{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:MMH3ERJQU75VRFGVYK7A6VNAQM","short_pith_number":"pith:MMH3ERJQ","schema_version":"1.0","canonical_sha256":"630fb24530a7fb5894d5c2be0f55a0830239a158be04ab522600ad5e7b33bdca","source":{"kind":"arxiv","id":"cond-mat/0510613","version":2},"attestation_state":"computed","paper":{"title":"Detecting topological order in a ground state wave function","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Michael Levin, Xiao-Gang Wen","submitted_at":"2005-10-23T19:26:35Z","abstract_excerpt":"A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d_i, F^{ijk}_{lmn}, \\delta_{ijk}). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the ``topological entropy'' which directly measures the quantum dimension D = \\sum_i d^2_i."},"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":"cond-mat/0510613","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2005-10-23T19:26:35Z","cross_cats_sorted":[],"title_canon_sha256":"677a1c6ae6a3006a4fd3ff9992fe3c02c1e6bc46ad1e7d3c96b032b37863234f","abstract_canon_sha256":"ae9cff12133df6f47a23a0707ca0e123bc14f346acf1c23c67bc481bc15ca932"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:54:46.412450Z","signature_b64":"6kUSBJSnGgUUBVGkpz5wkWelI2Qw+J0pCW66t2LTqZNOEpAKsPye2KxAEvhd7U5IUq8Arcx5V0G0cUkZJefhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"630fb24530a7fb5894d5c2be0f55a0830239a158be04ab522600ad5e7b33bdca","last_reissued_at":"2026-07-04T16:54:46.412068Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:54:46.412068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Detecting topological order in a ground state wave function","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Michael Levin, Xiao-Gang Wen","submitted_at":"2005-10-23T19:26:35Z","abstract_excerpt":"A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d_i, F^{ijk}_{lmn}, \\delta_{ijk}). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the ``topological entropy'' which directly measures the quantum dimension D = \\sum_i d^2_i."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0510613","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/cond-mat/0510613/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":"cond-mat/0510613","created_at":"2026-07-04T16:54:46.412122+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0510613v2","created_at":"2026-07-04T16:54:46.412122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0510613","created_at":"2026-07-04T16:54:46.412122+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMH3ERJQU75V","created_at":"2026-07-04T16:54:46.412122+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMH3ERJQU75VRFGV","created_at":"2026-07-04T16:54:46.412122+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMH3ERJQ","created_at":"2026-07-04T16:54:46.412122+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":17,"internal_anchor_count":16,"sample":[{"citing_arxiv_id":"2607.06050","citing_title":"Genuine Multi-Entropy in the Toric Code","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2606.18361","citing_title":"Universal entanglement probes of topological order and locally-achiral manifolds","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2606.13388","citing_title":"From 2D Yang-Mills to Calogero-Sutherland via a colored particle","ref_index":36,"is_internal_anchor":true},{"citing_arxiv_id":"2606.29311","citing_title":"Pseudo entropy and topological phases of matter","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2605.26208","citing_title":"Mapping twist fields to local operators via tensor networks","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"1907.08126","citing_title":"Lectures on entanglement entropy in field theory and holography","ref_index":25,"is_internal_anchor":true},{"citing_arxiv_id":"2212.11740","citing_title":"Separability and entanglement of resonating valence-bond states","ref_index":55,"is_internal_anchor":true},{"citing_arxiv_id":"2301.05687","citing_title":"Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions","ref_index":39,"is_internal_anchor":true},{"citing_arxiv_id":"2501.17912","citing_title":"De Sitter Horizon Edge Partition Functions","ref_index":81,"is_internal_anchor":true},{"citing_arxiv_id":"2605.17438","citing_title":"Holographic entanglement entropy under external magnetic field from the EMD model","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2508.05494","citing_title":"Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State","ref_index":22,"is_internal_anchor":true},{"citing_arxiv_id":"2509.00593","citing_title":"Genuine multientropy, dihedral invariants and Lifshitz theory","ref_index":22,"is_internal_anchor":true},{"citing_arxiv_id":"2511.01366","citing_title":"Symmetry-Resolved Entanglement Entropy from Heat Kernels","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2511.11059","citing_title":"Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls","ref_index":82,"is_internal_anchor":true},{"citing_arxiv_id":"2512.04649","citing_title":"Probing chiral topological states with permutation defects","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2512.15969","citing_title":"Quantum Liouville Cosmology","ref_index":57,"is_internal_anchor":true},{"citing_arxiv_id":"2605.02883","citing_title":"de Sitter Vacua & pUniverses","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM","json":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM.json","graph_json":"https://pith.science/api/pith-number/MMH3ERJQU75VRFGVYK7A6VNAQM/graph.json","events_json":"https://pith.science/api/pith-number/MMH3ERJQU75VRFGVYK7A6VNAQM/events.json","paper":"https://pith.science/paper/MMH3ERJQ"},"agent_actions":{"view_html":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM","download_json":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM.json","view_paper":"https://pith.science/paper/MMH3ERJQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0510613&json=true","fetch_graph":"https://pith.science/api/pith-number/MMH3ERJQU75VRFGVYK7A6VNAQM/graph.json","fetch_events":"https://pith.science/api/pith-number/MMH3ERJQU75VRFGVYK7A6VNAQM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM/action/storage_attestation","attest_author":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM/action/author_attestation","sign_citation":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM/action/citation_signature","submit_replication":"https://pith.science/pith/MMH3ERJQU75VRFGVYK7A6VNAQM/action/replication_record"}},"created_at":"2026-07-04T16:54:46.412122+00:00","updated_at":"2026-07-04T16:54:46.412122+00:00"}