{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5DPGDN2LNP2A2A2Z543HAJAQEU","short_pith_number":"pith:5DPGDN2L","schema_version":"1.0","canonical_sha256":"e8de61b74b6bf40d0359ef36702410252c13531448e318ffe5ecd7a45fb49b36","source":{"kind":"arxiv","id":"2606.28681","version":1},"attestation_state":"computed","paper":{"title":"Dimensional entropy of amenable group actions over stable sets and fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Xinyao He","submitted_at":"2026-06-27T01:46:12Z","abstract_excerpt":"This paper is devoted to the study of Bowen's dimensional entropy on subsets for actions of amenable groups. We prove three main results. (1) First, topological conditional entropy is characterized by the dimensional entropy of stable sets (Theorem 1.1), answering a question of Dou, Wang and the second author of the present paper raised in [Fund. Math., 2025]. We remark that our Theorem 1.1 is the first characterization of topological conditional entropy via Bowen's dimensional entropy of stable sets even for $\\mathbb{Z}$-actions. (2) Second, we establish a dimensional entropy inequality for f"},"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":"2606.28681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-27T01:46:12Z","cross_cats_sorted":[],"title_canon_sha256":"28aebc12b27644d19a5ee1b368d888e678de56d5996d965d922bc2a32e1f98a1","abstract_canon_sha256":"aa19ee362229ccd87f44fe16cf8714ead252fd219465062e4454278468f3da85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:16:47.344778Z","signature_b64":"zz/cl596Atu3lXDWfiUJ/Vt6vNJIzXEToMuuQRjvNgiLWtfdrF8UOGvyrNRxl/YBDZqpOF/ZPZz6BBXVW9usDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8de61b74b6bf40d0359ef36702410252c13531448e318ffe5ecd7a45fb49b36","last_reissued_at":"2026-06-30T01:16:47.344097Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:16:47.344097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimensional entropy of amenable group actions over stable sets and fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Xinyao He","submitted_at":"2026-06-27T01:46:12Z","abstract_excerpt":"This paper is devoted to the study of Bowen's dimensional entropy on subsets for actions of amenable groups. We prove three main results. (1) First, topological conditional entropy is characterized by the dimensional entropy of stable sets (Theorem 1.1), answering a question of Dou, Wang and the second author of the present paper raised in [Fund. Math., 2025]. We remark that our Theorem 1.1 is the first characterization of topological conditional entropy via Bowen's dimensional entropy of stable sets even for $\\mathbb{Z}$-actions. (2) Second, we establish a dimensional entropy inequality for f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28681","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28681/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.28681","created_at":"2026-06-30T01:16:47.344178+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.28681v1","created_at":"2026-06-30T01:16:47.344178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28681","created_at":"2026-06-30T01:16:47.344178+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DPGDN2LNP2A","created_at":"2026-06-30T01:16:47.344178+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DPGDN2LNP2A2A2Z","created_at":"2026-06-30T01:16:47.344178+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DPGDN2L","created_at":"2026-06-30T01:16:47.344178+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/5DPGDN2LNP2A2A2Z543HAJAQEU","json":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU.json","graph_json":"https://pith.science/api/pith-number/5DPGDN2LNP2A2A2Z543HAJAQEU/graph.json","events_json":"https://pith.science/api/pith-number/5DPGDN2LNP2A2A2Z543HAJAQEU/events.json","paper":"https://pith.science/paper/5DPGDN2L"},"agent_actions":{"view_html":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU","download_json":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU.json","view_paper":"https://pith.science/paper/5DPGDN2L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.28681&json=true","fetch_graph":"https://pith.science/api/pith-number/5DPGDN2LNP2A2A2Z543HAJAQEU/graph.json","fetch_events":"https://pith.science/api/pith-number/5DPGDN2LNP2A2A2Z543HAJAQEU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU/action/storage_attestation","attest_author":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU/action/author_attestation","sign_citation":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU/action/citation_signature","submit_replication":"https://pith.science/pith/5DPGDN2LNP2A2A2Z543HAJAQEU/action/replication_record"}},"created_at":"2026-06-30T01:16:47.344178+00:00","updated_at":"2026-06-30T01:16:47.344178+00:00"}