{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GJWCFWAZOIXNBAQWBX3WKDLESZ","short_pith_number":"pith:GJWCFWAZ","schema_version":"1.0","canonical_sha256":"326c22d819722ed082160df7650d6496445d78dbd8735bcccd078f2ccd61a39f","source":{"kind":"arxiv","id":"2405.17379","version":1},"attestation_state":"computed","paper":{"title":"Classifying 2D topological phases: mapping ground states to string-nets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Daniel Ranard, Isaac H. Kim","submitted_at":"2024-05-27T17:36:17Z","abstract_excerpt":"We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth quantum circuit. It is conjectured that the Levin-Wen string-net models exhaust all possible gapped phases with gappable boundary, and these phases are labeled by unitary modular tensor categories. We prove this under the assumption that every phase has a representative state with zero correlation length "},"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":"2405.17379","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-05-27T17:36:17Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math-ph","math.MP"],"title_canon_sha256":"aa697d8f467b15e2416de2d90f5c756d8b19d0cddff8260acc918914910a6c00","abstract_canon_sha256":"61bda51369c67ed12776be00c1424fd170058e878ed0ef2463942b9f5eb06e3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:23:43.775244Z","signature_b64":"PFHZ0xoumM/xoXroKgoEimkwObvZ9kB3SPnYaXqsgjuSdg1m8Hji11AzbxlzVcvtoulvc/tdaKuuJpNyFqQfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"326c22d819722ed082160df7650d6496445d78dbd8735bcccd078f2ccd61a39f","last_reissued_at":"2026-07-05T08:23:43.774761Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:23:43.774761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classifying 2D topological phases: mapping ground states to string-nets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Daniel Ranard, Isaac H. Kim","submitted_at":"2024-05-27T17:36:17Z","abstract_excerpt":"We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth quantum circuit. It is conjectured that the Levin-Wen string-net models exhaust all possible gapped phases with gappable boundary, and these phases are labeled by unitary modular tensor categories. We prove this under the assumption that every phase has a representative state with zero correlation length "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.17379","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.17379/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":"2405.17379","created_at":"2026-07-05T08:23:43.774819+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.17379v1","created_at":"2026-07-05T08:23:43.774819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.17379","created_at":"2026-07-05T08:23:43.774819+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJWCFWAZOIXN","created_at":"2026-07-05T08:23:43.774819+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJWCFWAZOIXNBAQW","created_at":"2026-07-05T08:23:43.774819+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJWCFWAZ","created_at":"2026-07-05T08:23:43.774819+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.20472","citing_title":"Many-body chirality of topological stabilizer states","ref_index":27,"is_internal_anchor":false},{"citing_arxiv_id":"2606.12540","citing_title":"Toward Entanglement Bootstrap for Conformal Field Theory in Any Dimension","ref_index":50,"is_internal_anchor":false},{"citing_arxiv_id":"2605.22424","citing_title":"Long-range nonstabilizerness of topologically encoded states from mutual information","ref_index":70,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ","json":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ.json","graph_json":"https://pith.science/api/pith-number/GJWCFWAZOIXNBAQWBX3WKDLESZ/graph.json","events_json":"https://pith.science/api/pith-number/GJWCFWAZOIXNBAQWBX3WKDLESZ/events.json","paper":"https://pith.science/paper/GJWCFWAZ"},"agent_actions":{"view_html":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ","download_json":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ.json","view_paper":"https://pith.science/paper/GJWCFWAZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.17379&json=true","fetch_graph":"https://pith.science/api/pith-number/GJWCFWAZOIXNBAQWBX3WKDLESZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GJWCFWAZOIXNBAQWBX3WKDLESZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ/action/storage_attestation","attest_author":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ/action/author_attestation","sign_citation":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ/action/citation_signature","submit_replication":"https://pith.science/pith/GJWCFWAZOIXNBAQWBX3WKDLESZ/action/replication_record"}},"created_at":"2026-07-05T08:23:43.774819+00:00","updated_at":"2026-07-05T08:23:43.774819+00:00"}