{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TGZQS2W3IBAD74GSVOBOL42FGT","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":"e2f48ceb2a625d8e203a66738c5e2441f0f177af26693c78b00b4e05207ac37f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-07T20:00:49Z","title_canon_sha256":"e3f497e927ec4a72a170a190d0edf5c5e2ef5a7da5bfe41eb50f8ab35425feab"},"schema_version":"1.0","source":{"id":"1504.01738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01738","created_at":"2026-05-18T01:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01738v1","created_at":"2026-05-18T01:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01738","created_at":"2026-05-18T01:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"TGZQS2W3IBAD","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TGZQS2W3IBAD74GS","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TGZQS2W3","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:7a7324a982e54151033564f8387a56e5d6b51ccb6c22f36a54da4e27973c0232","target":"graph","created_at":"2026-05-18T01:20:46Z","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 analyse the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kahler formalism, we extract the coefficient of the leading divergence in $\\sim A\\Lambda^2 (\\ln A\\Lambda^2)^2$. This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence $","authors_text":"Adel Bilal, Laetitia Leduc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-07T20:00:49Z","title":"2D quantum gravity at three loops: a counterterm investigation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01738","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:ef55aee2cb231f6c94d5fe85e3c0e8901205026d81adb3f5a2a8256d4518422a","target":"record","created_at":"2026-05-18T01:20:46Z","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":"e2f48ceb2a625d8e203a66738c5e2441f0f177af26693c78b00b4e05207ac37f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-07T20:00:49Z","title_canon_sha256":"e3f497e927ec4a72a170a190d0edf5c5e2ef5a7da5bfe41eb50f8ab35425feab"},"schema_version":"1.0","source":{"id":"1504.01738","kind":"arxiv","version":1}},"canonical_sha256":"99b3096adb40403ff0d2ab82e5f34534c084685c22d0f9d5581f61eb0004a9cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99b3096adb40403ff0d2ab82e5f34534c084685c22d0f9d5581f61eb0004a9cf","first_computed_at":"2026-05-18T01:20:46.661749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:46.661749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FsstOGQIQGAF8sgERuO9Vv1zCmQnpGx9DZTS2S2iun7Vb0DRdXPH5tJ5JBc62QiLmx4URbGYuQ4dMwrTYlEmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:46.662376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef55aee2cb231f6c94d5fe85e3c0e8901205026d81adb3f5a2a8256d4518422a","sha256:7a7324a982e54151033564f8387a56e5d6b51ccb6c22f36a54da4e27973c0232"],"state_sha256":"b31010b5ff573a25ae19465ccedafe1c39d732aec69fe7326161a5cb36ec263a"}