{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KVBCOFEGYXUXWKCNNXFLDZIBTK","short_pith_number":"pith:KVBCOFEG","canonical_record":{"source":{"id":"2109.00275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-09-01T09:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"6237f750716c00e415d565d05a54e98675d7a61882f2ba40ec767747b44d03e0","abstract_canon_sha256":"974b6a925a46db795a70b1fc9753c5eee0783696a6bf88d352266e13cb948e7a"},"schema_version":"1.0"},"canonical_sha256":"5542271486c5e97b284d6dcab1e5019aa536d94edfbf4d9092c9f91f215e5e1a","source":{"kind":"arxiv","id":"2109.00275","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.00275","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"arxiv_version","alias_value":"2109.00275v2","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.00275","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"pith_short_12","alias_value":"KVBCOFEGYXUX","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"pith_short_16","alias_value":"KVBCOFEGYXUXWKCN","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"pith_short_8","alias_value":"KVBCOFEG","created_at":"2026-07-05T04:53:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KVBCOFEGYXUXWKCNNXFLDZIBTK","target":"record","payload":{"canonical_record":{"source":{"id":"2109.00275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-09-01T09:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"6237f750716c00e415d565d05a54e98675d7a61882f2ba40ec767747b44d03e0","abstract_canon_sha256":"974b6a925a46db795a70b1fc9753c5eee0783696a6bf88d352266e13cb948e7a"},"schema_version":"1.0"},"canonical_sha256":"5542271486c5e97b284d6dcab1e5019aa536d94edfbf4d9092c9f91f215e5e1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:53:25.154444Z","signature_b64":"yyy5usE9Btbp4PSpnxJCXJQN/+iSZQGIBT2Yyax9LLJJELx09eIpJfeAAjY3HbZsKfBesQb+h8n3+Cq9xObmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5542271486c5e97b284d6dcab1e5019aa536d94edfbf4d9092c9f91f215e5e1a","last_reissued_at":"2026-07-05T04:53:25.153965Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:53:25.153965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.00275","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:53:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CCk83iHlT9nxav0nKkG8fluMuPz6mUMEyNtM7w+vq5MBqe1+cRppTdcFPDSPs8kJMW+62O6fw1ZIf1ZjYkOEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T18:22:35.587378Z"},"content_sha256":"68e2ad79ebce2d37925afb338f23e4ab4af82c5cd5efaab425e794cdb50524f0","schema_version":"1.0","event_id":"sha256:68e2ad79ebce2d37925afb338f23e4ab4af82c5cd5efaab425e794cdb50524f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KVBCOFEGYXUXWKCNNXFLDZIBTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mating of trees for critical Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ellen Powell, Juhan Aru, Nina Holden, Xin Sun","submitted_at":"2021-09-01T09:39:02Z","abstract_excerpt":"In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by the mating of two continuum random trees. In this paper, we consider the counterpart of their result for critical LQG and SLE, i.e., for the case when $\\gamma^2=\\kappa=16/\\kappa=4$. We prove that as one sends $\\kappa \\downarrow 4$ in the subcritical setting, the space-filling SLE$_\\kappa$ in a disk degenerates to the CLE$_4$ exploration introduced by Werner and Wu, along with a collection of i.i.d.\\ coin tosses inde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.00275","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/2109.00275/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:53:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVKj6MPzmmb7yypxKwdt4xFI4DlPneyQKPCwcNqWesOHyfHqOizP69Q2/No+/GyzZhPjtE7NuARFIUbiY7d1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T18:22:35.587756Z"},"content_sha256":"5c2787651ad99b964257f4d361620e95451695d37061b857e7795da791c4cae1","schema_version":"1.0","event_id":"sha256:5c2787651ad99b964257f4d361620e95451695d37061b857e7795da791c4cae1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK/bundle.json","state_url":"https://pith.science/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-10T18:22:35Z","links":{"resolver":"https://pith.science/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK","bundle":"https://pith.science/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK/bundle.json","state":"https://pith.science/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KVBCOFEGYXUXWKCNNXFLDZIBTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KVBCOFEGYXUXWKCNNXFLDZIBTK","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":"974b6a925a46db795a70b1fc9753c5eee0783696a6bf88d352266e13cb948e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-09-01T09:39:02Z","title_canon_sha256":"6237f750716c00e415d565d05a54e98675d7a61882f2ba40ec767747b44d03e0"},"schema_version":"1.0","source":{"id":"2109.00275","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.00275","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"arxiv_version","alias_value":"2109.00275v2","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.00275","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"pith_short_12","alias_value":"KVBCOFEGYXUX","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"pith_short_16","alias_value":"KVBCOFEGYXUXWKCN","created_at":"2026-07-05T04:53:25Z"},{"alias_kind":"pith_short_8","alias_value":"KVBCOFEG","created_at":"2026-07-05T04:53:25Z"}],"graph_snapshots":[{"event_id":"sha256:5c2787651ad99b964257f4d361620e95451695d37061b857e7795da791c4cae1","target":"graph","created_at":"2026-07-05T04:53:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.00275/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by the mating of two continuum random trees. In this paper, we consider the counterpart of their result for critical LQG and SLE, i.e., for the case when $\\gamma^2=\\kappa=16/\\kappa=4$. We prove that as one sends $\\kappa \\downarrow 4$ in the subcritical setting, the space-filling SLE$_\\kappa$ in a disk degenerates to the CLE$_4$ exploration introduced by Werner and Wu, along with a collection of i.i.d.\\ coin tosses inde","authors_text":"Ellen Powell, Juhan Aru, Nina Holden, Xin Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-09-01T09:39:02Z","title":"Mating of trees for critical Liouville quantum gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.00275","kind":"arxiv","version":2},"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":"sha256:68e2ad79ebce2d37925afb338f23e4ab4af82c5cd5efaab425e794cdb50524f0","target":"record","created_at":"2026-07-05T04:53:25Z","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":"974b6a925a46db795a70b1fc9753c5eee0783696a6bf88d352266e13cb948e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-09-01T09:39:02Z","title_canon_sha256":"6237f750716c00e415d565d05a54e98675d7a61882f2ba40ec767747b44d03e0"},"schema_version":"1.0","source":{"id":"2109.00275","kind":"arxiv","version":2}},"canonical_sha256":"5542271486c5e97b284d6dcab1e5019aa536d94edfbf4d9092c9f91f215e5e1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5542271486c5e97b284d6dcab1e5019aa536d94edfbf4d9092c9f91f215e5e1a","first_computed_at":"2026-07-05T04:53:25.153965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:53:25.153965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yyy5usE9Btbp4PSpnxJCXJQN/+iSZQGIBT2Yyax9LLJJELx09eIpJfeAAjY3HbZsKfBesQb+h8n3+Cq9xObmBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:53:25.154444Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.00275","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68e2ad79ebce2d37925afb338f23e4ab4af82c5cd5efaab425e794cdb50524f0","sha256:5c2787651ad99b964257f4d361620e95451695d37061b857e7795da791c4cae1"],"state_sha256":"c486e70ea51d24482a2a1f77444090793f324608dd732ce1c4a688a4f39ef665"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9AdnrMcHGYXobSkIOkrC64YcbBUMqbLTbKWPuhmZMh2Zt06Fl88+Tvd3Z/OMTA5OhJ1gNAvOSb3GxU2blXAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T18:22:35.590094Z","bundle_sha256":"2b01aa90e8b9556a46361af0b411e39ba032371a2fdce4a57f4862a3b38fd78e"}}