{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ANJSPL6LPUUG6SMPVMK3BDSDOW","short_pith_number":"pith:ANJSPL6L","canonical_record":{"source":{"id":"2411.14921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-22T13:22:30Z","cross_cats_sorted":[],"title_canon_sha256":"2c9045e94bb02960b073332a0052e9da02f6e9f267cc43a9c38ccc0109925097","abstract_canon_sha256":"ac79ffc4a8c6a044ebd8a8917063ba5b28b776b77d4943a04f96c5ee309bb120"},"schema_version":"1.0"},"canonical_sha256":"035327afcb7d286f498fab15b08e4375abcd180193c29916d282383184e1792a","source":{"kind":"arxiv","id":"2411.14921","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14921","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14921v1","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14921","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"ANJSPL6LPUUG","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"ANJSPL6LPUUG6SMP","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"ANJSPL6L","created_at":"2026-07-05T09:39:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ANJSPL6LPUUG6SMPVMK3BDSDOW","target":"record","payload":{"canonical_record":{"source":{"id":"2411.14921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-22T13:22:30Z","cross_cats_sorted":[],"title_canon_sha256":"2c9045e94bb02960b073332a0052e9da02f6e9f267cc43a9c38ccc0109925097","abstract_canon_sha256":"ac79ffc4a8c6a044ebd8a8917063ba5b28b776b77d4943a04f96c5ee309bb120"},"schema_version":"1.0"},"canonical_sha256":"035327afcb7d286f498fab15b08e4375abcd180193c29916d282383184e1792a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:13.683392Z","signature_b64":"QB4fBscdOYJRYMTZBKsFw857eav0NO2/eiFFgOWZ9/XM5sADLEGewfGfRtJypLaAeX9yrz2kOnkAr1fp/WdxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"035327afcb7d286f498fab15b08e4375abcd180193c29916d282383184e1792a","last_reissued_at":"2026-07-05T09:39:13.682963Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:13.682963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.14921","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":"2026-07-05T09:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzIP6QuSlGlJdhIDzNTCnbSvHN76V89HKElx8I7bXS0yjiCG/+cyoqGrZNKybwY6L0ogofPiz2Za47rJChIoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T12:48:30.799940Z"},"content_sha256":"26322b6a725fc10cb7af68a8f9b2e79ee0394254498c62bf6885cb0619b5edbe","schema_version":"1.0","event_id":"sha256:26322b6a725fc10cb7af68a8f9b2e79ee0394254498c62bf6885cb0619b5edbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ANJSPL6LPUUG6SMPVMK3BDSDOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Runsheng Liu, Xiangyi Liu, Xinyi Li, Yifan Gao, Yifan Li","submitted_at":"2024-11-22T13:22:30Z","abstract_excerpt":"We show that a domain in $\\mathbb{R}^3$ with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that the intersection exponents for 3D Brownian motion are analytic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14921","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/2411.14921/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":"2026-07-05T09:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ToyRZepe/nyUc+G7of1ekwS+VuxtB1qluYpBtzgDEtytDvD+2ph3OHHCI0MtETOmt1gEZ2ppKoUweS6lDKnXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T12:48:30.800302Z"},"content_sha256":"86c4a0d19a0f66fd1f54c728c967b0c806871bef40e3f03f59323e3d4f25199b","schema_version":"1.0","event_id":"sha256:86c4a0d19a0f66fd1f54c728c967b0c806871bef40e3f03f59323e3d4f25199b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW/bundle.json","state_url":"https://pith.science/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW/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":"2026-07-17T12:48:30Z","links":{"resolver":"https://pith.science/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW","bundle":"https://pith.science/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW/bundle.json","state":"https://pith.science/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ANJSPL6LPUUG6SMPVMK3BDSDOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ANJSPL6LPUUG6SMPVMK3BDSDOW","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":"ac79ffc4a8c6a044ebd8a8917063ba5b28b776b77d4943a04f96c5ee309bb120","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-22T13:22:30Z","title_canon_sha256":"2c9045e94bb02960b073332a0052e9da02f6e9f267cc43a9c38ccc0109925097"},"schema_version":"1.0","source":{"id":"2411.14921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14921","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14921v1","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14921","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"ANJSPL6LPUUG","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"ANJSPL6LPUUG6SMP","created_at":"2026-07-05T09:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"ANJSPL6L","created_at":"2026-07-05T09:39:13Z"}],"graph_snapshots":[{"event_id":"sha256:86c4a0d19a0f66fd1f54c728c967b0c806871bef40e3f03f59323e3d4f25199b","target":"graph","created_at":"2026-07-05T09:39:13Z","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/2411.14921/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a domain in $\\mathbb{R}^3$ with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that the intersection exponents for 3D Brownian motion are analytic.","authors_text":"Runsheng Liu, Xiangyi Liu, Xinyi Li, Yifan Gao, Yifan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-22T13:22:30Z","title":"A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14921","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":"sha256:26322b6a725fc10cb7af68a8f9b2e79ee0394254498c62bf6885cb0619b5edbe","target":"record","created_at":"2026-07-05T09:39:13Z","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":"ac79ffc4a8c6a044ebd8a8917063ba5b28b776b77d4943a04f96c5ee309bb120","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-22T13:22:30Z","title_canon_sha256":"2c9045e94bb02960b073332a0052e9da02f6e9f267cc43a9c38ccc0109925097"},"schema_version":"1.0","source":{"id":"2411.14921","kind":"arxiv","version":1}},"canonical_sha256":"035327afcb7d286f498fab15b08e4375abcd180193c29916d282383184e1792a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"035327afcb7d286f498fab15b08e4375abcd180193c29916d282383184e1792a","first_computed_at":"2026-07-05T09:39:13.682963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:13.682963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QB4fBscdOYJRYMTZBKsFw857eav0NO2/eiFFgOWZ9/XM5sADLEGewfGfRtJypLaAeX9yrz2kOnkAr1fp/WdxAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:13.683392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26322b6a725fc10cb7af68a8f9b2e79ee0394254498c62bf6885cb0619b5edbe","sha256:86c4a0d19a0f66fd1f54c728c967b0c806871bef40e3f03f59323e3d4f25199b"],"state_sha256":"21356a79b4fecfa7575c368fedbfa058a4ac4c50cb9a5b8bbc77f95d9b607be9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nujEYEAX3aSHZxHqdNVPog1MKHIV7g4qVCnnZgFcF+MwH3hFBQF3Y/0+s5MIwYQdQX05Ze94bVA6WDCVYTGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T12:48:30.802372Z","bundle_sha256":"aba128abeab278dbe86c555a511aacee41b6fffd8c93d479982597061079113a"}}