{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CM4U243UFYKDZLE47EQ2UWFROB","short_pith_number":"pith:CM4U243U","canonical_record":{"source":{"id":"2607.26439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-29T03:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"592a4418deaad554525137fc9fdac3e53413dece8f67471a4b41b23c74f9760c","abstract_canon_sha256":"5e562eac2357eb85096478978392f17297f74da41494d6dc665b66c5dca5e609"},"schema_version":"1.0"},"canonical_sha256":"13394d73742e143cac9cf921aa58b1705622e6e630c26a8ea1e0e9b95cde8c97","source":{"kind":"arxiv","id":"2607.26439","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26439","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26439v1","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26439","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"CM4U243UFYKD","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"CM4U243UFYKDZLE4","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"CM4U243U","created_at":"2026-07-30T01:18:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CM4U243UFYKDZLE47EQ2UWFROB","target":"record","payload":{"canonical_record":{"source":{"id":"2607.26439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-29T03:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"592a4418deaad554525137fc9fdac3e53413dece8f67471a4b41b23c74f9760c","abstract_canon_sha256":"5e562eac2357eb85096478978392f17297f74da41494d6dc665b66c5dca5e609"},"schema_version":"1.0"},"canonical_sha256":"13394d73742e143cac9cf921aa58b1705622e6e630c26a8ea1e0e9b95cde8c97","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13394d73742e143cac9cf921aa58b1705622e6e630c26a8ea1e0e9b95cde8c97","last_reissued_at":"2026-07-30T01:18:25.840768Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:18:25.840768Z"},"source_kind":"arxiv","source_id":"2607.26439","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":"2026-07-30T01:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0x3zHBBE2T+w+iU1IXUSPctoghXR4zEikFSWG3o0srvcTjXABHljyCmYSIwwxl4+bFNfs/qJfepFsUIdoB/xDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T09:27:40.010395Z"},"content_sha256":"56218d1801ed551b003cd2690da45858c0beb06a95c64b2d460d522c5fe37312","schema_version":"1.0","event_id":"sha256:56218d1801ed551b003cd2690da45858c0beb06a95c64b2d460d522c5fe37312"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CM4U243UFYKDZLE47EQ2UWFROB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small Brownian Loops Hitting SLE$_2$: An Exact Natural-Content Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zhengwen Qiao","submitted_at":"2026-07-29T03:37:21Z","abstract_excerpt":"Let $D$ be a bounded analytic Jordan domain and let $\\gamma$ be chordal $\\mathrm{SLE}_2$ in $D$, equipped with its $5/4$-dimensional natural-content measure $\\mu_\\gamma$. We retain the root in the standard integrated Brownian-bridge representation of Brownian loop measure and let $\\mathcal M_\\varepsilon^\\gamma$ be the root-intensity measure of loops with duration in $[\\varepsilon^2,t_0]$ whose traces hit $\\gamma$. For every $f\\in C_c(D)$, we prove that $\\varepsilon^{5/4}\\mathcal M_\\varepsilon^\\gamma(f)$ converges in $L^1$ to $\\frac{4}{5\\pi}\\bar v_{\\mathrm{BB}}\\mu_\\gamma(f)$, where $\\bar v_{\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26439","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/2607.26439/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":"2026-07-30T01:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jwRwlU8Q1lqcuv0P1eF61fuT5yen1vBapsc+ZjqJMRV+wWj/YKs+fQAGa2Oo+655x2JiMSDM733QLMz69QyMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T09:27:40.010939Z"},"content_sha256":"893b1981667bcf5fa33661d980fdc49d49834786dacb653372a0eac123ae49c2","schema_version":"1.0","event_id":"sha256:893b1981667bcf5fa33661d980fdc49d49834786dacb653372a0eac123ae49c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CM4U243UFYKDZLE47EQ2UWFROB/bundle.json","state_url":"https://pith.science