{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FXKIILFBB2CSPB2X2WEXW42GLI","short_pith_number":"pith:FXKIILFB","canonical_record":{"source":{"id":"2507.15589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-21T13:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"8459a779f1bafe7dea07b014bebbd894271c8843efbe1287424d36b0fe8150e3","abstract_canon_sha256":"34ebd3a66b19edb54f32b500012fa330be1947de3f851e92e6742fe221b8a807"},"schema_version":"1.0"},"canonical_sha256":"2dd4842ca10e85278757d5897b73465a29373c4baa69068d2350bf83eb67de8a","source":{"kind":"arxiv","id":"2507.15589","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.15589","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"2507.15589v1","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15589","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"FXKIILFBB2CS","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"pith_short_16","alias_value":"FXKIILFBB2CSPB2X","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"pith_short_8","alias_value":"FXKIILFB","created_at":"2026-07-05T11:40:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FXKIILFBB2CSPB2X2WEXW42GLI","target":"record","payload":{"canonical_record":{"source":{"id":"2507.15589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-21T13:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"8459a779f1bafe7dea07b014bebbd894271c8843efbe1287424d36b0fe8150e3","abstract_canon_sha256":"34ebd3a66b19edb54f32b500012fa330be1947de3f851e92e6742fe221b8a807"},"schema_version":"1.0"},"canonical_sha256":"2dd4842ca10e85278757d5897b73465a29373c4baa69068d2350bf83eb67de8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:39.563349Z","signature_b64":"kN+8D3rMEmYAhZu+y2QobbpXv+iqtPJMgWEWFRji9dfZizrl0AnKde+cAyPViPhgC2s0oL3Pn54ZbNuRBUTkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dd4842ca10e85278757d5897b73465a29373c4baa69068d2350bf83eb67de8a","last_reissued_at":"2026-07-05T11:40:39.562861Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:39.562861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.15589","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":"2026-07-05T11:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vUh6cMSlWZidaBJb+uWVCghsS724NUkwaw2hQ7FR0sMp007Y5OMzh9b80YmXDpFm0YYoxkyPwRY9FbuQCm3uDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T00:22:27.193342Z"},"content_sha256":"fcb09a490a9f47a9090fae41a4954f3253ce90e8fcc01b6a0d8d7fd7924af3a7","schema_version":"1.0","event_id":"sha256:fcb09a490a9f47a9090fae41a4954f3253ce90e8fcc01b6a0d8d7fd7924af3a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FXKIILFBB2CSPB2X2WEXW42GLI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tightness of approximations to metrics on non-simple conformal loop ensemble gaskets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jason Miller, Valeria Ambrosio, Yizheng Yuan","submitted_at":"2025-07-21T13:11:54Z","abstract_excerpt":"We study a class of approximation schemes aimed at constructing conformally covariant metrics defined in the gasket of a conformal loop ensemble (CLE$_\\kappa$) for $\\kappa \\in (4,8)$. This is the range of parameter values so that the loops of a CLE$_\\kappa$ intersect themselves, each other, and the domain boundary. Its gasket is the closure of the union of the set of points not surrounded by a loop. The class of approximation schemes includes approximations to the geodesic metric and to the resistance metric. We show that the laws of these approximations are tight, and that every subsequential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15589","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/2507.15589/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":"2026-07-05T11:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cq/h/Lm85G58ZHtG8h6W72NMO2mqYrTeOXq7Ps3LyF4Oy7jRIudj8neQIUJ1FobwrnDdxhUxBksUCeCBuHXcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T00:22:27.193846Z"},"content_sha256":"76f1e994a9169313f1ba3cb08be078e6699818754ed98313f53da0637511700b","schema_version":"1.0","event_id":"sha256:76f1e994a9169313f1ba3cb08be078e6699818754ed98313f53da0637511700b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXKIILFBB2CSPB2X2WEXW42GLI/bundle.json","state_url