{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OVBWRPCC64ZWROGY3IIAZXH3YO","short_pith_number":"pith:OVBWRPCC","schema_version":"1.0","canonical_sha256":"754368bc42f73368b8d8da100cdcfbc3bc121ba7fbca6063f81986c10b52d110","source":{"kind":"arxiv","id":"1206.0518","version":2},"attestation_state":"computed","paper":{"title":"Lowering topological entropy over subsets revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Wen Huang, Xiangdong Ye","submitted_at":"2012-06-04T05:06:51Z","abstract_excerpt":"Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\\subseteq X$, respectively. $(X, T)$ is called D-{\\it lowerable} (resp. {\\it lowerable}) if for each $0\\le h\\le h (T, X)$ there is a subset (resp. closed subset) $K_h$ with $h^B (T, K_h)= h$ (resp. $h (T, K_h)= h$); is called D-{\\it hereditarily lowerable} (resp. {\\it hereditarily lowerable}) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable).\n  In this paper it is proved that each topological dynamical system is not only lowerable b"},"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":"1206.0518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-06-04T05:06:51Z","cross_cats_sorted":[],"title_canon_sha256":"4492e8d403ae51814315ad8e6a8b97c1285faa03a2a6214b163912da96b50680","abstract_canon_sha256":"ea909e8183f3e817523b80da04040a6c6f77348859013f9c7d9e6166255b0a6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:32.852623Z","signature_b64":"lu+jN+BXABDXV3OGWA8GgTt1xwGuOy+5mOibi3MLGhkC6iaY/+NUu3w4oYFOPOzqQZKK3iM2dRJF7ZW1u+A+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"754368bc42f73368b8d8da100cdcfbc3bc121ba7fbca6063f81986c10b52d110","last_reissued_at":"2026-05-18T03:20:32.851596Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:32.851596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lowering topological entropy over subsets revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Wen Huang, Xiangdong Ye","submitted_at":"2012-06-04T05:06:51Z","abstract_excerpt":"Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\\subseteq X$, respectively. $(X, T)$ is called D-{\\it lowerable} (resp. {\\it lowerable}) if for each $0\\le h\\le h (T, X)$ there is a subset (resp. closed subset) $K_h$ with $h^B (T, K_h)= h$ (resp. $h (T, K_h)= h$); is called D-{\\it hereditarily lowerable} (resp. {\\it hereditarily lowerable}) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable).\n  In this paper it is proved that each topological dynamical system is not only lowerable b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0518","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":"1206.0518","created_at":"2026-05-18T03:20:32.851726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.0518v2","created_at":"2026-05-18T03:20:32.851726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0518","created_at":"2026-05-18T03:20:32.851726+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVBWRPCC64ZW","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVBWRPCC64ZWROGY","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVBWRPCC","created_at":"2026-05-18T12:27:16.716162+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/OVBWRPCC64ZWROGY3IIAZXH3YO","json":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO.json","graph_json":"https://pith.science/api/pith-number/OVBWRPCC64ZWROGY3IIAZXH3YO/graph.json","events_json":"https://pith.science/api/pith-number/OVBWRPCC64ZWROGY3IIAZXH3YO/events.json","paper":"https://pith.science/paper/OVBWRPCC"},"agent_actions":{"view_html":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO","download_json":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO.json","view_paper":"https://pith.science/paper/OVBWRPCC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.0518&json=true","fetch_graph":"https://pith.science/api/pith-number/OVBWRPCC64ZWROGY3IIAZXH3YO/graph.json","fetch_events":"https://pith.science/api/pith-number/OVBWRPCC64ZWROGY3IIAZXH3YO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO/action/storage_attestation","attest_author":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO/action/author_attestation","sign_citation":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO/action/citation_signature","submit_replication":"https://pith.science/pith/OVBWRPCC64ZWROGY3IIAZXH3YO/action/replication_record"}},"created_at":"2026-05-18T03:20:32.851726+00:00","updated_at":"2026-05-18T03:20:32.851726+00:00"}