{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KKJXPYH7IDYLPOGS5H6H5MDWWR","short_pith_number":"pith:KKJXPYH7","canonical_record":{"source":{"id":"0907.0793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-04T20:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"9d2604583e419b9f996e66c976839c1657c3bb8735ecfcb66bba3a395fe923dd","abstract_canon_sha256":"403c2a61be0395a0034cf589d1d2f598cfd07b3ef87d04ab6045d1ce1b5b915b"},"schema_version":"1.0"},"canonical_sha256":"529377e0ff40f0b7b8d2e9fc7eb076b46328691372863c1534bf2d610e2240a8","source":{"kind":"arxiv","id":"0907.0793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0793","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0793v1","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0793","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"KKJXPYH7IDYL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KKJXPYH7IDYLPOGS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KKJXPYH7","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KKJXPYH7IDYLPOGS5H6H5MDWWR","target":"record","payload":{"canonical_record":{"source":{"id":"0907.0793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-04T20:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"9d2604583e419b9f996e66c976839c1657c3bb8735ecfcb66bba3a395fe923dd","abstract_canon_sha256":"403c2a61be0395a0034cf589d1d2f598cfd07b3ef87d04ab6045d1ce1b5b915b"},"schema_version":"1.0"},"canonical_sha256":"529377e0ff40f0b7b8d2e9fc7eb076b46328691372863c1534bf2d610e2240a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:09.014826Z","signature_b64":"hHrielJMFHeYvEncoSmdh5M2pZBuJJOebwiMyehKxAPlE3UVuANe7XlT38kLnxrinU+Y7i+79j055ouSM5a9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"529377e0ff40f0b7b8d2e9fc7eb076b46328691372863c1534bf2d610e2240a8","last_reissued_at":"2026-05-18T04:34:09.014370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:09.014370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.0793","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":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sF5Ym5/WlTgUk8FfdgWvY7decQ9cl3rmoIbx/CiW1WGqpDjAo5XAU8XqFoD0JhyS/Qsmm+5bEZmNEsAN2aBPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:59:15.873399Z"},"content_sha256":"f5ac49aa64b99659b929db5acbbbf637964b8e0d4a82d597262abda4e0ee59fc","schema_version":"1.0","event_id":"sha256:f5ac49aa64b99659b929db5acbbbf637964b8e0d4a82d597262abda4e0ee59fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KKJXPYH7IDYLPOGS5H6H5MDWWR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary Harnack Inequality for alpha-harmonic functions on the Sierpi\\'nski triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Kaleta, Mateusz Kwa\\'snicki","submitted_at":"2009-07-04T20:36:23Z","abstract_excerpt":"We prove an uniform boundary Harnack inequality for nonnegative functions harmonic with respect to $\\alpha$-stable process on the Sierpi{\\'n}ski triangle, where $\\alpha \\in (0, 1)$. Our result requires no regularity assumptions on the domain of harmonicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0793","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":""},"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":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWGXRL2G9zQ9NbA/YBIJZ0v/pe0TJpNmU/cF+vfeA/Dv8iW2GxNLp8kSbGI1A0etgAd2sdSYK3qTuDJqUej/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:59:15.874010Z"},"content_sha256":"3e9613cba3f8dc0ebebd993c6d6bec2371f4bcafc9315aa68bd618a67ef54c7e","schema_version":"1.0","event_id":"sha256:3e9613cba3f8dc0ebebd993c6d6bec2371f4bcafc9315aa68bd618a67ef54c7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR/bundle.json","state_url":"https://pith.science/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR/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":"2026-05-27T17:59:15Z","links":{"resolver":"https://pith.science/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR","bundle":"https://pith.science/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR/bundle.json","state":"https://pith.science/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKJXPYH7IDYLPOGS5H6H5MDWWR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KKJXPYH7IDYLPOGS5H6H5MDWWR","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":"403c2a61be0395a0034cf589d1d2f598cfd07b3ef87d04ab6045d1ce1b5b915b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-04T20:36:23Z","title_canon_sha256":"9d2604583e419b9f996e66c976839c1657c3bb8735ecfcb66bba3a395fe923dd"},"schema_version":"1.0","source":{"id":"0907.0793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0793","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0793v1","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0793","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"KKJXPYH7IDYL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KKJXPYH7IDYLPOGS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KKJXPYH7","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:3e9613cba3f8dc0ebebd993c6d6bec2371f4bcafc9315aa68bd618a67ef54c7e","target":"graph","created_at":"2026-05-18T04:34:09Z","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"},"paper":{"abstract_excerpt":"We prove an uniform boundary Harnack inequality for nonnegative functions harmonic with respect to $\\alpha$-stable process on the Sierpi{\\'n}ski triangle, where $\\alpha \\in (0, 1)$. Our result requires no regularity assumptions on the domain of harmonicity.","authors_text":"Kamil Kaleta, Mateusz Kwa\\'snicki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-04T20:36:23Z","title":"Boundary Harnack Inequality for alpha-harmonic functions on the Sierpi\\'nski triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0793","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:f5ac49aa64b99659b929db5acbbbf637964b8e0d4a82d597262abda4e0ee59fc","target":"record","created_at":"2026-05-18T04:34:09Z","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":"403c2a61be0395a0034cf589d1d2f598cfd07b3ef87d04ab6045d1ce1b5b915b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-04T20:36:23Z","title_canon_sha256":"9d2604583e419b9f996e66c976839c1657c3bb8735ecfcb66bba3a395fe923dd"},"schema_version":"1.0","source":{"id":"0907.0793","kind":"arxiv","version":1}},"canonical_sha256":"529377e0ff40f0b7b8d2e9fc7eb076b46328691372863c1534bf2d610e2240a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"529377e0ff40f0b7b8d2e9fc7eb076b46328691372863c1534bf2d610e2240a8","first_computed_at":"2026-05-18T04:34:09.014370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:09.014370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHrielJMFHeYvEncoSmdh5M2pZBuJJOebwiMyehKxAPlE3UVuANe7XlT38kLnxrinU+Y7i+79j055ouSM5a9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:09.014826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5ac49aa64b99659b929db5acbbbf637964b8e0d4a82d597262abda4e0ee59fc","sha256:3e9613cba3f8dc0ebebd993c6d6bec2371f4bcafc9315aa68bd618a67ef54c7e"],"state_sha256":"1b6c16fb11dbcc74e939ac19e7731a0db9c14b1fa31c35cea1cf94b57bf9b862"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"62KdHjlKmFsqSAbWIHJkCarRTIWV/1WZKJ3yzUZuCn73HLVnNNgnJngIwL+hy2KTK+agHnBkdkAaOTFGEFDuAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:59:15.877143Z","bundle_sha256":"07a5fa82df98b9b6d332b73a9dd0339b96c8c6cac24b82258817330a1ef4e7f8"}}