{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Z6WEX25O6LYQZM2OYUJ27QL3ZV","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":"5c96fcc42a7ec4e4519b18577608db98afb2d38500e5a36c46a315124e62bf79","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-08T19:30:53Z","title_canon_sha256":"3faf95d79047dc2f2cfc4518a0eada3e6d0caffcadf924f387cdcaa417b7ef0d"},"schema_version":"1.0","source":{"id":"2104.04020","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.04020","created_at":"2026-07-05T08:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"2104.04020v3","created_at":"2026-07-05T08:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.04020","created_at":"2026-07-05T08:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z6WEX25O6LYQ","created_at":"2026-07-05T08:39:16Z"},{"alias_kind":"pith_short_16","alias_value":"Z6WEX25O6LYQZM2O","created_at":"2026-07-05T08:39:16Z"},{"alias_kind":"pith_short_8","alias_value":"Z6WEX25O","created_at":"2026-07-05T08:39:16Z"}],"graph_snapshots":[{"event_id":"sha256:281027875e5dca4783234408a73e62fa1896730008f54ed142f03194a46dbc54","target":"graph","created_at":"2026-07-05T08:39:16Z","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/2104.04020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics considerations suggest that a theory of Liouville quantum gravity (LQG) should exist for all values of matter central charge $\\mathbf{c} \\in (-\\infty,25)$. Probabilists have rigorously defined LQG as a random metric measure space for $\\mathbf{c} < 1$; however, they have only very recently begun to explore LQG in the $\\mathbf{c} \\in (1,25)$ phase. We define a random metric associated to LQG for all $\\mathbf{c} < 25$ by a collection of axioms analogous to axioms stated in the $\\mathbf{c} < 1$ setting. We show that such a metric exists for each $\\mathbf{c}$ by considering an approximating","authors_text":"Joshua Pfeffer","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-08T19:30:53Z","title":"Weak Liouville quantum gravity metrics with matter central charge $\\mathbf{c} \\in (-\\infty, 25)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04020","kind":"arxiv","version":3},"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:f0529caf569ecf615bbebab2d674c97d5a7cc9ee02f6c8cf9b2b38512d986189","target":"record","created_at":"2026-07-05T08:39:16Z","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":"5c96fcc42a7ec4e4519b18577608db98afb2d38500e5a36c46a315124e62bf79","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-04-08T19:30:53Z","title_canon_sha256":"3faf95d79047dc2f2cfc4518a0eada3e6d0caffcadf924f387cdcaa417b7ef0d"},"schema_version":"1.0","source":{"id":"2104.04020","kind":"arxiv","version":3}},"canonical_sha256":"cfac4bebaef2f10cb34ec513afc17bcd50a97f35d1ed6edafd6ede7291288d05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfac4bebaef2f10cb34ec513afc17bcd50a97f35d1ed6edafd6ede7291288d05","first_computed_at":"2026-07-05T08:39:16.651934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:16.651934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h8EdS7Bvnz1jL0gcRe7HrkVBXU7LzxRkhhLEft7g/iUkJLh7MESTladtIAgpKNn1LSmeF+TmtEI9hBYdBloAAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:16.652329Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.04020","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0529caf569ecf615bbebab2d674c97d5a7cc9ee02f6c8cf9b2b38512d986189","sha256:281027875e5dca4783234408a73e62fa1896730008f54ed142f03194a46dbc54"],"state_sha256":"6a4a6f9785782c6b03712e24dad19e71facb0926450088a19f67f4b43b90bbba"}