{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QI3HVLGFUEQ7KIQ6AX7ZPXYX3R","short_pith_number":"pith:QI3HVLGF","canonical_record":{"source":{"id":"2410.12724","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-16T16:32:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5a45e4b3d5e9d8576f9ea8a1c7a189edce70bb8d196c8887a9e45ee370fc9c91","abstract_canon_sha256":"4cbbde5fb8401a6a889ec55087229a355ac356284768e1e33562a284dd88f371"},"schema_version":"1.0"},"canonical_sha256":"82367aacc5a121f5221e05ff97df17dc4d678cb087277ff2c330ad6f200dd1db","source":{"kind":"arxiv","id":"2410.12724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.12724","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"2410.12724v1","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.12724","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"QI3HVLGFUEQ7","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"pith_short_16","alias_value":"QI3HVLGFUEQ7KIQ6","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"pith_short_8","alias_value":"QI3HVLGF","created_at":"2026-07-05T09:21:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QI3HVLGFUEQ7KIQ6AX7ZPXYX3R","target":"record","payload":{"canonical_record":{"source":{"id":"2410.12724","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-16T16:32:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5a45e4b3d5e9d8576f9ea8a1c7a189edce70bb8d196c8887a9e45ee370fc9c91","abstract_canon_sha256":"4cbbde5fb8401a6a889ec55087229a355ac356284768e1e33562a284dd88f371"},"schema_version":"1.0"},"canonical_sha256":"82367aacc5a121f5221e05ff97df17dc4d678cb087277ff2c330ad6f200dd1db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:21:33.171668Z","signature_b64":"4vLDGYXcbPJ6X9ImYxxTBFdkFL1I5WFBImLMJr6eNxjoqQJk5ibxGMDub922qg8UpMDTZbkzSKmiff/BkA5tAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82367aacc5a121f5221e05ff97df17dc4d678cb087277ff2c330ad6f200dd1db","last_reissued_at":"2026-07-05T09:21:33.171138Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:21:33.171138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.12724","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ov4BXa+vS8+7jalc9JDnHT9qrljyiiNA+le8vIL0zLBPTxbv9HiXZrhl6GEcwa2PDmOOjIpxeu+hwxsV5xSYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:38:15.936435Z"},"content_sha256":"2fb38eccc08d7f4d887e06cec61177746962debfee5c1f2e9f8de95e88f1665b","schema_version":"1.0","event_id":"sha256:2fb38eccc08d7f4d887e06cec61177746962debfee5c1f2e9f8de95e88f1665b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QI3HVLGFUEQ7KIQ6AX7ZPXYX3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The bulk one-arm exponent for the CLE$_{\\kappa'}$ percolations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Haoyu Liu, Pu Yu, Xin Sun, Zijie Zhuang","submitted_at":"2024-10-16T16:32:57Z","abstract_excerpt":"The conformal loop ensemble (CLE) is a conformally invariant random collection of loops. In the non-simple regime $\\kappa'\\in (4,8)$, it describes the scaling limit of the critical Fortuin-Kasteleyn (FK) percolations. CLE percolations were introduced by Miller-Sheffield-Werner (2017). The CLE$_{\\kappa'}$ percolations describe the scaling limit of a natural variant of the FK percolation called the fuzzy Potts model, which has an additional percolation parameter $r$. Based on CLE percolations and assuming that the convergence of the FK percolation to CLE, K{\\\"o}hler-Schindler and Lehmkuehler (20"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.12724","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.12724/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":"2026-07-05T09:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VeH2rSMQwCY9lbL1o37cIL68sV6I4l1AJ6dQzj0kfDvbNrTqDjisXUl1apXLcnCMnzLjk8sDn8DJRQcbQODAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:38:15.936939Z"},"content_sha256":"9f8694c658fb31f6a5acb93897261705c146a05131b3150630d99bb48780a8f6","schema_version":"1.0","event_id":"sha256:9f8694c658fb31f6a5acb93897261705c146a05131b3150630d99bb48780a8f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R/bundle.json","state_url":"https://pith.science/