{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NW5LD3ELHEMAKFXW2VFKVK4WFK","short_pith_number":"pith:NW5LD3EL","schema_version":"1.0","canonical_sha256":"6dbab1ec8b39180516f6d54aaaab962ab75f0a003a0d79a46ea855f86eab8383","source":{"kind":"arxiv","id":"1206.0235","version":1},"attestation_state":"computed","paper":{"title":"Rank as a function of measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawid Huczek, Tomasz Downarowicz, Yonatan Gutman","submitted_at":"2012-06-01T16:12:15Z","abstract_excerpt":"We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing sequence of upper semicontinuous functions)"},"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":"1206.0235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-06-01T16:12:15Z","cross_cats_sorted":[],"title_canon_sha256":"2721e4787cb51cb268f56f83ee399772b499ea38c96bfb0ab814b8ddf6903973","abstract_canon_sha256":"7aee876c81701e5655e6389cab10f11bfcc18aab66a3e24a983e7f0c9c6c03be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:26.744608Z","signature_b64":"l01ZNlAjtT5pbzYuDjJUubXflkI5NvXBaLflCt3KfW+9/aLTnC9E6J6PY28P0rkyUORAU6Vyj1nQJT+COIpIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dbab1ec8b39180516f6d54aaaab962ab75f0a003a0d79a46ea855f86eab8383","last_reissued_at":"2026-05-18T03:54:26.743910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:26.743910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank as a function of measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawid Huczek, Tomasz Downarowicz, Yonatan Gutman","submitted_at":"2012-06-01T16:12:15Z","abstract_excerpt":"We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing sequence of upper semicontinuous functions)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0235","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":"1206.0235","created_at":"2026-05-18T03:54:26.744012+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.0235v1","created_at":"2026-05-18T03:54:26.744012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0235","created_at":"2026-05-18T03:54:26.744012+00:00"},{"alias_kind":"pith_short_12","alias_value":"NW5LD3ELHEMA","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NW5LD3ELHEMAKFXW","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NW5LD3EL","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/NW5LD3ELHEMAKFXW2VFKVK4WFK","json":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK.json","graph_json":"https://pith.science/api/pith-number/NW5LD3ELHEMAKFXW2VFKVK4WFK/graph.json","events_json":"https://pith.science/api/pith-number/NW5LD3ELHEMAKFXW2VFKVK4WFK/events.json","paper":"https://pith.science/paper/NW5LD3EL"},"agent_actions":{"view_html":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK","download_json":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK.json","view_paper":"https://pith.science/paper/NW5LD3EL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.0235&json=true","fetch_graph":"https://pith.science/api/pith-number/NW5LD3ELHEMAKFXW2VFKVK4WFK/graph.json","fetch_events":"https://pith.science/api/pith-number/NW5LD3ELHEMAKFXW2VFKVK4WFK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK/action/storage_attestation","attest_author":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK/action/author_attestation","sign_citation":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK/action/citation_signature","submit_replication":"https://pith.science/pith/NW5LD3ELHEMAKFXW2VFKVK4WFK/action/replication_record"}},"created_at":"2026-05-18T03:54:26.744012+00:00","updated_at":"2026-05-18T03:54:26.744012+00:00"}