8"}