{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:H5OXSTCYJGJDQHILJW3QGQ4UPZ","short_pith_number":"pith:H5OXSTCY","canonical_record":{"source":{"id":"2312.08546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-13T22:18:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"dacbf34f7f92e0d944abd0de5c2880f891c848541bb29924b831cd5d6f54d09f","abstract_canon_sha256":"0856f8b74ebe3e15bf209eb9a90cc4cd2b9bb2dde2392be40d1f15466ffc3c0e"},"schema_version":"1.0"},"canonical_sha256":"3f5d794c584992381d0b4db70343947e6bddc521b8860a04f85bc259308915a1","source":{"kind":"arxiv","id":"2312.08546","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.08546","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2312.08546v3","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.08546","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"H5OXSTCYJGJD","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"H5OXSTCYJGJDQHIL","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"H5OXSTCY","created_at":"2026-07-05T10:17:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:H5OXSTCYJGJDQHILJW3QGQ4UPZ","target":"record","payload":{"canonical_record":{"source":{"id":"2312.08546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-13T22:18:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"dacbf34f7f92e0d944abd0de5c2880f891c848541bb29924b831cd5d6f54d09f","abstract_canon_sha256":"0856f8b74ebe3e15bf209eb9a90cc4cd2b9bb2dde2392be40d1f15466ffc3c0e"},"schema_version":"1.0"},"canonical_sha256":"3f5d794c584992381d0b4db70343947e6bddc521b8860a04f85bc259308915a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:17:45.707611Z","signature_b64":"MV/qILUr9JUvNkmaSrNeSBmJnKrO7KyRWdIUaMzvmWpbtfJy+5WiX0sNHsTfDvidgX1OHsGMlyo/ywNshS0dBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f5d794c584992381d0b4db70343947e6bddc521b8860a04f85bc259308915a1","last_reissued_at":"2026-07-05T10:17:45.707122Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:17:45.707122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.08546","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJWJYr+1KZIjug7LGMmSbmC+6gREfzICnLQU9GLvJfsYYnyG0lJZ+Q3MmL4vUCdEDVW9CrOACA/Z+Mw9bm5qDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:41:52.917874Z"},"content_sha256":"17ad18005a19d16ec0a30603f579f7844a5d8021c6462b7f8bfbca9c52179f5a","schema_version":"1.0","event_id":"sha256:17ad18005a19d16ec0a30603f579f7844a5d8021c6462b7f8bfbca9c52179f5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:H5OXSTCYJGJDQHILJW3QGQ4UPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heat kernel estimates for boundary traces of reflected diffusions on uniform domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Mathav Murugan, Naotaka Kajino","submitted_at":"2023-12-13T22:18:07Z","abstract_excerpt":"We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\\\"im kernel to the topological boundary, and the Doob--Na\\\"im formula identifying the Dirichlet form of the boundary trace process as the pure-j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.08546","kind":"arxiv","version":3},"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/2312.08546/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":"2026-07-05T10:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQxU//X369hxmAZaIlTcVePjIVpxq30tJEXv/7VHZ4zVak66HSyn8PaMt3E5dv4Z2fpAkwQeIdH5RPLp5aI0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:41:52.918242Z"},"content_sha256":"6852f73ba51ee2203890a4973bb1b4c8013e9b585ef20a23efa88ffee38aa94b","schema_version":"1.0","event_id":"sha256:6852f73ba51ee2203890a4973bb1b4c8013e9b585ef20a23efa88ffee38aa94b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ/bundle.json","state_url":"https://pith.science/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ/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":"2026-07-07T09:41:52Z","links":{"resolver":"https://pith.science/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ","bundle":"https://pith.science/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ/bundle.json","state":"https://pith.science/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5OXSTCYJGJDQHILJW3QGQ4UPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:H5OXSTCYJGJDQHILJW3QGQ4UPZ","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":"0856f8b74ebe3e15bf209eb9a90cc4cd2b9bb2dde2392be40d1f15466ffc3c0e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-13T22:18:07Z","title_canon_sha256":"dacbf34f7f92e0d944abd0de5c2880f891c848541bb29924b831cd5d6f54d09f"},"schema_version":"1.0","source":{"id":"2312.08546","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.08546","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2312.08546v3","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.08546","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"H5OXSTCYJGJD","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"H5OXSTCYJGJDQHIL","created_at":"2026-07-05T10:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"H5OXSTCY","created_at":"2026-07-05T10:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:6852f73ba51ee2203890a4973bb1b4c8013e9b585ef20a23efa88ffee38aa94b","target":"graph","created_at":"2026-07-05T10:17:45Z","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/2312.08546/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\\\"im kernel to the topological boundary, and the Doob--Na\\\"im formula identifying the Dirichlet form of the boundary trace process as the pure-j","authors_text":"Mathav Murugan, Naotaka Kajino","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-13T22:18:07Z","title":"Heat kernel estimates for boundary traces of reflected diffusions on uniform domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.08546","kind":"arxiv","version":3},"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":"sha256:17ad18005a19d16ec0a30603f579f7844a5d8021c6462b7f8bfbca9c52179f5a","target":"record","created_at":"2026-07-05T10:17:45Z","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":"0856f8b74ebe3e15bf209eb9a90cc4cd2b9bb2dde2392be40d1f15466ffc3c0e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-13T22:18:07Z","title_canon_sha256":"dacbf34f7f92e0d944abd0de5c2880f891c848541bb29924b831cd5d6f54d09f"},"schema_version":"1.0","source":{"id":"2312.08546","kind":"arxiv","version":3}},"canonical_sha256":"3f5d794c584992381d0b4db70343947e6bddc521b8860a04f85bc259308915a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f5d794c584992381d0b4db70343947e6bddc521b8860a04f85bc259308915a1","first_computed_at":"2026-07-05T10:17:45.707122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:17:45.707122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MV/qILUr9JUvNkmaSrNeSBmJnKrO7KyRWdIUaMzvmWpbtfJy+5WiX0sNHsTfDvidgX1OHsGMlyo/ywNshS0dBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:17:45.707611Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.08546","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17ad18005a19d16ec0a30603f579f7844a5d8021c6462b7f8bfbca9c52179f5a","sha256:6852f73ba51ee2203890a4973bb1b4c8013e9b585ef20a23efa88ffee38aa94b"],"state_sha256":"025a17bcd50930931c71001a11eda52972970ecdc47097a05384871d16edbdf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"442VZcQmyZu5XT0oCnjV+b8wNXpoP9gFO63NqinZB5ktfKqmuSDFu8DjcqwXVf6GrnfqvcZea6MIcfNdnrRCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:41:52.920222Z","bundle_sha256":"5a98c735331411f4c2eb8220c6620ad53cee7cfdc03d521cf2572ad5c2986354"}}