{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:C4NNZ7WFJBVISKL5FIR27FJHTS","short_pith_number":"pith:C4NNZ7WF","schema_version":"1.0","canonical_sha256":"171adcfec5486a89297d2a23af95279c8ecc2383c0285eb5e70a7fb42cd0de30","source":{"kind":"arxiv","id":"2211.09127","version":2},"attestation_state":"computed","paper":{"title":"Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Gautam Nambiar, Maissam Barkeshli, Naren Manjunath, Yuxuan Zhang","submitted_at":"2022-11-16T19:00:00Z","abstract_excerpt":"We show how to define a quantized many-body charge polarization $\\vec{\\mathscr{P}}$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. For invertible topological states, $\\vec{\\mathscr{P}}$ is a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$, $\\mathbb{Z}_3$, $\\mathbb{Z}_2$, or $\\mathbb{Z}_1$ topological invariant in the presence of $M = 2$, $3$, $4$, or $6$-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. $\\vec{\\mathscr{P}}$ manifests in the bulk of the system as (i) a fractional quantized contribution of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.09127","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2022-11-16T19:00:00Z","cross_cats_sorted":["cond-mat.mes-hall","quant-ph"],"title_canon_sha256":"217f933f26d007d92533fb886a0216fb7ea02747687f0e765382d84e6ca4c154","abstract_canon_sha256":"369295190f5d48eac0bde1b857db702f3ef348c07fc708580df2e8458ad1d8a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:31:06.870324Z","signature_b64":"W/imJu5zCVchDcdYBdr7A+hnSm6dDuMfnaljK0Bfur/DyN9HYtpmwWED/+xwO1sESwwsOjEjzsi6I3uMQHkjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"171adcfec5486a89297d2a23af95279c8ecc2383c0285eb5e70a7fb42cd0de30","last_reissued_at":"2026-07-05T06:31:06.869898Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:31:06.869898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Gautam Nambiar, Maissam Barkeshli, Naren Manjunath, Yuxuan Zhang","submitted_at":"2022-11-16T19:00:00Z","abstract_excerpt":"We show how to define a quantized many-body charge polarization $\\vec{\\mathscr{P}}$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. For invertible topological states, $\\vec{\\mathscr{P}}$ is a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$, $\\mathbb{Z}_3$, $\\mathbb{Z}_2$, or $\\mathbb{Z}_1$ topological invariant in the presence of $M = 2$, $3$, $4$, or $6$-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. $\\vec{\\mathscr{P}}$ manifests in the bulk of the system as (i) a fractional quantized contribution of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09127","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.09127/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.09127","created_at":"2026-07-05T06:31:06.869965+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.09127v2","created_at":"2026-07-05T06:31:06.869965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.09127","created_at":"2026-07-05T06:31:06.869965+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4NNZ7WFJBVI","created_at":"2026-07-05T06:31:06.869965+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4NNZ7WFJBVISKL5","created_at":"2026-07-05T06:31:06.869965+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4NNZ7WF","created_at":"2026-07-05T06:31:06.869965+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.19691","citing_title":"Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation","ref_index":82,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS","json":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS.json","graph_json":"https://pith.science/api/pith-number/C4NNZ7WFJBVISKL5FIR27FJHTS/graph.json","events_json":"https://pith.science/api/pith-number/C4NNZ7WFJBVISKL5FIR27FJHTS/events.json","paper":"https://pith.science/paper/C4NNZ7WF"},"agent_actions":{"view_html":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS","download_json":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS.json","view_paper":"https://pith.science/paper/C4NNZ7WF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.09127&json=true","fetch_graph":"https://pith.science/api/pith-number/C4NNZ7WFJBVISKL5FIR27FJHTS/graph.json","fetch_events":"https://pith.science/api/pith-number/C4NNZ7WFJBVISKL5FIR27FJHTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS/action/storage_attestation","attest_author":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS/action/author_attestation","sign_citation":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS/action/citation_signature","submit_replication":"https://pith.science/pith/C4NNZ7WFJBVISKL5FIR27FJHTS/action/replication_record"}},"created_at":"2026-07-05T06:31:06.869965+00:00","updated_at":"2026-07-05T06:31:06.869965+00:00"}