{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:A36NQFQKXCME7TQO2MR6STS2UZ","short_pith_number":"pith:A36NQFQK","schema_version":"1.0","canonical_sha256":"06fcd8160ab8984fce0ed323e94e5aa6766af73056927256721a934919daed52","source":{"kind":"arxiv","id":"1411.1738","version":1},"attestation_state":"computed","paper":{"title":"Heat kernels on 2d Liouville quantum gravity: a numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alexander Teplyaev, Grigory Bonik, Joe P. Chen","submitted_at":"2014-11-06T20:43:32Z","abstract_excerpt":"We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore, when diffusion is started from a high point of the underlying Gaussian free field, our numerics indicates superdiffusive space-time scaling with respect to the Euclidean metric in the small space-to-time regime. The implications of this result require further investigation, but seem to coincide with the notion that the Euclidean metric is not the right geodesi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.1738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-06T20:43:32Z","cross_cats_sorted":["hep-lat","math.MP","math.PR"],"title_canon_sha256":"af352c66741da9fc06c1a6abfac7ed148c43cda68a7a68bcc8338219e8e5f958","abstract_canon_sha256":"1b4bb5f562c050f792edc845078951ca16a3b872104153378314ef92865fd52b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:27.012829Z","signature_b64":"ngahQDVLYh/bNTMIWusbYypESuUktd4CCpbig7F2vDm/LKdZQbwtpiaNfOfwigd1rSUyKiBro/dzAtFgi/NOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06fcd8160ab8984fce0ed323e94e5aa6766af73056927256721a934919daed52","last_reissued_at":"2026-05-18T02:38:27.012097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:27.012097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat kernels on 2d Liouville quantum gravity: a numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alexander Teplyaev, Grigory Bonik, Joe P. Chen","submitted_at":"2014-11-06T20:43:32Z","abstract_excerpt":"We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore, when diffusion is started from a high point of the underlying Gaussian free field, our numerics indicates superdiffusive space-time scaling with respect to the Euclidean metric in the small space-to-time regime. The implications of this result require further investigation, but seem to coincide with the notion that the Euclidean metric is not the right geodesi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1738","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.1738","created_at":"2026-05-18T02:38:27.012215+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1738v1","created_at":"2026-05-18T02:38:27.012215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1738","created_at":"2026-05-18T02:38:27.012215+00:00"},{"alias_kind":"pith_short_12","alias_value":"A36NQFQKXCME","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"A36NQFQKXCME7TQO","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"A36NQFQK","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ","json":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ.json","graph_json":"https://pith.science/api/pith-number/A36NQFQKXCME7TQO2MR6STS2UZ/graph.json","events_json":"https://pith.science/api/pith-number/A36NQFQKXCME7TQO2MR6STS2UZ/events.json","paper":"https://pith.science/paper/A36NQFQK"},"agent_actions":{"view_html":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ","download_json":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ.json","view_paper":"https://pith.science/paper/A36NQFQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1738&json=true","fetch_graph":"https://pith.science/api/pith-number/A36NQFQKXCME7TQO2MR6STS2UZ/graph.json","fetch_events":"https://pith.science/api/pith-number/A36NQFQKXCME7TQO2MR6STS2UZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ/action/storage_attestation","attest_author":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ/action/author_attestation","sign_citation":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ/action/citation_signature","submit_replication":"https://pith.science/pith/A36NQFQKXCME7TQO2MR6STS2UZ/action/replication_record"}},"created_at":"2026-05-18T02:38:27.012215+00:00","updated_at":"2026-05-18T02:38:27.012215+00:00"}