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is {\\it hereditarily uniformly lowerable} if for each non-empty compact subset $K$ and each $0\\le h\\le h (T, K)$ there is a non-empty compact subset $K_h\\subseteq K$ with $h (T, K_h)= h$ and $K_h$ has at most one limit point.\n  It is shown that each TDS with finite entropy is lowerable, a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0811.4230","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-26T06:16:06Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"693bcfd93c3cc33e70edd4f1158723d54fd5d733c85233c1ffd2807f28b84cb5","abstract_canon_sha256":"1f3bb354648be32f86f15a8318458933bab50cf19aaef202c8e3413b569c3b9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:53.490000Z","signature_b64":"loGcVnUl1NQp8P9uNPmitgaNQFjLGdR4vifkC50KBuDvaKbxLCNU/Lh7ZwSI1a+ayVOgM5/BejasHp6AI+zwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d1ef2114f790e8a64bb644d093ce2ff2d7409f842cb505250be139e1922723d","last_reissued_at":"2026-05-18T04:18:53.489499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:53.489499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lowering topological entropy over subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Wen Huang, Xiangdong Ye","submitted_at":"2008-11-26T06:16:06Z","abstract_excerpt":"Let $(X, T)$ be a topological dynamical system (TDS), and $h (T, K)$ the topological entropy of a subset $K$ of $X$. $(X, T)$ is {\\it lowerable} if for each $0\\le h\\le h (T, X)$ there is a non-empty compact subset with entropy $h$; is {\\it hereditarily lowerable} if each non-empty compact subset is lowerable; is {\\it hereditarily uniformly lowerable} if for each non-empty compact subset $K$ and each $0\\le h\\le h (T, K)$ there is a non-empty compact subset $K_h\\subseteq K$ with $h (T, K_h)= h$ and $K_h$ has at most one limit point.\n  It is shown that each TDS with finite entropy is lowerable, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4230","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0811.4230","created_at":"2026-05-18T04:18:53.489568+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.4230v2","created_at":"2026-05-18T04:18:53.489568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4230","created_at":"2026-05-18T04:18:53.489568+00:00"},{"alias_kind":"pith_short_12","alias_value":"DUPPEEKPPEHI","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"DUPPEEKPPEHIUZF3","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"DUPPEEKP","created_at":"2026-05-18T12:25:57.157939+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74","json":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74.json","graph_json":"https://pith.science/api/pith-number/DUPPEEKPPEHIUZF3MRGQSPHC74/graph.json","events_json":"https://pith.science/api/pith-number/DUPPEEKPPEHIUZF3MRGQSPHC74/events.json","paper":"https://pith.science/paper/DUPPEEKP"},"agent_actions":{"view_html":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74","download_json":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74.json","view_paper":"https://pith.science/paper/DUPPEEKP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.4230&json=true","fetch_graph":"https://pith.science/api/pith-number/DUPPEEKPPEHIUZF3MRGQSPHC74/graph.json","fetch_events":"https://pith.science/api/pith-number/DUPPEEKPPEHIUZF3MRGQSPHC74/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74/action/storage_attestation","attest_author":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74/action/author_attestation","sign_citation":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74/action/citation_signature","submit_replication":"https://pith.science/pith/DUPPEEKPPEHIUZF3MRGQSPHC74/action/replication_record"}},"created_at":"2026-05-18T04:18:53.489568+00:00","updated_at":"2026-05-18T04:18:53.489568+00:00"}