{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VRG27BHS2PYM4PSRLNRSR5APG6","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":"8d1ffaec79f1445cafedce6d1a39535c4a83f23914cd50b1dca1c4a43677ba90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-05T03:38:42Z","title_canon_sha256":"a06c405ec60467b330199cff7f6fa1561491f4c005b9ea43e2a119f84df0d381"},"schema_version":"1.0","source":{"id":"1701.01201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01201","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01201v1","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01201","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"pith_short_12","alias_value":"VRG27BHS2PYM","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VRG27BHS2PYM4PSR","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VRG27BHS","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:546faeead7dda19b368f4ee334909f3386ff7bf0f169be6fa384497fd5fa2390","target":"graph","created_at":"2026-05-18T00:53:20Z","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 study the Liouville heat kernel (in the $L^2$ phase) associated with a class of logarithmically correlated Gaussian fields on the two dimensional torus. We show that for each $\\varepsilon>0$ there exists such a field, whose covariance is a bounded perturbation of that of the two dimensional Gaussian free field, and such that the associated Liouville heat kernel satisfies the short time estimates, $$ \\exp \\left( - t^{ - \\frac 1 { 1 + \\frac 1 2 \\gamma^2 } - \\varepsilon } \\right) \\le p_t^\\gamma (x, y) \\le \\exp \\left( - t^{- \\frac 1 { 1 + \\frac 1 2 \\gamma^2 } + \\varepsilon } \\right) , $$ for $\\","authors_text":"Fuxi Zhang, Jian Ding, Ofer Zeitouni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-05T03:38:42Z","title":"On the Liouville heat kernel for k-coarse MBRW and nonuniversality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01201","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:d24fe31f4c59a776bafc84caabb691747e072e8897b6ffdcf61ab38237cff62e","target":"record","created_at":"2026-05-18T00:53:20Z","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":"8d1ffaec79f1445cafedce6d1a39535c4a83f23914cd50b1dca1c4a43677ba90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-05T03:38:42Z","title_canon_sha256":"a06c405ec60467b330199cff7f6fa1561491f4c005b9ea43e2a119f84df0d381"},"schema_version":"1.0","source":{"id":"1701.01201","kind":"arxiv","version":1}},"canonical_sha256":"ac4daf84f2d3f0ce3e515b6328f40f378d348383a733ee9242a314151e9e1909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4daf84f2d3f0ce3e515b6328f40f378d348383a733ee9242a314151e9e1909","first_computed_at":"2026-05-18T00:53:20.194832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:20.194832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OlZkRuAWqWoMwjIisfcrP6W5kOowJ9BAn64wpnVPaNbi/UTd5h/fi6cnrCP9P63qKAkndWQyvzpoxNydRcNvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:20.195228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d24fe31f4c59a776bafc84caabb691747e072e8897b6ffdcf61ab38237cff62e","sha256:546faeead7dda19b368f4ee334909f3386ff7bf0f169be6fa384497fd5fa2390"],"state_sha256":"04132457bc851ab3b1694718cfe7be44597e686c85121ddab1d3df881995e11e"}