{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NIBG7VUPRA2XRA7LYGAMMSELRY","short_pith_number":"pith:NIBG7VUP","schema_version":"1.0","canonical_sha256":"6a026fd68f88357883ebc180c6488b8e19f2b4dd26b186364c508762e0688831","source":{"kind":"arxiv","id":"1311.4241","version":2},"attestation_state":"computed","paper":{"title":"Non-conformal repellers and the continuity of pressure for matrix cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"De-Jun Feng, Pablo Shmerkin","submitted_at":"2013-11-18T01:33:29Z","abstract_excerpt":"The pressure function $P(A, s)$ plays a fundamental role in the calculation of the dimension of \"typical\" self-affine sets, where $A=(A_1,\\ldots, A_k)$ is the family of linear mappings in the corresponding generating iterated function system. We prove that this function depends continuously on $A$. As a consequence, we show that the dimension of \"typical\" self-affine sets is a continuous function of the defining maps. This resolves a folklore open problem in the community of fractal geometry. Furthermore we extend the continuity result to more general sub-additive pressure functions generated "},"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":"1311.4241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-18T01:33:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"85f71e2ef9dc7a62632c4983dce9104811c8540bbd1c1b68a85278c3597cf49e","abstract_canon_sha256":"0ba5d9cd2d66a8e132c10762498e40b0e766ab7748a09b689f5d4f260938bd46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:46.741028Z","signature_b64":"TYG+ZujQECW9N2OFC/5zJKv0v5kGKFKGiGMOO2W7Yyekfqat443lnDBVNSmhLbLYGWx+9rWVfJhOYCM1QEi1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a026fd68f88357883ebc180c6488b8e19f2b4dd26b186364c508762e0688831","last_reissued_at":"2026-05-18T01:27:46.740431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:46.740431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-conformal repellers and the continuity of pressure for matrix cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"De-Jun Feng, Pablo Shmerkin","submitted_at":"2013-11-18T01:33:29Z","abstract_excerpt":"The pressure function $P(A, s)$ plays a fundamental role in the calculation of the dimension of \"typical\" self-affine sets, where $A=(A_1,\\ldots, A_k)$ is the family of linear mappings in the corresponding generating iterated function system. We prove that this function depends continuously on $A$. As a consequence, we show that the dimension of \"typical\" self-affine sets is a continuous function of the defining maps. This resolves a folklore open problem in the community of fractal geometry. Furthermore we extend the continuity result to more general sub-additive pressure functions generated "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4241","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":"1311.4241","created_at":"2026-05-18T01:27:46.740526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4241v2","created_at":"2026-05-18T01:27:46.740526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4241","created_at":"2026-05-18T01:27:46.740526+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIBG7VUPRA2X","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIBG7VUPRA2XRA7L","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIBG7VUP","created_at":"2026-05-18T12:27:52.871228+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/NIBG7VUPRA2XRA7LYGAMMSELRY","json":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY.json","graph_json":"https://pith.science/api/pith-number/NIBG7VUPRA2XRA7LYGAMMSELRY/graph.json","events_json":"https://pith.science/api/pith-number/NIBG7VUPRA2XRA7LYGAMMSELRY/events.json","paper":"https://pith.science/paper/NIBG7VUP"},"agent_actions":{"view_html":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY","download_json":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY.json","view_paper":"https://pith.science/paper/NIBG7VUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4241&json=true","fetch_graph":"https://pith.science/api/pith-number/NIBG7VUPRA2XRA7LYGAMMSELRY/graph.json","fetch_events":"https://pith.science/api/pith-number/NIBG7VUPRA2XRA7LYGAMMSELRY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY/action/storage_attestation","attest_author":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY/action/author_attestation","sign_citation":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY/action/citation_signature","submit_replication":"https://pith.science/pith/NIBG7VUPRA2XRA7LYGAMMSELRY/action/replication_record"}},"created_at":"2026-05-18T01:27:46.740526+00:00","updated_at":"2026-05-18T01:27:46.740526+00:00"}