{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FEZK4SU6S4FD4WX6K6TVSFCBLA","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":"b060387125bfe8e85e589bfc3f1786af360ba25f437a50dd483e07e115b7b007","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T01:21:05Z","title_canon_sha256":"223705fb3d7af491ccd4a6f5d372f27c6a72fb9eb34d1b85b027ecefd93a6c68"},"schema_version":"1.0","source":{"id":"1710.03369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03369","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03369v1","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03369","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"FEZK4SU6S4FD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FEZK4SU6S4FD4WX6","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FEZK4SU6","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:cd1226d519e962b7c22459d45d62f78f55f7afade01b22aa94a8f1a545231e30","target":"graph","created_at":"2026-05-18T00:33:12Z","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 give examples of endomorphisms in dimension one with infinite topological entropy which are $\\alpha$-H\\\"older and $(1,p)$-Sobolev for all $0\\leq\\alpha<1$ and $1\\leq p<\\infty$. This is constructed within a family of endomorphisms with infinite topological entropy and which traverse all $\\alpha$-H\\\"older and $(1,p)$-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.","authors_text":"Peter Hazard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T01:21:05Z","title":"Maps in Dimension One with Infinite Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03369","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:cd4707346c0f6a0867fcef7134ed773f30066dec4d3cf09ee80c0b1db3a548de","target":"record","created_at":"2026-05-18T00:33:12Z","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":"b060387125bfe8e85e589bfc3f1786af360ba25f437a50dd483e07e115b7b007","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T01:21:05Z","title_canon_sha256":"223705fb3d7af491ccd4a6f5d372f27c6a72fb9eb34d1b85b027ecefd93a6c68"},"schema_version":"1.0","source":{"id":"1710.03369","kind":"arxiv","version":1}},"canonical_sha256":"2932ae4a9e970a3e5afe57a7591441583aaeab824aff7572c2ee379c7064bea4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2932ae4a9e970a3e5afe57a7591441583aaeab824aff7572c2ee379c7064bea4","first_computed_at":"2026-05-18T00:33:12.208593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:12.208593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xB6j/jcFqe0FC5irvOV/X9a5FETtUDcac+yzSNjamq985mbd+T/VgapvUOPnKgENUBeok6pZoV+HEFSka/wmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:12.209203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd4707346c0f6a0867fcef7134ed773f30066dec4d3cf09ee80c0b1db3a548de","sha256:cd1226d519e962b7c22459d45d62f78f55f7afade01b22aa94a8f1a545231e30"],"state_sha256":"0a89905a0b47f153a3ca5aaddc63b8e7cc5fd824770679194709d035558790c8"}