{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ERQTV4UFIZXHLAWYX2HXFBCCDJ","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":"c99c60e35c742e5d2c7a9c5ab2737030bb55ac8e824ae2c10db2d0bfbfa80350","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2007-06-04T02:14:28Z","title_canon_sha256":"5d3874d5ed421c87d5a12c8fbb0c2fbabf41bcd430d7d08a0606dffcc0fc2fc8"},"schema_version":"1.0","source":{"id":"0706.0365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0365","created_at":"2026-07-04T15:24:16Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0365v1","created_at":"2026-07-04T15:24:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0365","created_at":"2026-07-04T15:24:16Z"},{"alias_kind":"pith_short_12","alias_value":"ERQTV4UFIZXH","created_at":"2026-07-04T15:24:16Z"},{"alias_kind":"pith_short_16","alias_value":"ERQTV4UFIZXHLAWY","created_at":"2026-07-04T15:24:16Z"},{"alias_kind":"pith_short_8","alias_value":"ERQTV4UF","created_at":"2026-07-04T15:24:16Z"}],"graph_snapshots":[{"event_id":"sha256:aa32e4bc6f34e21b165d5c927e5b9b1fabdf86c0d14121a683d95b454e8f3788","target":"graph","created_at":"2026-07-04T15:24:16Z","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/0706.0365/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The continuation of the Liouville conformal field theory to c<=1 is considered. The viability of an interpretation involving a timelike boson which is the conformal factor for two-dimensional asymptotically de Sitter geometries is examined. The conformal bootstrap leads to a three-point function with a unique analytic factor which is the same as that which appears along with the fusion coefficients in the minimal models. A corresponding non-analytic factor produces a well-defined metric on fields only when the central charge is restricted to those of the topological minimal models, and when th","authors_text":"Will McElgin","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-06-04T02:14:28Z","title":"Notes on Liouville Theory at c<=1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0365","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":"sha256:5990f65d098cadb686501c81bc0be98671e06416293b139b644850616784badc","target":"record","created_at":"2026-07-04T15:24:16Z","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":"c99c60e35c742e5d2c7a9c5ab2737030bb55ac8e824ae2c10db2d0bfbfa80350","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2007-06-04T02:14:28Z","title_canon_sha256":"5d3874d5ed421c87d5a12c8fbb0c2fbabf41bcd430d7d08a0606dffcc0fc2fc8"},"schema_version":"1.0","source":{"id":"0706.0365","kind":"arxiv","version":1}},"canonical_sha256":"24613af285466e7582d8be8f7284421a4edf2cd42cb094e3e941140be4296ca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24613af285466e7582d8be8f7284421a4edf2cd42cb094e3e941140be4296ca7","first_computed_at":"2026-07-04T15:24:16.975981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:24:16.975981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L2N07Tx8YHxk30pL2CjEzoXlm1a2U/+iop+TnMIUP74boyGGbWG1sr9yd2aB2WsrXwKO4TCW59EIZlPjaTluBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:24:16.976354Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.0365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5990f65d098cadb686501c81bc0be98671e06416293b139b644850616784badc","sha256:aa32e4bc6f34e21b165d5c927e5b9b1fabdf86c0d14121a683d95b454e8f3788"],"state_sha256":"02080b91c821bae26c08c109491a1e37c079f1af9f38e9a0640fbd747c9a6a33"}