{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6WJXQHA4W4KNFB6JMZQSDFZ2VH","short_pith_number":"pith:6WJXQHA4","canonical_record":{"source":{"id":"1610.02563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-08T18:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"86a8464f58ebaab6c2ca3d737294b25ba84e6bd24b3a7902bac8e3b8272df4bd","abstract_canon_sha256":"ff208e445c4281b5daa04f92b2b3469688a81c29e37646ad2aa1bafe8340df4d"},"schema_version":"1.0"},"canonical_sha256":"f593781c1cb714d287c9666121973aa9ef792c18b531e282146a95c4258f3e62","source":{"kind":"arxiv","id":"1610.02563","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02563","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02563v1","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02563","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"6WJXQHA4W4KN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6WJXQHA4W4KNFB6J","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6WJXQHA4","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6WJXQHA4W4KNFB6JMZQSDFZ2VH","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-08T18:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"86a8464f58ebaab6c2ca3d737294b25ba84e6bd24b3a7902bac8e3b8272df4bd","abstract_canon_sha256":"ff208e445c4281b5daa04f92b2b3469688a81c29e37646ad2aa1bafe8340df4d"},"schema_version":"1.0"},"canonical_sha256":"f593781c1cb714d287c9666121973aa9ef792c18b531e282146a95c4258f3e62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:44.618578Z","signature_b64":"sIGYPXi3orSzkrVgcNd77Uu8DxOewSka1xBG2BtkY1O+9w6HBwbtdSP8XdJ3Z+ao0hlg/V7QbXnKxaxUAdSuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f593781c1cb714d287c9666121973aa9ef792c18b531e282146a95c4258f3e62","last_reissued_at":"2026-05-17T23:51:44.618082Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:44.618082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02563","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":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDSsLjSWnGVp4YGhfSnn1gpnB4G0IpAb86m9/VkQ1tGHJSgheoEf8PAacsTGId2XmOChwvfQNfC/H9egkxltDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:34:02.999415Z"},"content_sha256":"ea20d0ef476a7766cb3760cabd5b11612131a05d8644d55e38b15c8b85ceb398","schema_version":"1.0","event_id":"sha256:ea20d0ef476a7766cb3760cabd5b11612131a05d8644d55e38b15c8b85ceb398"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6WJXQHA4W4KNFB6JMZQSDFZ2VH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diabolical entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Neil Dobbs, Nicolae Mihalache","submitted_at":"2016-10-08T18:10:46Z","abstract_excerpt":"Milnor and Thurston's famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is H\\\"older continuous. We obtain a precise formula for the H\\\"older exponent at almost every quadratic parameter.\n  Furthermore, the entropy of most parameters is proven to be in a set of Hausdorff dimension smaller than one, while most values of the entropy arise from a set of parameters of dimension smaller than one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02563","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":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V953sNEbhYVcMjOx9C1CcLnuNi07xvvPYJl2FZ5QzlHQjlqoA3YKqXoxJvX+IWqpFg4oiMQbAJbmJBsZiDJVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:34:02.999761Z"},"content_sha256":"92c3a8bbe0ad9644e0e9fe2269d96a14548c158ef71f6358573fb18f8c1ea273","schema_version":"1.0","event_id":"sha256:92c3a8bbe0ad9644e0e9fe2269d96a14548c158ef71f6358573fb18f8c1ea273"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH/bundle.json","state_url":"https://pith.science/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH/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":"2026-06-26T23:34:03Z","links":{"resolver":"https://pith.science/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH","bundle":"https://pith.science/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH/bundle.json","state":"https://pith.science/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WJXQHA4W4KNFB6JMZQSDFZ2VH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6WJXQHA4W4KNFB6JMZQSDFZ2VH","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":"ff208e445c4281b5daa04f92b2b3469688a81c29e37646ad2aa1bafe8340df4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-08T18:10:46Z","title_canon_sha256":"86a8464f58ebaab6c2ca3d737294b25ba84e6bd24b3a7902bac8e3b8272df4bd"},"schema_version":"1.0","source":{"id":"1610.02563","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02563","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02563v1","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02563","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"6WJXQHA4W4KN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6WJXQHA4W4KNFB6J","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6WJXQHA4","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:92c3a8bbe0ad9644e0e9fe2269d96a14548c158ef71f6358573fb18f8c1ea273","target":"graph","created_at":"2026-05-17T23:51:44Z","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":"Milnor and Thurston's famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is H\\\"older continuous. We obtain a precise formula for the H\\\"older exponent at almost every quadratic parameter.\n  Furthermore, the entropy of most parameters is proven to be in a set of Hausdorff dimension smaller than one, while most values of the entropy arise from a set of parameters of dimension smaller than one.","authors_text":"Neil Dobbs, Nicolae Mihalache","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-08T18:10:46Z","title":"Diabolical entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02563","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:ea20d0ef476a7766cb3760cabd5b11612131a05d8644d55e38b15c8b85ceb398","target":"record","created_at":"2026-05-17T23:51:44Z","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":"ff208e445c4281b5daa04f92b2b3469688a81c29e37646ad2aa1bafe8340df4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-08T18:10:46Z","title_canon_sha256":"86a8464f58ebaab6c2ca3d737294b25ba84e6bd24b3a7902bac8e3b8272df4bd"},"schema_version":"1.0","source":{"id":"1610.02563","kind":"arxiv","version":1}},"canonical_sha256":"f593781c1cb714d287c9666121973aa9ef792c18b531e282146a95c4258f3e62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f593781c1cb714d287c9666121973aa9ef792c18b531e282146a95c4258f3e62","first_computed_at":"2026-05-17T23:51:44.618082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:44.618082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sIGYPXi3orSzkrVgcNd77Uu8DxOewSka1xBG2BtkY1O+9w6HBwbtdSP8XdJ3Z+ao0hlg/V7QbXnKxaxUAdSuBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:44.618578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02563","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea20d0ef476a7766cb3760cabd5b11612131a05d8644d55e38b15c8b85ceb398","sha256:92c3a8bbe0ad9644e0e9fe2269d96a14548c158ef71f6358573fb18f8c1ea273"],"state_sha256":"3faef280abe09cdb1ffee65670691a9cd25648a8736c1ab2a5c1306c53c91327"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVkDQsC2lYumL1JWX8s17cv/UWpL4Fd7hJkFHgcnyfBqt7TTw6fYGcd0r0CdrXAf1WUuDqflAJsJs0IKnemuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:34:03.001662Z","bundle_sha256":"199c08b61bdf3eae49e49b0babf1136938c2d48d282d03994bec1805138bd0dd"}}