{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PZ7ZCNTYB3M2FEYJV3PI2K2KBE","short_pith_number":"pith:PZ7ZCNTY","schema_version":"1.0","canonical_sha256":"7e7f9136780ed9a29309aede8d2b4a093316dc40f279c0c1a19df34f60b4cb29","source":{"kind":"arxiv","id":"1110.6144","version":1},"attestation_state":"computed","paper":{"title":"Characterization of Entropy for Spacing shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawoud Ahmadi Dastjerdi, Maliheh Dabbaghian Amiri","submitted_at":"2011-10-27T17:37:50Z","abstract_excerpt":"Suppose $P\\subseteq \\mathbb{N}$ and let $(\\Sigma_P,\\,\\sigma_P)$ be the space of a spacing shift. We show that if entropy $h_{\\sigma_P}=0$ then $(\\Sigma_P,\\,\\sigma_P)$ is proximal. Also $h_{\\sigma_P}=0$ if and only if $P=\\mathbb N\\setminus E$ where $E$ is an intersective set. Moreover, we show that\n  $h_{\\sigma_P}>0$ implies that $P$ is a $\\Delta^*$ set; and by giving a class of examples, we show that this is not a sufficient condition. Then there is enough results to solve question 5 given in [J. Banks et al., \\textit{Dynamics of Spacing Shifts}, Discrete Contin. Dyn. Syst., to appear.]."},"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":"1110.6144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-27T17:37:50Z","cross_cats_sorted":[],"title_canon_sha256":"a2140f15fffd783ed12f93ae9cfd8042fee71d752b37ce465657ccd6f8c5f301","abstract_canon_sha256":"bda40598beb257d88948e97a7092337f46435e71f66ab1e69a41e0ee14d6a7e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:09.468536Z","signature_b64":"HWusrGMLNW5qP+UG5j//LJTotMGMjK3YFoOA8nJK7dQ58Lq2SEh+B4fDymuR900MVW14tOayLx3bQcbEVzSPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e7f9136780ed9a29309aede8d2b4a093316dc40f279c0c1a19df34f60b4cb29","last_reissued_at":"2026-05-18T04:10:09.467854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:09.467854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of Entropy for Spacing shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawoud Ahmadi Dastjerdi, Maliheh Dabbaghian Amiri","submitted_at":"2011-10-27T17:37:50Z","abstract_excerpt":"Suppose $P\\subseteq \\mathbb{N}$ and let $(\\Sigma_P,\\,\\sigma_P)$ be the space of a spacing shift. We show that if entropy $h_{\\sigma_P}=0$ then $(\\Sigma_P,\\,\\sigma_P)$ is proximal. Also $h_{\\sigma_P}=0$ if and only if $P=\\mathbb N\\setminus E$ where $E$ is an intersective set. Moreover, we show that\n  $h_{\\sigma_P}>0$ implies that $P$ is a $\\Delta^*$ set; and by giving a class of examples, we show that this is not a sufficient condition. Then there is enough results to solve question 5 given in [J. Banks et al., \\textit{Dynamics of Spacing Shifts}, Discrete Contin. Dyn. Syst., to appear.]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6144","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1110.6144","created_at":"2026-05-18T04:10:09.467951+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6144v1","created_at":"2026-05-18T04:10:09.467951+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6144","created_at":"2026-05-18T04:10:09.467951+00:00"},{"alias_kind":"pith_short_12","alias_value":"PZ7ZCNTYB3M2","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PZ7ZCNTYB3M2FEYJ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PZ7ZCNTY","created_at":"2026-05-18T12:26:39.201973+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/PZ7ZCNTYB3M2FEYJV3PI2K2KBE","json":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE.json","graph_json":"https://pith.science/api/pith-number/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/graph.json","events_json":"https://pith.science/api/pith-number/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/events.json","paper":"https://pith.science/paper/PZ7ZCNTY"},"agent_actions":{"view_html":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE","download_json":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE.json","view_paper":"https://pith.science/paper/PZ7ZCNTY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6144&json=true","fetch_graph":"https://pith.science/api/pith-number/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/graph.json","fetch_events":"https://pith.science/api/pith-number/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/action/storage_attestation","attest_author":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/action/author_attestation","sign_citation":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/action/citation_signature","submit_replication":"https://pith.science/pith/PZ7ZCNTYB3M2FEYJV3PI2K2KBE/action/replication_record"}},"created_at":"2026-05-18T04:10:09.467951+00:00","updated_at":"2026-05-18T04:10:09.467951+00:00"}