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Also let $\\kappa = 16/\\gamma^2 >4$ and let $\\eta$ be a whole-plane space-filling SLE$_\\kappa$ curve sampled independent from $h$ and parametrized by $\\gamma$-quantum mass with respect to $h$. We study a family $\\{\\mathcal G^\\epsilon\\}_{\\epsilon>0}$ of planar maps associated with $(h, \\eta)$ called the \\textit{LQG structure graphs} (a.k.a.\\ \\textit{mated-CRT maps}) which we conjecture converge in probability in the scaling limit with respect to the Gromov"},"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":"1606.01214","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-03T18:30:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"de7b1cfd32562e05bb561c77e01b72e949475368d9f59435ac007ba10e215501","abstract_canon_sha256":"8dcc315a0dd0d1fe45d21607fe3d15c126c3413549495d0352b2d0dc63a59d6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:51.094187Z","signature_b64":"hTDdytrkKFRRIlE92SuXsqxgdgRcjS5aFsELfISuXeIWa/L6ogS660qyCquioQ3gqFhe9gTRCk/wfyi4+s25Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b69a55abd828560120dc23132fb64f329b2d2743d63b7568b68385a0210fae0d","last_reissued_at":"2026-05-18T00:11:51.093569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:51.093569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A distance exponent for 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":"Ewain Gwynne, Nina Holden, Xin Sun","submitted_at":"2016-06-03T18:30:36Z","abstract_excerpt":"Let $\\gamma \\in (0,2)$ and let $h$ be the random distribution on $\\mathbb C$ which describes a $\\gamma$-Liouville quantum gravity (LQG) cone. 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We study a family $\\{\\mathcal G^\\epsilon\\}_{\\epsilon>0}$ of planar maps associated with $(h, \\eta)$ called the \\textit{LQG structure graphs} (a.k.a.\\ \\textit{mated-CRT maps}) which we conjecture converge in probability in the scaling limit with respect to the Gromov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01214","kind":"arxiv","version":4},"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":"1606.01214","created_at":"2026-05-18T00:11:51.093677+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01214v4","created_at":"2026-05-18T00:11:51.093677+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01214","created_at":"2026-05-18T00:11:51.093677+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2NFLK6YFBLA","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2NFLK6YFBLACIG4","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2NFLK6Y","created_at":"2026-05-18T12:30:48.956258+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/W2NFLK6YFBLACIG4EMJS7NSPGK","json":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK.json","graph_json":"https://pith.science/api/pith-number/W2NFLK6YFBLACIG4EMJS7NSPGK/graph.json","events_json":"https://pith.science/api/pith-number/W2NFLK6YFBLACIG4EMJS7NSPGK/events.json","paper":"https://pith.science/paper/W2NFLK6Y"},"agent_actions":{"view_html":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK","download_json":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK.json","view_paper":"https://pith.science/paper/W2NFLK6Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01214&json=true","fetch_graph":"https://pith.science/api/pith-number/W2NFLK6YFBLACIG4EMJS7NSPGK/graph.json","fetch_events":"https://pith.science/api/pith-number/W2NFLK6YFBLACIG4EMJS7NSPGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK/action/storage_attestation","attest_author":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK/action/author_attestation","sign_citation":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK/action/citation_signature","submit_replication":"https://pith.science/pith/W2NFLK6YFBLACIG4EMJS7NSPGK/action/replication_record"}},"created_at":"2026-05-18T00:11:51.093677+00:00","updated_at":"2026-05-18T00:11:51.093677+00:00"}