{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:6JY65TJEP6OK56S5KZL4DUDKSM","short_pith_number":"pith:6JY65TJE","schema_version":"1.0","canonical_sha256":"f271eecd247f9caefa5d5657c1d06a930a0e769b26a0bbfe2c9907d5547d01d5","source":{"kind":"arxiv","id":"2001.11467","version":2},"attestation_state":"computed","paper":{"title":"Volume of metric balls in Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hugo Falconet, Morris Ang, Xin Sun","submitted_at":"2020-01-30T17:26:54Z","abstract_excerpt":"We study the volume of metric balls in Liouville quantum gravity (LQG). For $\\gamma \\in (0,2)$, it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG volume of Euclidean balls has finite moments exactly for $p \\in (-\\infty, 4/\\gamma^2)$. Here, we prove that the LQG volume of LQG metric balls admits all finite moments. This answers a question of Gwynne and Miller and generalizes a result obtained by Le Gall for the Brownian map, namely, the $\\gamma = \\sqrt{8/3}$ case. We use this moment bound to show that on a compact set the volume of metric balls of size $r$ "},"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":"2001.11467","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-01-30T17:26:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0a5e1a3146ef7ca9c4786953f8706dcb17dca63aed214de249315ca4e3d51539","abstract_canon_sha256":"a10d6eec9661757b8eec1db82d476c87a4b6a571ae953396143f92953e3259ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:55:08.123888Z","signature_b64":"xn9gZxm8rxJStYnWH+Dwp0UbNwxhMWWspxQTM78ZrvPZuLPkJupYj/PC1i2D/9Q//4CZvzurKO7n1hWkQiYfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f271eecd247f9caefa5d5657c1d06a930a0e769b26a0bbfe2c9907d5547d01d5","last_reissued_at":"2026-07-05T01:55:08.123544Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:55:08.123544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume of metric balls in Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hugo Falconet, Morris Ang, Xin Sun","submitted_at":"2020-01-30T17:26:54Z","abstract_excerpt":"We study the volume of metric balls in Liouville quantum gravity (LQG). For $\\gamma \\in (0,2)$, it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG volume of Euclidean balls has finite moments exactly for $p \\in (-\\infty, 4/\\gamma^2)$. Here, we prove that the LQG volume of LQG metric balls admits all finite moments. This answers a question of Gwynne and Miller and generalizes a result obtained by Le Gall for the Brownian map, namely, the $\\gamma = \\sqrt{8/3}$ case. We use this moment bound to show that on a compact set the volume of metric balls of size $r$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11467","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.11467/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2001.11467","created_at":"2026-07-05T01:55:08.123599+00:00"},{"alias_kind":"arxiv_version","alias_value":"2001.11467v2","created_at":"2026-07-05T01:55:08.123599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11467","created_at":"2026-07-05T01:55:08.123599+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JY65TJEP6OK","created_at":"2026-07-05T01:55:08.123599+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JY65TJEP6OK56S5","created_at":"2026-07-05T01:55:08.123599+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JY65TJE","created_at":"2026-07-05T01:55:08.123599+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.10496","citing_title":"Dimension lower bounds in random geometry via Lipschitz functions","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM","json":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM.json","graph_json":"https://pith.science/api/pith-number/6JY65TJEP6OK56S5KZL4DUDKSM/graph.json","events_json":"https://pith.science/api/pith-number/6JY65TJEP6OK56S5KZL4DUDKSM/events.json","paper":"https://pith.science/paper/6JY65TJE"},"agent_actions":{"view_html":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM","download_json":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM.json","view_paper":"https://pith.science/paper/6JY65TJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2001.11467&json=true","fetch_graph":"https://pith.science/api/pith-number/6JY65TJEP6OK56S5KZL4DUDKSM/graph.json","fetch_events":"https://pith.science/api/pith-number/6JY65TJEP6OK56S5KZL4DUDKSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM/action/storage_attestation","attest_author":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM/action/author_attestation","sign_citation":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM/action/citation_signature","submit_replication":"https://pith.science/pith/6JY65TJEP6OK56S5KZL4DUDKSM/action/replication_record"}},"created_at":"2026-07-05T01:55:08.123599+00:00","updated_at":"2026-07-05T01:55:08.123599+00:00"}