{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QY2B6ENKMO72AE34L7FK7VCP32","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":"148412625b84a7b68f04ceb695b1ae1a5ebd153d2015085f2358b0d59622faba","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-10-27T16:01:30Z","title_canon_sha256":"8675eee2f45e6cd229c59ce152721d43cf178df3a4de01cb5b5f394edf0d34a7"},"schema_version":"1.0","source":{"id":"2310.18226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.18226","created_at":"2026-07-05T07:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"2310.18226v1","created_at":"2026-07-05T07:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.18226","created_at":"2026-07-05T07:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"QY2B6ENKMO72","created_at":"2026-07-05T07:05:59Z"},{"alias_kind":"pith_short_16","alias_value":"QY2B6ENKMO72AE34","created_at":"2026-07-05T07:05:59Z"},{"alias_kind":"pith_short_8","alias_value":"QY2B6ENK","created_at":"2026-07-05T07:05:59Z"}],"graph_snapshots":[{"event_id":"sha256:d42b4501d5f467d6c89c832ce6129c7320bd694ec4ec4d9a7b4e78cf81416501","target":"graph","created_at":"2026-07-05T07:05:59Z","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/2310.18226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On a given Riemann surface, we construct a path integral based on the Liouville action functional with imaginary parameters. The construction relies on the compactified Gaussian Free Field (GFF), which we perturb with a curvature term and an exponential potential. In physics this path integral is conjectured to describe the scaling limit of critical loop models such as Potts and O(n) models. The potential term is defined by means of imaginary Gaussian Multiplicative Chaos theory. The curvature term involves integrated 1-forms, which are multivalued on the manifold, and requires a delicate regu","authors_text":"Antti Kupiainen, Colin Guillarmou, R\\'emi Rhodes","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-10-27T16:01:30Z","title":"Compactified Imaginary Liouville Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.18226","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":"sha256:9d3fbdb2df96ee0607d289da492f21b1b2f42cdcea3a40c92e1a22284343f914","target":"record","created_at":"2026-07-05T07:05:59Z","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":"148412625b84a7b68f04ceb695b1ae1a5ebd153d2015085f2358b0d59622faba","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-10-27T16:01:30Z","title_canon_sha256":"8675eee2f45e6cd229c59ce152721d43cf178df3a4de01cb5b5f394edf0d34a7"},"schema_version":"1.0","source":{"id":"2310.18226","kind":"arxiv","version":1}},"canonical_sha256":"86341f11aa63bfa0137c5fcaafd44fdea03c42f4576e3c2bc458549362731093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86341f11aa63bfa0137c5fcaafd44fdea03c42f4576e3c2bc458549362731093","first_computed_at":"2026-07-05T07:05:59.118839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:05:59.118839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q8oofv2OZv/UWiqqYn61whiVQLaxA3rS+MbkLDNdYwjJV/u6eeXM3LBFQIbY9wwwPzNLTpqn6xQ3xMeV1gLyDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:05:59.119229Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.18226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d3fbdb2df96ee0607d289da492f21b1b2f42cdcea3a40c92e1a22284343f914","sha256:d42b4501d5f467d6c89c832ce6129c7320bd694ec4ec4d9a7b4e78cf81416501"],"state_sha256":"45d3a4268fce149585dca3e90068d15d10de476f88a0ff2e758731dc1c0979c2"}