{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E5XBKJ6XOEGZ5AF3Y3SDEGUBAF","short_pith_number":"pith:E5XBKJ6X","canonical_record":{"source":{"id":"1711.07982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-21T19:00:00Z","cross_cats_sorted":["cond-mat.str-el","math.QA"],"title_canon_sha256":"14b4e60ead5d1823a19fe1cfdbd9f24e2588b236c4733ff32dcddeba150f12ad","abstract_canon_sha256":"756f1e223036e4697ea6f4fe317a84317cca3205e29dec60c2a715c05c4cd22e"},"schema_version":"1.0"},"canonical_sha256":"276e1527d7710d9e80bbc6e4321a8101600a66b6030672871e534a672bcec61c","source":{"kind":"arxiv","id":"1711.07982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07982","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07982v1","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07982","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"E5XBKJ6XOEGZ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5XBKJ6XOEGZ5AF3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5XBKJ6X","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E5XBKJ6XOEGZ5AF3Y3SDEGUBAF","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-21T19:00:00Z","cross_cats_sorted":["cond-mat.str-el","math.QA"],"title_canon_sha256":"14b4e60ead5d1823a19fe1cfdbd9f24e2588b236c4733ff32dcddeba150f12ad","abstract_canon_sha256":"756f1e223036e4697ea6f4fe317a84317cca3205e29dec60c2a715c05c4cd22e"},"schema_version":"1.0"},"canonical_sha256":"276e1527d7710d9e80bbc6e4321a8101600a66b6030672871e534a672bcec61c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:36.342398Z","signature_b64":"uQ8h+G18+exfFCbMhOhkw5OyBZCQenrBbLnxbSZE2PjCpOUh8axSJFByy5rPWKjNqJlyTp//JzKuqJO71soECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"276e1527d7710d9e80bbc6e4321a8101600a66b6030672871e534a672bcec61c","last_reissued_at":"2026-05-18T00:29:36.341865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:36.341865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07982","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":"2026-05-18T00:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5tIi1bO8EiLlrtHdBDQbJueSGpdRVQFErhQL7gR9w/BumPpznjFnhfsRU/hWF/WmYzuBOHze4xq69j2ukBATCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:26:03.325552Z"},"content_sha256":"4acbdef52c1a306b6e3b798ed1fb42382e4d75b2f3cc536e13ecaf7e075de296","schema_version":"1.0","event_id":"sha256:4acbdef52c1a306b6e3b798ed1fb42382e4d75b2f3cc536e13ecaf7e075de296"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E5XBKJ6XOEGZ5AF3Y3SDEGUBAF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math.QA"],"primary_cat":"quant-ph","authors_text":"Dominic J. Williamson, Frank Verstraete, Nick Bultinck","submitted_at":"2017-11-21T19:00:00Z","abstract_excerpt":"We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion categories is established. Tensor network representations of the topological defect superselection sectors are constructed for all domain walls. The emergent symmetry-enriched topological order is extracted from these representations, including the symmetry action on the underlying anyons. Dual phase transitions, induced by gauging a global symmetry, and conden"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07982","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":"2026-05-18T00:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b8AbXyxrLyR2q8CS9ZvplSM4U9Qle2xb+D/jlyAastjv/AQnYDJapsxbSIfzfabcY8LO7Xj0YrDvqyahqdrSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:26:03.325910Z"},"content_sha256":"0b083fa9ca64c31deadb819d36c0db3b1397ef9f602a73d83aa240051b4d68c1","schema_version":"1.0","event_id":"sha256:0b083fa9ca64c31deadb819d36c0db3b1397ef9f602a73d83aa240051b4d68c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF/bundle.json","state_url":"https://pith.science/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF/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":"2026-05-30T00:26:03Z","links":{"resolver":"https://pith.science/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF","bundle":"https://pith.science/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF/bundle.json","state":"https://pith.science/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5XBKJ6XOEGZ5AF3Y3SDEGUBAF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E5XBKJ6XOEGZ5AF3Y3SDEGUBAF","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":"756f1e223036e4697ea6f4fe317a84317cca3205e29dec60c2a715c05c4cd22e","cross_cats_sorted":["cond-mat.str-el","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-21T19:00:00Z","title_canon_sha256":"14b4e60ead5d1823a19fe1cfdbd9f24e2588b236c4733ff32dcddeba150f12ad"},"schema_version":"1.0","source":{"id":"1711.07982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07982","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07982v1","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07982","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"E5XBKJ6XOEGZ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5XBKJ6XOEGZ5AF3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5XBKJ6X","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:0b083fa9ca64c31deadb819d36c0db3b1397ef9f602a73d83aa240051b4d68c1","target":"graph","created_at":"2026-05-18T00:29:36Z","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 study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion categories is established. Tensor network representations of the topological defect superselection sectors are constructed for all domain walls. The emergent symmetry-enriched topological order is extracted from these representations, including the symmetry action on the underlying anyons. Dual phase transitions, induced by gauging a global symmetry, and conden","authors_text":"Dominic J. Williamson, Frank Verstraete, Nick Bultinck","cross_cats":["cond-mat.str-el","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-21T19:00:00Z","title":"Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07982","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":"sha256:4acbdef52c1a306b6e3b798ed1fb42382e4d75b2f3cc536e13ecaf7e075de296","target":"record","created_at":"2026-05-18T00:29:36Z","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":"756f1e223036e4697ea6f4fe317a84317cca3205e29dec60c2a715c05c4cd22e","cross_cats_sorted":["cond-mat.str-el","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-21T19:00:00Z","title_canon_sha256":"14b4e60ead5d1823a19fe1cfdbd9f24e2588b236c4733ff32dcddeba150f12ad"},"schema_version":"1.0","source":{"id":"1711.07982","kind":"arxiv","version":1}},"canonical_sha256":"276e1527d7710d9e80bbc6e4321a8101600a66b6030672871e534a672bcec61c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"276e1527d7710d9e80bbc6e4321a8101600a66b6030672871e534a672bcec61c","first_computed_at":"2026-05-18T00:29:36.341865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:36.341865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uQ8h+G18+exfFCbMhOhkw5OyBZCQenrBbLnxbSZE2PjCpOUh8axSJFByy5rPWKjNqJlyTp//JzKuqJO71soECA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:36.342398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4acbdef52c1a306b6e3b798ed1fb42382e4d75b2f3cc536e13ecaf7e075de296","sha256:0b083fa9ca64c31deadb819d36c0db3b1397ef9f602a73d83aa240051b4d68c1"],"state_sha256":"a7fa531edf6acd7062cb7682792871b3ca409c30e30a8c16d17134fcca927e2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wovWVmqkeDhwpYx6JdNbN1rSbcfI80Y8UxPkbPKNsb0ZVf88hjxZvpxQoyuUNzi7S/9o8ZPPu4E8Vx88VylUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:26:03.328026Z","bundle_sha256":"f51c68087a6c82e8f51503e7178c997f2cc5e59227fa34dec17e3c88a6a1117c"}}