{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Z2K7ARNMQN2PTC7K7SL7ISPRCN","short_pith_number":"pith:Z2K7ARNM","schema_version":"1.0","canonical_sha256":"ce95f045ac8374f98beafc97f449f1134c493a5fa5e4a7ed2025c7f5627c12ce","source":{"kind":"arxiv","id":"1309.4730","version":1},"attestation_state":"computed","paper":{"title":"Self-affine sets and the continuity of subadditive pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pablo Shmerkin","submitted_at":"2013-09-18T18:07:26Z","abstract_excerpt":"The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open problem, by proving that the affinity dimension is a continuous function of the defining maps. The proof also yields the continuity of a topological pressure arising in the study of random matrix products. I survey the definition, motivation and main properties of the affinity dimension and the associated SVF topological pressure, and give a proof of their continui"},"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":"1309.4730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-18T18:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"82f4cac93c28936c7db6e8ebe3cb60d403cd5448cfb1c03a75cbbf2fe1a2e28d","abstract_canon_sha256":"6ecc28512aea8f25c14022723e12a1ada2000fe2d7e0dfe1646a3655e129aa53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.470600Z","signature_b64":"OXQtyNLxqKuATQ24eqvgx9t96GH2NpMEU3n/sUyZilde5xgf7UKsH6rjn/Z7X8wUjLZDrC3epHPPQmQmUsJgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce95f045ac8374f98beafc97f449f1134c493a5fa5e4a7ed2025c7f5627c12ce","last_reissued_at":"2026-05-18T03:12:58.469744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.469744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-affine sets and the continuity of subadditive pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pablo Shmerkin","submitted_at":"2013-09-18T18:07:26Z","abstract_excerpt":"The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open problem, by proving that the affinity dimension is a continuous function of the defining maps. The proof also yields the continuity of a topological pressure arising in the study of random matrix products. I survey the definition, motivation and main properties of the affinity dimension and the associated SVF topological pressure, and give a proof of their continui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4730","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":"1309.4730","created_at":"2026-05-18T03:12:58.469851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.4730v1","created_at":"2026-05-18T03:12:58.469851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4730","created_at":"2026-05-18T03:12:58.469851+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2K7ARNMQN2P","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2K7ARNMQN2PTC7K","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2K7ARNM","created_at":"2026-05-18T12:28:09.283467+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/Z2K7ARNMQN2PTC7K7SL7ISPRCN","json":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN.json","graph_json":"https://pith.science/api/pith-number/Z2K7ARNMQN2PTC7K7SL7ISPRCN/graph.json","events_json":"https://pith.science/api/pith-number/Z2K7ARNMQN2PTC7K7SL7ISPRCN/events.json","paper":"https://pith.science/paper/Z2K7ARNM"},"agent_actions":{"view_html":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN","download_json":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN.json","view_paper":"https://pith.science/paper/Z2K7ARNM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.4730&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2K7ARNMQN2PTC7K7SL7ISPRCN/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2K7ARNMQN2PTC7K7SL7ISPRCN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN/action/storage_attestation","attest_author":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN/action/author_attestation","sign_citation":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN/action/citation_signature","submit_replication":"https://pith.science/pith/Z2K7ARNMQN2PTC7K7SL7ISPRCN/action/replication_record"}},"created_at":"2026-05-18T03:12:58.469851+00:00","updated_at":"2026-05-18T03:12:58.469851+00:00"}