{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KGRWTV3ZBI4JELHY5YQGEVNGBZ","short_pith_number":"pith:KGRWTV3Z","canonical_record":{"source":{"id":"1102.4933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-24T09:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"692159583842944ddbe2ce1a6a11aa6433d7ca4d33d8cf32238029d8aeb676fb","abstract_canon_sha256":"feea9717e63d0c2676015c79a731d491c708f4e74ce69edfc4513a6aa6643499"},"schema_version":"1.0"},"canonical_sha256":"51a369d7790a38922cf8ee206255a60e6f6ad969dbe90d694517bee5cbc70bbf","source":{"kind":"arxiv","id":"1102.4933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4933","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4933v1","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4933","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"KGRWTV3ZBI4J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KGRWTV3ZBI4JELHY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KGRWTV3Z","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KGRWTV3ZBI4JELHY5YQGEVNGBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-24T09:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"692159583842944ddbe2ce1a6a11aa6433d7ca4d33d8cf32238029d8aeb676fb","abstract_canon_sha256":"feea9717e63d0c2676015c79a731d491c708f4e74ce69edfc4513a6aa6643499"},"schema_version":"1.0"},"canonical_sha256":"51a369d7790a38922cf8ee206255a60e6f6ad969dbe90d694517bee5cbc70bbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:58.440746Z","signature_b64":"Djt3fXVEeCaSkE8x6qHOSaWgxBwR3OgRYW6a67EbDIgDpfVZP9BsOqnzxv1jaM/QYMs0WGtEBreh73kamsnOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51a369d7790a38922cf8ee206255a60e6f6ad969dbe90d694517bee5cbc70bbf","last_reissued_at":"2026-05-18T04:27:58.440185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:58.440185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4933","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":"2026-05-18T04:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KFbn8X98qGQnbiHYoPjynZ1KQVMJ46IPymtpsdVVgZxhMwKtCeO3HR3EH4pAh/Ke02XTilTXiLVApmVOWDDSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T04:45:51.484154Z"},"content_sha256":"8f98c76a09e32e88c5223e8c51751dfb35538b21c328e6811179848ab200d211","schema_version":"1.0","event_id":"sha256:8f98c76a09e32e88c5223e8c51751dfb35538b21c328e6811179848ab200d211"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KGRWTV3ZBI4JELHY5YQGEVNGBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hausdorff measure of escaping and Julia sets for bounded type functions of finite order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J\\\"orn Peter","submitted_at":"2011-02-24T09:08:20Z","abstract_excerpt":"We show that the escaping sets and the Julia sets of bounded type transcendental entire functions of order $\\rho$ become 'smaller' as $\\rho\\to\\infty$. More precisely, their Hausdorff measures are infinite with respect to the gauge function $h_\\gamma(t)=t^2g(1/t)^\\gamma$, where $g$ is the inverse of a linearizer of some exponential map and $\\gamma\\geq(\\log\\rho(f)+K_1)/c$, but for $\\rho$ large enough, there exists a function $f_\\rho$ of bounded type with order $\\rho$ such that the Hausdorff measures of the escaping set and the Julia set of $f_\\rho$ with respect to $h_{\\gamma'}$ are zero whenever"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4933","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":"2026-05-18T04:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q02acXsYmqfxIV9cutOT24gvqoHVq3GoRA5L+3H6mcdwYpvi+KC8RF76M8UyTj0Vu8dDFm687mmVRqFBOT6MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T04:45:51.484517Z"},"content_sha256":"d1cac4f070aeb76124d7108750450a45850b1d45b484b8302bef7e5977b185bf","schema_version":"1.0","event_id":"sha256:d1cac4f070aeb76124d7108750450a45850b1d45b484b8302bef7e5977b185bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ/bundle.json","state_url":"https://pith.science/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ/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":"2026-06-25T04:45:51Z","links":{"resolver":"https://pith.science/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ","bundle":"https://pith.science/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ/bundle.json","state":"https://pith.science/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGRWTV3ZBI4JELHY5YQGEVNGBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KGRWTV3ZBI4JELHY5YQGEVNGBZ","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":"feea9717e63d0c2676015c79a731d491c708f4e74ce69edfc4513a6aa6643499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-24T09:08:20Z","title_canon_sha256":"692159583842944ddbe2ce1a6a11aa6433d7ca4d33d8cf32238029d8aeb676fb"},"schema_version":"1.0","source":{"id":"1102.4933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4933","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4933v1","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4933","created_at":"2026-05-18T04:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"KGRWTV3ZBI4J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KGRWTV3ZBI4JELHY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KGRWTV3Z","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:d1cac4f070aeb76124d7108750450a45850b1d45b484b8302bef7e5977b185bf","target":"graph","created_at":"2026-05-18T04:27:58Z","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 show that the escaping sets and the Julia sets of bounded type transcendental entire functions of order $\\rho$ become 'smaller' as $\\rho\\to\\infty$. More precisely, their Hausdorff measures are infinite with respect to the gauge function $h_\\gamma(t)=t^2g(1/t)^\\gamma$, where $g$ is the inverse of a linearizer of some exponential map and $\\gamma\\geq(\\log\\rho(f)+K_1)/c$, but for $\\rho$ large enough, there exists a function $f_\\rho$ of bounded type with order $\\rho$ such that the Hausdorff measures of the escaping set and the Julia set of $f_\\rho$ with respect to $h_{\\gamma'}$ are zero whenever","authors_text":"J\\\"orn Peter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-24T09:08:20Z","title":"Hausdorff measure of escaping and Julia sets for bounded type functions of finite order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4933","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":"sha256:8f98c76a09e32e88c5223e8c51751dfb35538b21c328e6811179848ab200d211","target":"record","created_at":"2026-05-18T04:27:58Z","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":"feea9717e63d0c2676015c79a731d491c708f4e74ce69edfc4513a6aa6643499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-24T09:08:20Z","title_canon_sha256":"692159583842944ddbe2ce1a6a11aa6433d7ca4d33d8cf32238029d8aeb676fb"},"schema_version":"1.0","source":{"id":"1102.4933","kind":"arxiv","version":1}},"canonical_sha256":"51a369d7790a38922cf8ee206255a60e6f6ad969dbe90d694517bee5cbc70bbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51a369d7790a38922cf8ee206255a60e6f6ad969dbe90d694517bee5cbc70bbf","first_computed_at":"2026-05-18T04:27:58.440185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:58.440185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Djt3fXVEeCaSkE8x6qHOSaWgxBwR3OgRYW6a67EbDIgDpfVZP9BsOqnzxv1jaM/QYMs0WGtEBreh73kamsnOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:58.440746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f98c76a09e32e88c5223e8c51751dfb35538b21c328e6811179848ab200d211","sha256:d1cac4f070aeb76124d7108750450a45850b1d45b484b8302bef7e5977b185bf"],"state_sha256":"033d40d1583157c6361f33a44a3249c373c93cb256f6d15ebbf23673093bc901"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLQq3stitO1wCLC1Fa72RGYJI4mo69fX6Dve6F+42d3KRwu1wgkH05Aq89IAne1GuIdeBvR2bHPHccRE5oQ6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T04:45:51.486625Z","bundle_sha256":"ff201bb804b08c76e63170a7b2418f781d4480a704e37aa53412e70a1972c93e"}}