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R/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":"2026-08-08T10:38:15Z","links":{"resolver":"https://pith.science/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R","bundle":"https://pith.science/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R/bundle.json","state":"https://pith.science/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QI3HVLGFUEQ7KIQ6AX7ZPXYX3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QI3HVLGFUEQ7KIQ6AX7ZPXYX3R","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":"4cbbde5fb8401a6a889ec55087229a355ac356284768e1e33562a284dd88f371","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-16T16:32:57Z","title_canon_sha256":"5a45e4b3d5e9d8576f9ea8a1c7a189edce70bb8d196c8887a9e45ee370fc9c91"},"schema_version":"1.0","source":{"id":"2410.12724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.12724","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"2410.12724v1","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.12724","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"QI3HVLGFUEQ7","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"pith_short_16","alias_value":"QI3HVLGFUEQ7KIQ6","created_at":"2026-07-05T09:21:33Z"},{"alias_kind":"pith_short_8","alias_value":"QI3HVLGF","created_at":"2026-07-05T09:21:33Z"}],"graph_snapshots":[{"event_id":"sha256:9f8694c658fb31f6a5acb93897261705c146a05131b3150630d99bb48780a8f6","target":"graph","created_at":"2026-07-05T09:21:33Z","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/2410.12724/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The conformal loop ensemble (CLE) is a conformally invariant random collection of loops. In the non-simple regime $\\kappa'\\in (4,8)$, it describes the scaling limit of the critical Fortuin-Kasteleyn (FK) percolations. CLE percolations were introduced by Miller-Sheffield-Werner (2017). The CLE$_{\\kappa'}$ percolations describe the scaling limit of a natural variant of the FK percolation called the fuzzy Potts model, which has an additional percolation parameter $r$. Based on CLE percolations and assuming that the convergence of the FK percolation to CLE, K{\\\"o}hler-Schindler and Lehmkuehler (20","authors_text":"Haoyu Liu, Pu Yu, Xin Sun, Zijie Zhuang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-16T16:32:57Z","title":"The bulk one-arm exponent for the CLE$_{\\kappa'}$ percolations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.12724","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":"sha256:2fb38eccc08d7f4d887e06cec61177746962debfee5c1f2e9f8de95e88f1665b","target":"record","created_at":"2026-07-05T09:21:33Z","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":"4cbbde5fb8401a6a889ec55087229a355ac356284768e1e33562a284dd88f371","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-16T16:32:57Z","title_canon_sha256":"5a45e4b3d5e9d8576f9ea8a1c7a189edce70bb8d196c8887a9e45ee370fc9c91"},"schema_version":"1.0","source":{"id":"2410.12724","kind":"arxiv","version":1}},"canonical_sha256":"82367aacc5a121f5221e05ff97df17dc4d678cb087277ff2c330ad6f200dd1db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82367aacc5a121f5221e05ff97df17dc4d678cb087277ff2c330ad6f200dd1db","first_computed_at":"2026-07-05T09:21:33.171138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:33.171138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vLDGYXcbPJ6X9ImYxxTBFdkFL1I5WFBImLMJr6eNxjoqQJk5ibxGMDub922qg8UpMDTZbkzSKmiff/BkA5tAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:33.171668Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.12724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fb38eccc08d7f4d887e06cec61177746962debfee5c1f2e9f8de95e88f1665b","sha256:9f8694c658fb31f6a5acb93897261705c146a05131b3150630d99bb48780a8f6"],"state_sha256":"e6d0c179653ff72876ff1582eeab5e9e04856296b01bcc2f6e43656b36963009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSby5aIp4IUu3ejtlwLE7/s8dZFjcifGJzfP4uGpedYAHQ2D/k4b/33Gcb0gVCSWzMTne4dexKimoJ27UXtkBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T10:38:15.940901Z","bundle_sha256":"828dc0bc26e298d5de32cb3cdb88836ffbf964cdf03fb3f3255fb49e0565f69a"}}