/pith/CM4U243UFYKDZLE47EQ2UWFROB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CM4U243UFYKDZLE47EQ2UWFROB/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":"2026-08-18T09:27:40Z","links":{"resolver":"https://pith.science/pith/CM4U243UFYKDZLE47EQ2UWFROB","bundle":"https://pith.science/pith/CM4U243UFYKDZLE47EQ2UWFROB/bundle.json","state":"https://pith.science/pith/CM4U243UFYKDZLE47EQ2UWFROB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CM4U243UFYKDZLE47EQ2UWFROB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CM4U243UFYKDZLE47EQ2UWFROB","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":"5e562eac2357eb85096478978392f17297f74da41494d6dc665b66c5dca5e609","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-29T03:37:21Z","title_canon_sha256":"592a4418deaad554525137fc9fdac3e53413dece8f67471a4b41b23c74f9760c"},"schema_version":"1.0","source":{"id":"2607.26439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26439","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26439v1","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26439","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"CM4U243UFYKD","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"CM4U243UFYKDZLE4","created_at":"2026-07-30T01:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"CM4U243U","created_at":"2026-07-30T01:18:25Z"}],"graph_snapshots":[{"event_id":"sha256:893b1981667bcf5fa33661d980fdc49d49834786dacb653372a0eac123ae49c2","target":"graph","created_at":"2026-07-30T01:18:25Z","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/2607.26439/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $D$ be a bounded analytic Jordan domain and let $\\gamma$ be chordal $\\mathrm{SLE}_2$ in $D$, equipped with its $5/4$-dimensional natural-content measure $\\mu_\\gamma$. We retain the root in the standard integrated Brownian-bridge representation of Brownian loop measure and let $\\mathcal M_\\varepsilon^\\gamma$ be the root-intensity measure of loops with duration in $[\\varepsilon^2,t_0]$ whose traces hit $\\gamma$. For every $f\\in C_c(D)$, we prove that $\\varepsilon^{5/4}\\mathcal M_\\varepsilon^\\gamma(f)$ converges in $L^1$ to $\\frac{4}{5\\pi}\\bar v_{\\mathrm{BB}}\\mu_\\gamma(f)$, where $\\bar v_{\\ma","authors_text":"Zhengwen Qiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-29T03:37:21Z","title":"Small Brownian Loops Hitting SLE$_2$: An Exact Natural-Content Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26439","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":"sha256:56218d1801ed551b003cd2690da45858c0beb06a95c64b2d460d522c5fe37312","target":"record","created_at":"2026-07-30T01:18:25Z","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":"5e562eac2357eb85096478978392f17297f74da41494d6dc665b66c5dca5e609","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-29T03:37:21Z","title_canon_sha256":"592a4418deaad554525137fc9fdac3e53413dece8f67471a4b41b23c74f9760c"},"schema_version":"1.0","source":{"id":"2607.26439","kind":"arxiv","version":1}},"canonical_sha256":"13394d73742e143cac9cf921aa58b1705622e6e630c26a8ea1e0e9b95cde8c97","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13394d73742e143cac9cf921aa58b1705622e6e630c26a8ea1e0e9b95cde8c97","first_computed_at":"2026-07-30T01:18:25.840768Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:18:25.840768Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.26439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56218d1801ed551b003cd2690da45858c0beb06a95c64b2d460d522c5fe37312","sha256:893b1981667bcf5fa33661d980fdc49d49834786dacb653372a0eac123ae49c2"],"state_sha256":"5493aaa22ce42d84cb3cdf3c478be869b4d84d05631b99238f09aea7b7217a10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cVuaJiq4ocGDovj8xLw1mXZhFsVrq4XlCkPu5IsU9KVyB8mv6VxO+e4GyDqT9Bl639DCZpW+APq/RQNjpT1uDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T09:27:40.016179Z","bundle_sha256":"39a6826334bce476a61ab7d2388f0d6c03148a592c1c9cbb6e35c392ac490fce"}}