":"https://pith.science/pith/FXKIILFBB2CSPB2X2WEXW42GLI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXKIILFBB2CSPB2X2WEXW42GLI/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":"2026-08-02T00:22:27Z","links":{"resolver":"https://pith.science/pith/FXKIILFBB2CSPB2X2WEXW42GLI","bundle":"https://pith.science/pith/FXKIILFBB2CSPB2X2WEXW42GLI/bundle.json","state":"https://pith.science/pith/FXKIILFBB2CSPB2X2WEXW42GLI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXKIILFBB2CSPB2X2WEXW42GLI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FXKIILFBB2CSPB2X2WEXW42GLI","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":"34ebd3a66b19edb54f32b500012fa330be1947de3f851e92e6742fe221b8a807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-21T13:11:54Z","title_canon_sha256":"8459a779f1bafe7dea07b014bebbd894271c8843efbe1287424d36b0fe8150e3"},"schema_version":"1.0","source":{"id":"2507.15589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.15589","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"2507.15589v1","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15589","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"FXKIILFBB2CS","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"pith_short_16","alias_value":"FXKIILFBB2CSPB2X","created_at":"2026-07-05T11:40:39Z"},{"alias_kind":"pith_short_8","alias_value":"FXKIILFB","created_at":"2026-07-05T11:40:39Z"}],"graph_snapshots":[{"event_id":"sha256:76f1e994a9169313f1ba3cb08be078e6699818754ed98313f53da0637511700b","target":"graph","created_at":"2026-07-05T11:40:39Z","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/2507.15589/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of approximation schemes aimed at constructing conformally covariant metrics defined in the gasket of a conformal loop ensemble (CLE$_\\kappa$) for $\\kappa \\in (4,8)$. This is the range of parameter values so that the loops of a CLE$_\\kappa$ intersect themselves, each other, and the domain boundary. Its gasket is the closure of the union of the set of points not surrounded by a loop. The class of approximation schemes includes approximations to the geodesic metric and to the resistance metric. We show that the laws of these approximations are tight, and that every subsequential","authors_text":"Jason Miller, Valeria Ambrosio, Yizheng Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-21T13:11:54Z","title":"Tightness of approximations to metrics on non-simple conformal loop ensemble gaskets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15589","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:fcb09a490a9f47a9090fae41a4954f3253ce90e8fcc01b6a0d8d7fd7924af3a7","target":"record","created_at":"2026-07-05T11:40:39Z","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":"34ebd3a66b19edb54f32b500012fa330be1947de3f851e92e6742fe221b8a807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-21T13:11:54Z","title_canon_sha256":"8459a779f1bafe7dea07b014bebbd894271c8843efbe1287424d36b0fe8150e3"},"schema_version":"1.0","source":{"id":"2507.15589","kind":"arxiv","version":1}},"canonical_sha256":"2dd4842ca10e85278757d5897b73465a29373c4baa69068d2350bf83eb67de8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dd4842ca10e85278757d5897b73465a29373c4baa69068d2350bf83eb67de8a","first_computed_at":"2026-07-05T11:40:39.562861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:39.562861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kN+8D3rMEmYAhZu+y2QobbpXv+iqtPJMgWEWFRji9dfZizrl0AnKde+cAyPViPhgC2s0oL3Pn54ZbNuRBUTkCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:39.563349Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.15589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcb09a490a9f47a9090fae41a4954f3253ce90e8fcc01b6a0d8d7fd7924af3a7","sha256:76f1e994a9169313f1ba3cb08be078e6699818754ed98313f53da0637511700b"],"state_sha256":"c8da00c7b7d3ba3b4e01fe448895133dbfd32b20dfccdd31c483ba77773a7367"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9ohgzYjRaf2JFEFgWTjy7OxpkSiJ0EftW8WOzQixBXucRalXfnSmodiJNayb2yUjKF7AFqohiJyygucy00KCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T00:22:27.197464Z","bundle_sha256":"a766674b13f785b1e4cd0de256de03ccf0c51cd8088575c9df77dde72e04e1a8"}}