{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CQVEK2UG2O7COET6O3JLOQ7347","short_pith_number":"pith:CQVEK2UG","schema_version":"1.0","canonical_sha256":"142a456a86d3be27127e76d2b743fbe7d93feea92da6f4804cacd46ebb41c913","source":{"kind":"arxiv","id":"1507.00642","version":4},"attestation_state":"computed","paper":{"title":"An inequality for the matrix pressure function and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ian D. Morris","submitted_at":"2015-07-02T16:02:56Z","abstract_excerpt":"We prove an a priori lower bound for the pressure, or $p$-norm joint spectral radius, of a measure on the set of $d \\times d$ real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to give new proofs of the continuity of the affinity dimension of a self-affine set and of the continuity of the singular-value pressure for invertible matrices, both of which had been previously established by D.-J. Feng and P. Shmerkin using multiplicative ergodic theory and the subadditive variational principle. Unlike the previous proof, our lower bound yields"},"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":"1507.00642","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-02T16:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"c49da74ec3efd25161b057f79a551cfd3d8fa83e8fa4a098908de3bc3fd03c36","abstract_canon_sha256":"abcc01a5b46503ca9514248dda4e3ebe09107fad3dd548487dbdd24465619711"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:20.360900Z","signature_b64":"XgxvIL6sSvh1aeNO/5qD8FGYaABTblaWWNv9bw7YUyL62syxDCLQzGroYEDxfcTb9EfODXtYszmxigSABVrfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"142a456a86d3be27127e76d2b743fbe7d93feea92da6f4804cacd46ebb41c913","last_reissued_at":"2026-05-18T01:10:20.360327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:20.360327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An inequality for the matrix pressure function and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ian D. Morris","submitted_at":"2015-07-02T16:02:56Z","abstract_excerpt":"We prove an a priori lower bound for the pressure, or $p$-norm joint spectral radius, of a measure on the set of $d \\times d$ real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to give new proofs of the continuity of the affinity dimension of a self-affine set and of the continuity of the singular-value pressure for invertible matrices, both of which had been previously established by D.-J. Feng and P. Shmerkin using multiplicative ergodic theory and the subadditive variational principle. Unlike the previous proof, our lower bound yields"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00642","kind":"arxiv","version":4},"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":"1507.00642","created_at":"2026-05-18T01:10:20.360405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00642v4","created_at":"2026-05-18T01:10:20.360405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00642","created_at":"2026-05-18T01:10:20.360405+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQVEK2UG2O7C","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQVEK2UG2O7COET6","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQVEK2UG","created_at":"2026-05-18T12:29:17.054201+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/CQVEK2UG2O7COET6O3JLOQ7347","json":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347.json","graph_json":"https://pith.science/api/pith-number/CQVEK2UG2O7COET6O3JLOQ7347/graph.json","events_json":"https://pith.science/api/pith-number/CQVEK2UG2O7COET6O3JLOQ7347/events.json","paper":"https://pith.science/paper/CQVEK2UG"},"agent_actions":{"view_html":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347","download_json":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347.json","view_paper":"https://pith.science/paper/CQVEK2UG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00642&json=true","fetch_graph":"https://pith.science/api/pith-number/CQVEK2UG2O7COET6O3JLOQ7347/graph.json","fetch_events":"https://pith.science/api/pith-number/CQVEK2UG2O7COET6O3JLOQ7347/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347/action/storage_attestation","attest_author":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347/action/author_attestation","sign_citation":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347/action/citation_signature","submit_replication":"https://pith.science/pith/CQVEK2UG2O7COET6O3JLOQ7347/action/replication_record"}},"created_at":"2026-05-18T01:10:20.360405+00:00","updated_at":"2026-05-18T01:10:20.360405+00:00"}