{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C4E2LKWKCJYPPAMMM2SGTVFOEO","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":"ee56cf39443f245f91b2834971e0f14bcd390040480a16b23bf3182175dc67fb","cross_cats_sorted":["cond-mat.mes-hall","math.AP","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-10T17:28:48Z","title_canon_sha256":"b45569b5a3a940b97193315caff8ce2780f5e55468ee9dfde2b0746ec6aeac6d"},"schema_version":"1.0","source":{"id":"1611.03408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03408","created_at":"2026-07-05T04:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03408v2","created_at":"2026-07-05T04:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03408","created_at":"2026-07-05T04:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"C4E2LKWKCJYP","created_at":"2026-07-05T04:50:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4E2LKWKCJYPPAMM","created_at":"2026-07-05T04:50:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4E2LKWK","created_at":"2026-07-05T04:50:08Z"}],"graph_snapshots":[{"event_id":"sha256:70f99fb6ded8193e93eacdfeb6308c9bfce36ed76882dcc76d0deaf9e26caa8b","target":"graph","created_at":"2026-07-05T04:50:08Z","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/1611.03408/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\\\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two dimensionless parameters: (re-scaled) Planck's constant and the ratio of the lattice spacing to the scale of variation of the external potential. We consider the special case where both parameters are equal and denote this parameter $\\epsilon$. In the limit $\\epsilon \\downarrow 0$, we prove the existence of solutions known as semiclassical wavepackets which are","authors_text":"Alexander B. Watson, Jianfeng Lu, Michael I. Weinstein","cross_cats":["cond-mat.mes-hall","math.AP","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-10T17:28:48Z","title":"Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03408","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":"sha256:828e04a64d5434353f4e26df62cdc422826273370d37a3f86be9d5d3429a6e66","target":"record","created_at":"2026-07-05T04:50:08Z","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":"ee56cf39443f245f91b2834971e0f14bcd390040480a16b23bf3182175dc67fb","cross_cats_sorted":["cond-mat.mes-hall","math.AP","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-10T17:28:48Z","title_canon_sha256":"b45569b5a3a940b97193315caff8ce2780f5e55468ee9dfde2b0746ec6aeac6d"},"schema_version":"1.0","source":{"id":"1611.03408","kind":"arxiv","version":2}},"canonical_sha256":"1709a5aaca1270f7818c66a469d4ae23b1b147d5a41e5f302740ed6dc2a5c4d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1709a5aaca1270f7818c66a469d4ae23b1b147d5a41e5f302740ed6dc2a5c4d2","first_computed_at":"2026-07-05T04:50:08.049581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:50:08.049581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q3/4KnL0LqcAOeRchgiq23Zi0nkZDYKcevc1rioP/H5j5QCqn6us34jF1l2O9eFTHXu5fh26gB+b+lYmeCwMAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:50:08.049934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:828e04a64d5434353f4e26df62cdc422826273370d37a3f86be9d5d3429a6e66","sha256:70f99fb6ded8193e93eacdfeb6308c9bfce36ed76882dcc76d0deaf9e26caa8b"],"state_sha256":"2ea69410510c1f9fe28ba1988723671306b10bba48818bf7be0a5720b63be393"}