{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IN5BMUK2DICLQ2EZBUONT3R22I","short_pith_number":"pith:IN5BMUK2","canonical_record":{"source":{"id":"1510.05800","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T09:15:15Z","cross_cats_sorted":[],"title_canon_sha256":"acec96ae6489684b6fe3d77878786471eff7295172eba077d455af8449724294","abstract_canon_sha256":"1eb7d8801bc2ca3e8f4f38c96c2c13c0019f98350d7275eb89185bfd3d3827db"},"schema_version":"1.0"},"canonical_sha256":"437a16515a1a04b868990d1cd9ee3ad2294be57a23678256658fc8b3856b0495","source":{"kind":"arxiv","id":"1510.05800","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05800","created_at":"2026-05-18T00:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05800v3","created_at":"2026-05-18T00:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05800","created_at":"2026-05-18T00:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"IN5BMUK2DICL","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IN5BMUK2DICLQ2EZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IN5BMUK2","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IN5BMUK2DICLQ2EZBUONT3R22I","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05800","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T09:15:15Z","cross_cats_sorted":[],"title_canon_sha256":"acec96ae6489684b6fe3d77878786471eff7295172eba077d455af8449724294","abstract_canon_sha256":"1eb7d8801bc2ca3e8f4f38c96c2c13c0019f98350d7275eb89185bfd3d3827db"},"schema_version":"1.0"},"canonical_sha256":"437a16515a1a04b868990d1cd9ee3ad2294be57a23678256658fc8b3856b0495","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:49.220179Z","signature_b64":"SJQLcxfsyx4/wLQdcO6M5bNILzfXQvba3osueIRccv1ziA9EH31+BSQFlhopFbUNdILlyyCQ8wL0rXRQkEg8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"437a16515a1a04b868990d1cd9ee3ad2294be57a23678256658fc8b3856b0495","last_reissued_at":"2026-05-18T00:59:49.219420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:49.219420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05800","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":"2026-05-18T00:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXFYt73f7BG3Q0LCi6mgB+Kqi2a90VzrujELzGQhMAfmzBkZcAYBwD/aWZ5PpUHVNsChnpR/D4+GzSJrNanBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:10:17.383534Z"},"content_sha256":"29c4c2b1597c0a4d3c9c85ed7773ad108239bb6e98dd4a519baacd6dd199f434","schema_version":"1.0","event_id":"sha256:29c4c2b1597c0a4d3c9c85ed7773ad108239bb6e98dd4a519baacd6dd199f434"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IN5BMUK2DICLQ2EZBUONT3R22I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intrinsic H\\\"older continuity of harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wolfhard Hansen","submitted_at":"2015-10-20T09:15:15Z","abstract_excerpt":"In a setting, where only exit measures are given, as they are associated with a right continuous strong Markov process on a separable metric space, we provide simple criteria for scaling invariant H\\\"older continuity of bounded harmonic functions with respect to a distance function which, in applications, may be adapted to the special situation. In particular, already a very weak scaling property ensures that Harnack inequalities imply H\\\"older continuity. Our approach covers recent results by M. Kassmann and A. Mimica as well as cases, where a Green function leads to an intrinsic metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05800","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":""},"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":"2026-05-18T00:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2TJ/dahV9RCTWGkcZvQsJxhe2Fy+tTzz41PS7p+y2wI79lBUvuRfKkmsD7P3Dfi5wa5sJn86e7L52vOpdCQCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:10:17.383897Z"},"content_sha256":"727a09daba02f045471b11e41d586265ed475c6048cff07216902a236991e35b","schema_version":"1.0","event_id":"sha256:727a09daba02f045471b11e41d586265ed475c6048cff07216902a236991e35b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IN5BMUK2DICLQ2EZBUONT3R22I/bundle.json","state_url":"https://pith.science/pith/IN5BMUK2DICLQ2EZBUONT3R22I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IN5BMUK2DICLQ2EZBUONT3R22I/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":"2026-06-25T05:10:17Z","links":{"resolver":"https://pith.science/pith/IN5BMUK2DICLQ2EZBUONT3R22I","bundle":"https://pith.science/pith/IN5BMUK2DICLQ2EZBUONT3R22I/bundle.json","state":"https://pith.science/pith/IN5BMUK2DICLQ2EZBUONT3R22I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IN5BMUK2DICLQ2EZBUONT3R22I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IN5BMUK2DICLQ2EZBUONT3R22I","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":"1eb7d8801bc2ca3e8f4f38c96c2c13c0019f98350d7275eb89185bfd3d3827db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T09:15:15Z","title_canon_sha256":"acec96ae6489684b6fe3d77878786471eff7295172eba077d455af8449724294"},"schema_version":"1.0","source":{"id":"1510.05800","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05800","created_at":"2026-05-18T00:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05800v3","created_at":"2026-05-18T00:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05800","created_at":"2026-05-18T00:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"IN5BMUK2DICL","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IN5BMUK2DICLQ2EZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IN5BMUK2","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:727a09daba02f045471b11e41d586265ed475c6048cff07216902a236991e35b","target":"graph","created_at":"2026-05-18T00:59:49Z","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":"In a setting, where only exit measures are given, as they are associated with a right continuous strong Markov process on a separable metric space, we provide simple criteria for scaling invariant H\\\"older continuity of bounded harmonic functions with respect to a distance function which, in applications, may be adapted to the special situation. In particular, already a very weak scaling property ensures that Harnack inequalities imply H\\\"older continuity. Our approach covers recent results by M. Kassmann and A. Mimica as well as cases, where a Green function leads to an intrinsic metric.","authors_text":"Wolfhard Hansen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T09:15:15Z","title":"Intrinsic H\\\"older continuity of harmonic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05800","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":"sha256:29c4c2b1597c0a4d3c9c85ed7773ad108239bb6e98dd4a519baacd6dd199f434","target":"record","created_at":"2026-05-18T00:59:49Z","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":"1eb7d8801bc2ca3e8f4f38c96c2c13c0019f98350d7275eb89185bfd3d3827db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T09:15:15Z","title_canon_sha256":"acec96ae6489684b6fe3d77878786471eff7295172eba077d455af8449724294"},"schema_version":"1.0","source":{"id":"1510.05800","kind":"arxiv","version":3}},"canonical_sha256":"437a16515a1a04b868990d1cd9ee3ad2294be57a23678256658fc8b3856b0495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"437a16515a1a04b868990d1cd9ee3ad2294be57a23678256658fc8b3856b0495","first_computed_at":"2026-05-18T00:59:49.219420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:49.219420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SJQLcxfsyx4/wLQdcO6M5bNILzfXQvba3osueIRccv1ziA9EH31+BSQFlhopFbUNdILlyyCQ8wL0rXRQkEg8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:49.220179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05800","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29c4c2b1597c0a4d3c9c85ed7773ad108239bb6e98dd4a519baacd6dd199f434","sha256:727a09daba02f045471b11e41d586265ed475c6048cff07216902a236991e35b"],"state_sha256":"37b30d65b3b7c15b44562749ed7f15443e79bc1d855f3fcb84b5b854ecc8242d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i7H58ayXS6Tke/inraQ0NgLi7h0bq1OqGFCGuU8XRVaTWlqJrRnA4y+tFwSRggLuln7TF06MNWn5YusnqZXKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:10:17.385917Z","bundle_sha256":"8ae202a0b2d6bee2d7db14a9fc20c9dbc410b974c3886d0650b40610725b6e5a"}}