{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EIOFYZRZJUDSRUF32AATQOMWV3","short_pith_number":"pith:EIOFYZRZ","canonical_record":{"source":{"id":"1402.4081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-02-17T17:45:32Z","cross_cats_sorted":[],"title_canon_sha256":"ea0d58451535cdcb4a737d58c2c0e5a6b13fb9940346c626144c16f9f0978f9f","abstract_canon_sha256":"816a358d4750fca682cc30cc0b7737ba60303b279f0f41b6a893f3174144cc34"},"schema_version":"1.0"},"canonical_sha256":"221c5c66394d0728d0bbd001383996aeef622a0851730b2bee061ee2b8a9ca01","source":{"kind":"arxiv","id":"1402.4081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4081","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4081v1","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4081","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"EIOFYZRZJUDS","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EIOFYZRZJUDSRUF3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EIOFYZRZ","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EIOFYZRZJUDSRUF32AATQOMWV3","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-02-17T17:45:32Z","cross_cats_sorted":[],"title_canon_sha256":"ea0d58451535cdcb4a737d58c2c0e5a6b13fb9940346c626144c16f9f0978f9f","abstract_canon_sha256":"816a358d4750fca682cc30cc0b7737ba60303b279f0f41b6a893f3174144cc34"},"schema_version":"1.0"},"canonical_sha256":"221c5c66394d0728d0bbd001383996aeef622a0851730b2bee061ee2b8a9ca01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:20.041979Z","signature_b64":"HXnFN98OhPzeJw8JYT3toOlxtnR0BhMWkhfI8FNORQUk6TK5+J/m4PEJrU+NIIWKx8C7XxDNEiyJtz6cR2V2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"221c5c66394d0728d0bbd001383996aeef622a0851730b2bee061ee2b8a9ca01","last_reissued_at":"2026-05-18T02:49:20.041294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:20.041294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4081","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROmEqgqJHYTKU1SC1Y60K4nK99/mGKm2VZFg6ne7TlMUeIIUc1vaRotMBUj9vlAFK8TxaU9TrOM9f0SCwVRBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:24:00.864869Z"},"content_sha256":"083bd95ca4fab8616362563c19d27b2fdb3e967742a099f5f47c0eba8c584857","schema_version":"1.0","event_id":"sha256:083bd95ca4fab8616362563c19d27b2fdb3e967742a099f5f47c0eba8c584857"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EIOFYZRZJUDSRUF32AATQOMWV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalizations and limitations of string-net models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Chien-Hung Lin, Michael Levin","submitted_at":"2014-02-17T17:45:32Z","abstract_excerpt":"We ask which topological phases can and cannot be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely those with abelian braiding statistics. Specifically, we find that an abelian topological phase can be realized by a string-net model if and only if (i) it has a vanishing thermal Hall conductance and (ii) it has at least one Lagrangian subgroup --- a subset of quasiparticles with particular topological properties. Equivalently, we find that an abelian topological phase is realizable if and only if it supports a gapped edg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4081","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDhhiPEUEMP7Vrr3eWjD49l5qe7O/Z06h1DWBhxMVQkcxp7Tx8HQ8jv52Y/9iYU3CGUmnppy6HDXpAru4gyZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:24:00.865253Z"},"content_sha256":"8e6c4f79185753e6c8e84b35989b3e88398f05ebe5679e6a338986e0c9544e12","schema_version":"1.0","event_id":"sha256:8e6c4f79185753e6c8e84b35989b3e88398f05ebe5679e6a338986e0c9544e12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIOFYZRZJUDSRUF32AATQOMWV3/bundle.json","state_url":"https://pith.science/pith/EIOFYZRZJUDSRUF32AATQOMWV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIOFYZRZJUDSRUF32AATQOMWV3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T19:24:00Z","links":{"resolver":"https://pith.science/pith/EIOFYZRZJUDSRUF32AATQOMWV3","bundle":"https://pith.science/pith/EIOFYZRZJUDSRUF32AATQOMWV3/bundle.json","state":"https://pith.science/pith/EIOFYZRZJUDSRUF32AATQOMWV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIOFYZRZJUDSRUF32AATQOMWV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EIOFYZRZJUDSRUF32AATQOMWV3","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":"816a358d4750fca682cc30cc0b7737ba60303b279f0f41b6a893f3174144cc34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-02-17T17:45:32Z","title_canon_sha256":"ea0d58451535cdcb4a737d58c2c0e5a6b13fb9940346c626144c16f9f0978f9f"},"schema_version":"1.0","source":{"id":"1402.4081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4081","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4081v1","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4081","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"EIOFYZRZJUDS","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EIOFYZRZJUDSRUF3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EIOFYZRZ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8e6c4f79185753e6c8e84b35989b3e88398f05ebe5679e6a338986e0c9544e12","target":"graph","created_at":"2026-05-18T02:49:20Z","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"},"paper":{"abstract_excerpt":"We ask which topological phases can and cannot be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely those with abelian braiding statistics. Specifically, we find that an abelian topological phase can be realized by a string-net model if and only if (i) it has a vanishing thermal Hall conductance and (ii) it has at least one Lagrangian subgroup --- a subset of quasiparticles with particular topological properties. Equivalently, we find that an abelian topological phase is realizable if and only if it supports a gapped edg","authors_text":"Chien-Hung Lin, Michael Levin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-02-17T17:45:32Z","title":"Generalizations and limitations of string-net models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4081","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":"sha256:083bd95ca4fab8616362563c19d27b2fdb3e967742a099f5f47c0eba8c584857","target":"record","created_at":"2026-05-18T02:49:20Z","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":"816a358d4750fca682cc30cc0b7737ba60303b279f0f41b6a893f3174144cc34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-02-17T17:45:32Z","title_canon_sha256":"ea0d58451535cdcb4a737d58c2c0e5a6b13fb9940346c626144c16f9f0978f9f"},"schema_version":"1.0","source":{"id":"1402.4081","kind":"arxiv","version":1}},"canonical_sha256":"221c5c66394d0728d0bbd001383996aeef622a0851730b2bee061ee2b8a9ca01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"221c5c66394d0728d0bbd001383996aeef622a0851730b2bee061ee2b8a9ca01","first_computed_at":"2026-05-18T02:49:20.041294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:20.041294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HXnFN98OhPzeJw8JYT3toOlxtnR0BhMWkhfI8FNORQUk6TK5+J/m4PEJrU+NIIWKx8C7XxDNEiyJtz6cR2V2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:20.041979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:083bd95ca4fab8616362563c19d27b2fdb3e967742a099f5f47c0eba8c584857","sha256:8e6c4f79185753e6c8e84b35989b3e88398f05ebe5679e6a338986e0c9544e12"],"state_sha256":"d2e89ebef70ae00ea77efeadbdfbf2fb875eba82958e8e15be5e849261ced26b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cgbFS2E2xFc0WJUKEtm+qzQ6mvrdv86RHtC+5WqH9yJDH4jGJxKSHYcfxqcEZWJCxKI3oTBvbGmga3HFgn3QBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:24:00.867204Z","bundle_sha256":"3b4bebf69004ae5abff4cc0f3546aaf14f5ae77012fa46b9c1e5fd473277a44b"}}