{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CQKOBWMYOH2Y7B2CW7DFBQKAEG","short_pith_number":"pith:CQKOBWMY","canonical_record":{"source":{"id":"1607.01271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-05T14:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"dffaf5f3eabdbe5ceede8131f61dbcdaa105eaa10a0d5dde50023c39435d0315","abstract_canon_sha256":"116c13b6a4de70d03501c685e9fc99b7a8c6be2623783bcc515a3e4410e77d6f"},"schema_version":"1.0"},"canonical_sha256":"1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567","source":{"kind":"arxiv","id":"1607.01271","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01271","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01271v1","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01271","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"CQKOBWMYOH2Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CQKOBWMYOH2Y7B2C","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CQKOBWMY","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CQKOBWMYOH2Y7B2CW7DFBQKAEG","target":"record","payload":{"canonical_record":{"source":{"id":"1607.01271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-05T14:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"dffaf5f3eabdbe5ceede8131f61dbcdaa105eaa10a0d5dde50023c39435d0315","abstract_canon_sha256":"116c13b6a4de70d03501c685e9fc99b7a8c6be2623783bcc515a3e4410e77d6f"},"schema_version":"1.0"},"canonical_sha256":"1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:54.165543Z","signature_b64":"9AypDt+qGT23AbXWLrKuBvWmpC4cNStkX301A6GzwlGztvVZHI5OU2QR84meisXxCj7VBMM5QXKzFoFaFBCuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567","last_reissued_at":"2026-05-18T00:18:54.164736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:54.164736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.01271","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":"2026-05-18T00:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8XEbpL7Nqx/+5LOk9XTzzmr/dbIFFvS/p5eB9eAO2N/3s/hEHfX62Fd5Py/LDKl/EDz83Spz/bzvviamJU9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:36:56.707698Z"},"content_sha256":"d735c27abd9b448aee2d74c6965cf28ba65385162b3e748e46d19d22386109f7","schema_version":"1.0","event_id":"sha256:d735c27abd9b448aee2d74c6965cf28ba65385162b3e748e46d19d22386109f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CQKOBWMYOH2Y7B2CW7DFBQKAEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov exponents and related concepts for entire functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jianhua Zheng, Walter Bergweiler, Xiao Yao","submitted_at":"2016-07-05T14:37:12Z","abstract_excerpt":"Let $f$ be an entire function and denote by $f^\\#$ be the spherical derivative of $f$ and by $f^n$ the $n$-th iterate of $f$. For an open set $U$ intersecting the Julia set $J(f)$, we consider how fast $\\sup_{z\\in U} (f^n)^\\#(z)$ and $\\int_U (f^n)^\\#(z)^2 dx\\:dy$ tend to $\\infty$. We also study the growth rate of the sequence $(f^n)^\\#(z)$ for $z\\in J(f)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01271","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":"2026-05-18T00:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gu+mhU+plOf8oJ3ElDa6qsRbbn0XD7nw1zp6wTq7Z/Lk2uqAQvU+fLOjMfRVdhDruRZOBCDI7/SZpPQcOJNSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:36:56.708035Z"},"content_sha256":"54226e3a1a569d302637501cfa5e8cc58499df6988b5361b3d1abf0c8cf86df8","schema_version":"1.0","event_id":"sha256:54226e3a1a569d302637501cfa5e8cc58499df6988b5361b3d1abf0c8cf86df8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG/bundle.json","state_url":"https://pith.science/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG/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":"2026-06-24T21:36:56Z","links":{"resolver":"https://pith.science/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG","bundle":"https://pith.science/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG/bundle.json","state":"https://pith.science/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQKOBWMYOH2Y7B2CW7DFBQKAEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CQKOBWMYOH2Y7B2CW7DFBQKAEG","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":"116c13b6a4de70d03501c685e9fc99b7a8c6be2623783bcc515a3e4410e77d6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-05T14:37:12Z","title_canon_sha256":"dffaf5f3eabdbe5ceede8131f61dbcdaa105eaa10a0d5dde50023c39435d0315"},"schema_version":"1.0","source":{"id":"1607.01271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01271","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01271v1","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01271","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"CQKOBWMYOH2Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CQKOBWMYOH2Y7B2C","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CQKOBWMY","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:54226e3a1a569d302637501cfa5e8cc58499df6988b5361b3d1abf0c8cf86df8","target":"graph","created_at":"2026-05-18T00:18:54Z","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":"Let $f$ be an entire function and denote by $f^\\#$ be the spherical derivative of $f$ and by $f^n$ the $n$-th iterate of $f$. For an open set $U$ intersecting the Julia set $J(f)$, we consider how fast $\\sup_{z\\in U} (f^n)^\\#(z)$ and $\\int_U (f^n)^\\#(z)^2 dx\\:dy$ tend to $\\infty$. We also study the growth rate of the sequence $(f^n)^\\#(z)$ for $z\\in J(f)$.","authors_text":"Jianhua Zheng, Walter Bergweiler, Xiao Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-05T14:37:12Z","title":"Lyapunov exponents and related concepts for entire functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01271","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:d735c27abd9b448aee2d74c6965cf28ba65385162b3e748e46d19d22386109f7","target":"record","created_at":"2026-05-18T00:18:54Z","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":"116c13b6a4de70d03501c685e9fc99b7a8c6be2623783bcc515a3e4410e77d6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-05T14:37:12Z","title_canon_sha256":"dffaf5f3eabdbe5ceede8131f61dbcdaa105eaa10a0d5dde50023c39435d0315"},"schema_version":"1.0","source":{"id":"1607.01271","kind":"arxiv","version":1}},"canonical_sha256":"1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567","first_computed_at":"2026-05-18T00:18:54.164736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:54.164736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9AypDt+qGT23AbXWLrKuBvWmpC4cNStkX301A6GzwlGztvVZHI5OU2QR84meisXxCj7VBMM5QXKzFoFaFBCuBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:54.165543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d735c27abd9b448aee2d74c6965cf28ba65385162b3e748e46d19d22386109f7","sha256:54226e3a1a569d302637501cfa5e8cc58499df6988b5361b3d1abf0c8cf86df8"],"state_sha256":"7731301d43dbfa1079270909946ff1a866d571efc04f99a89c67d1a9161a1564"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lns+SrCwIQm7wRagByrDz1lav6M7JzFlFGZySZOm6wcVBN2frltRCW9XHF3TU4S43Aj1WuXI72nmkPwOllXSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:36:56.709946Z","bundle_sha256":"418592a0bd9104cc35e25536da9f5c0f1abbbfd9dde31dc5bee657a6742ca328"}}