{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QJIRGRR37FP76KOTPS2Q2LTRIA","short_pith_number":"pith:QJIRGRR3","canonical_record":{"source":{"id":"0811.1809","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-12T03:06:25Z","cross_cats_sorted":["math.CV","math.PR"],"title_canon_sha256":"064157a993b78195e455537bb5a055af79363c0098d731c814435ef572895a5f","abstract_canon_sha256":"da11a7251a99ba487272634d5856262ba4e2b407c8fe7474fcc7dab420903d0a"},"schema_version":"1.0"},"canonical_sha256":"825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8","source":{"kind":"arxiv","id":"0811.1809","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1809","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1809v7","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1809","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"QJIRGRR37FP7","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QJIRGRR37FP76KOT","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QJIRGRR3","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QJIRGRR37FP76KOTPS2Q2LTRIA","target":"record","payload":{"canonical_record":{"source":{"id":"0811.1809","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-12T03:06:25Z","cross_cats_sorted":["math.CV","math.PR"],"title_canon_sha256":"064157a993b78195e455537bb5a055af79363c0098d731c814435ef572895a5f","abstract_canon_sha256":"da11a7251a99ba487272634d5856262ba4e2b407c8fe7474fcc7dab420903d0a"},"schema_version":"1.0"},"canonical_sha256":"825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:45.864826Z","signature_b64":"7qTOVej1kgnrc5GblG/68ZbH38S50FalsK3MzGcqdGfHt6BQCvEToorJwyFZLQ75YpNxmzCizwABasnQB0NuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8","last_reissued_at":"2026-05-18T04:28:45.864458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:45.864458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.1809","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Wqg8gtmFmKsfBcM71AOIVYfgEaakaJ4uL82jww8s3CTY/sRLFnskeocZ8GYwfZKqUUCWK5fQPD157budOF9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:47:51.198469Z"},"content_sha256":"73e0ac6719d0fc2ba9145a430eecc04e7c4379cfcb1130ba266c7e9e19147a13","schema_version":"1.0","event_id":"sha256:73e0ac6719d0fc2ba9145a430eecc04e7c4379cfcb1130ba266c7e9e19147a13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QJIRGRR37FP76KOTPS2Q2LTRIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.PR"],"primary_cat":"math.DS","authors_text":"Hiroki Sumi, Mariusz Urbanski","submitted_at":"2008-11-12T03:06:25Z","abstract_excerpt":"We consider the dynamics of semi-hyperbolic semigroups generated by finitely many rational maps on the Riemann sphere. Assuming that the nice open set condition holds it is proved that there exists a geometric measure on the Julia set with exponent $h$ equal to the Hausdorff dimension of the Julia set. Both $h$-dimensional Hausdorff and packing measures are finite and positive on the Julia set and are mutually equivalent with Radon-Nikodym derivatives uniformly separated from zero and infinity. All three fractal dimensions, Hausdorff, packing and box counting are equal. It is also proved that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1809","kind":"arxiv","version":7},"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":"2026-05-18T04:28:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ztRqlQUciTyGplWULu2meZLMDsMg9x5RWy6vjCl+qK3MubRCzxIW40KSlVZziK6L7pYJj/j1xYlirnONf41wDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:47:51.198808Z"},"content_sha256":"98c249548318171e684340ba21345ac4d528c2bbaef034cfadb7ad435627e3de","schema_version":"1.0","event_id":"sha256:98c249548318171e684340ba21345ac4d528c2bbaef034cfadb7ad435627e3de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJIRGRR37FP76KOTPS2Q2LTRIA/bundle.json","state_url":"https://pith.science/pith/QJIRGRR37FP76KOTPS2Q2LTRIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJIRGRR37FP76KOTPS2Q2LTRIA/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":"2026-06-23T06:47:51Z","links":{"resolver":"https://pith.science/pith/QJIRGRR37FP76KOTPS2Q2LTRIA","bundle":"https://pith.science/pith/QJIRGRR37FP76KOTPS2Q2LTRIA/bundle.json","state":"https://pith.science/pith/QJIRGRR37FP76KOTPS2Q2LTRIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJIRGRR37FP76KOTPS2Q2LTRIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QJIRGRR37FP76KOTPS2Q2LTRIA","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":"da11a7251a99ba487272634d5856262ba4e2b407c8fe7474fcc7dab420903d0a","cross_cats_sorted":["math.CV","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-12T03:06:25Z","title_canon_sha256":"064157a993b78195e455537bb5a055af79363c0098d731c814435ef572895a5f"},"schema_version":"1.0","source":{"id":"0811.1809","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1809","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1809v7","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1809","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"QJIRGRR37FP7","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QJIRGRR37FP76KOT","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QJIRGRR3","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:98c249548318171e684340ba21345ac4d528c2bbaef034cfadb7ad435627e3de","target":"graph","created_at":"2026-05-18T04:28:45Z","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"},"paper":{"abstract_excerpt":"We consider the dynamics of semi-hyperbolic semigroups generated by finitely many rational maps on the Riemann sphere. Assuming that the nice open set condition holds it is proved that there exists a geometric measure on the Julia set with exponent $h$ equal to the Hausdorff dimension of the Julia set. Both $h$-dimensional Hausdorff and packing measures are finite and positive on the Julia set and are mutually equivalent with Radon-Nikodym derivatives uniformly separated from zero and infinity. All three fractal dimensions, Hausdorff, packing and box counting are equal. It is also proved that ","authors_text":"Hiroki Sumi, Mariusz Urbanski","cross_cats":["math.CV","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-12T03:06:25Z","title":"Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1809","kind":"arxiv","version":7},"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":"sha256:73e0ac6719d0fc2ba9145a430eecc04e7c4379cfcb1130ba266c7e9e19147a13","target":"record","created_at":"2026-05-18T04:28:45Z","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":"da11a7251a99ba487272634d5856262ba4e2b407c8fe7474fcc7dab420903d0a","cross_cats_sorted":["math.CV","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-12T03:06:25Z","title_canon_sha256":"064157a993b78195e455537bb5a055af79363c0098d731c814435ef572895a5f"},"schema_version":"1.0","source":{"id":"0811.1809","kind":"arxiv","version":7}},"canonical_sha256":"825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8","first_computed_at":"2026-05-18T04:28:45.864458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:45.864458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7qTOVej1kgnrc5GblG/68ZbH38S50FalsK3MzGcqdGfHt6BQCvEToorJwyFZLQ75YpNxmzCizwABasnQB0NuCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:45.864826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1809","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73e0ac6719d0fc2ba9145a430eecc04e7c4379cfcb1130ba266c7e9e19147a13","sha256:98c249548318171e684340ba21345ac4d528c2bbaef034cfadb7ad435627e3de"],"state_sha256":"0caa27a875c6d939b3609305824a96f31dabd71e49c87c8906412c97a0960e9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLmiUdbVcXoFF1on4VwtU9obkTSKipgAv9qHYlysiOdmHA7jo93coassABAgzis0yHnTAZuDZrr+OdaX/2JDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:47:51.200630Z","bundle_sha256":"693213c4d7bef13d34fea8c36feba28c86ca1ba8ab6979b3b2e083182154260e"}}