{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WAHUCA43BC5VEHAO54NBQ27KQR","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":"01f1262796f96aa4553d88f96d254072b27b7438f13b8eb59a0ce06cb0f08e30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-07-13T05:09:22Z","title_canon_sha256":"fd19f94a3553f632809e93192d4ab0a01f624b17286237fd2d67d8c7c91dd469"},"schema_version":"1.0","source":{"id":"0807.2010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.2010","created_at":"2026-07-04T15:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"0807.2010v1","created_at":"2026-07-04T15:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.2010","created_at":"2026-07-04T15:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"WAHUCA43BC5V","created_at":"2026-07-04T15:39:07Z"},{"alias_kind":"pith_short_16","alias_value":"WAHUCA43BC5VEHAO","created_at":"2026-07-04T15:39:07Z"},{"alias_kind":"pith_short_8","alias_value":"WAHUCA43","created_at":"2026-07-04T15:39:07Z"}],"graph_snapshots":[{"event_id":"sha256:9f0512f6f8554b877bb77a56e4076da173a71de75a667bb48f00fd19f45b6a5e","target":"graph","created_at":"2026-07-04T15:39:07Z","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/0807.2010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net condensation. These phase transitions change topological order without changing any symmetries. This demonstrates that the tensor-entanglement renormalization group approach can be used to study the phase diagram of a quantum system with topologically ordered phases.","authors_text":"Michael Levin, Xiao-Gang Wen, Zheng-Cheng Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-07-13T05:09:22Z","title":"Tensor-entanglement renormalization group approach to topological phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.2010","kind":"arxiv","version":1},"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":"sha256:4a9ba2d3624f82d16726b24cb121e36f9c57a591ee7ad373baf482956d14e3cc","target":"record","created_at":"2026-07-04T15:39:07Z","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":"01f1262796f96aa4553d88f96d254072b27b7438f13b8eb59a0ce06cb0f08e30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-07-13T05:09:22Z","title_canon_sha256":"fd19f94a3553f632809e93192d4ab0a01f624b17286237fd2d67d8c7c91dd469"},"schema_version":"1.0","source":{"id":"0807.2010","kind":"arxiv","version":1}},"canonical_sha256":"b00f41039b08bb521c0eef1a186bea84514aa8cc3645610966a1e57c52d75364","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b00f41039b08bb521c0eef1a186bea84514aa8cc3645610966a1e57c52d75364","first_computed_at":"2026-07-04T15:39:07.533626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:39:07.533626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HsR8oNyQeep5AtPCHXqDkBlWACtqv5pE7xNGn3ghU21/EalihQhywLOAbIZyvquSf/7FX/PLqux79wMtHbojBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:39:07.534006Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.2010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a9ba2d3624f82d16726b24cb121e36f9c57a591ee7ad373baf482956d14e3cc","sha256:9f0512f6f8554b877bb77a56e4076da173a71de75a667bb48f00fd19f45b6a5e"],"state_sha256":"42defdfe9f804ba38c41f4e0fac908b22437ab8abc42ae1d4a3fe42b0b0536c2"}