{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O5SNPBEPQIOEVW72546GFYN5RZ","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":"d519d88504e3b8979324191d23ee1b896211116cea654c2fca950b685aa0d088","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-01-15T19:00:04Z","title_canon_sha256":"f47c92906786660bf537cc1505cd50c4d9f00334e900c35b80357eeda5aef6d3"},"schema_version":"1.0","source":{"id":"1801.04936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04936","created_at":"2026-05-18T00:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04936v2","created_at":"2026-05-18T00:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04936","created_at":"2026-05-18T00:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"O5SNPBEPQIOE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"O5SNPBEPQIOEVW72","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"O5SNPBEP","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:2545a54fe643db5f7ea5a9e382f700fe2343d6c1641129be33183d4909d4f861","target":"graph","created_at":"2026-05-18T00:16:02Z","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 consider a family of quantum loop models in 2+1 spacetime dimensions with marginally long-ranged and statistical interactions mediated by a U$(1)$ gauge field, both purely in 2+1 dimensions and on a surface in a 3+1 dimensional bulk system. In the absence of fractional spin, these theories have been shown to be self-dual under particle-vortex duality and shifts of the statistical angle of the loops by $2\\pi$, which form a subgroup of the modular group, PSL$(2,\\mathbb{Z})$. We show that careful consideration of fractional spin in these theories completely breaks their statistical periodicity","authors_text":"Eduardo Fradkin, Hart Goldman","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-01-15T19:00:04Z","title":"Loop Models, Modular Invariance, and Three Dimensional Bosonization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04936","kind":"arxiv","version":2},"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":"sha256:037cabf49c899e319e658cbb2e441bbea1e0290815713524b07bea3809d25f09","target":"record","created_at":"2026-05-18T00:16:02Z","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":"d519d88504e3b8979324191d23ee1b896211116cea654c2fca950b685aa0d088","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-01-15T19:00:04Z","title_canon_sha256":"f47c92906786660bf537cc1505cd50c4d9f00334e900c35b80357eeda5aef6d3"},"schema_version":"1.0","source":{"id":"1801.04936","kind":"arxiv","version":2}},"canonical_sha256":"7764d7848f821c4adbfaef3c62e1bd8e6f0e6cc9e0b2cc1823f9d697ace0dcf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7764d7848f821c4adbfaef3c62e1bd8e6f0e6cc9e0b2cc1823f9d697ace0dcf4","first_computed_at":"2026-05-18T00:16:02.900554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:02.900554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HIrFy6dsscg+E0P3waV+lVO40J6MNY6p45suPu1RF1ozScS8REMyzlniNd5Jo3liDe6zpYiFXOj2LT1Ry6e8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:02.901196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:037cabf49c899e319e658cbb2e441bbea1e0290815713524b07bea3809d25f09","sha256:2545a54fe643db5f7ea5a9e382f700fe2343d6c1641129be33183d4909d4f861"],"state_sha256":"95a224ac488eee1cf271599abb97e8af6469d867f3605b4b0a94c3ef2cbf18f2"}