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Suppose that for each $1\\le j_{1}<j_{2}\\le d$ there exists $i\\in\\Lambda$ so that $|r_{i,j_{1}}|\\ne|r_{i,j_{2}}|$, and that for each $1\\le j\\le d$ the IFS $\\left\\{ t\\rightarrow r_{i,j}t+a_{i,j}\\right\\} _{i\\in\\Lambda}$ on the real line is exponentially separated. Under these assumptions we show that the Hausdorff dimension of the attractor of $\\Phi$ is equal to $\\min\\left\\{ \\dim_{A}\\Phi,d\\right\\} $, where $\\dim_{A}\\Phi$ i"},"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":"2309.03985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-09-07T19:36:21Z","cross_cats_sorted":[],"title_canon_sha256":"d63afd6e546656a1d55f2c1a64b7428204bbb80ceb4dd78a57edcf0e0c215e7c","abstract_canon_sha256":"1442104d3d6ce718d2915625efa6817c459708c26b0689c8ab78f07cdafc3a1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:53.206506Z","signature_b64":"Y2A+B8CPGEdIiO8asU/3aUTmM3na45pCHFgWyWQei3qvIvqc1O/C0lTvOsU48hruXeD4JbOodCR95KPMjCSuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83b474443f8bfca581a7233de7019c82bff0698f33e406b8e3165467e98188a5","last_reissued_at":"2026-07-05T06:48:53.206127Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:53.206127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimension of diagonal self-affine sets and measures via non-conformal partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ariel Rapaport","submitted_at":"2023-09-07T19:36:21Z","abstract_excerpt":"Let $\\Phi:=\\left\\{ (x_{1},...,x_{d})\\rightarrow\\left(r_{i,1}x_{1}+a_{i,1},...,r_{i,d}x_{d}+a_{i,d}\\right)\\right\\} _{i\\in\\Lambda}$ be an affine diagonal IFS on $\\mathbb{R}^{d}$. Suppose that for each $1\\le j_{1}<j_{2}\\le d$ there exists $i\\in\\Lambda$ so that $|r_{i,j_{1}}|\\ne|r_{i,j_{2}}|$, and that for each $1\\le j\\le d$ the IFS $\\left\\{ t\\rightarrow r_{i,j}t+a_{i,j}\\right\\} _{i\\in\\Lambda}$ on the real line is exponentially separated. Under these assumptions we show that the Hausdorff dimension of the attractor of $\\Phi$ is equal to $\\min\\left\\{ \\dim_{A}\\Phi,d\\right\\} $, where $\\dim_{A}\\Phi$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.03985","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.03985/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2309.03985","created_at":"2026-07-05T06:48:53.206174+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.03985v1","created_at":"2026-07-05T06:48:53.206174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.03985","created_at":"2026-07-05T06:48:53.206174+00:00"},{"alias_kind":"pith_short_12","alias_value":"QO2HIRB7RP6K","created_at":"2026-07-05T06:48:53.206174+00:00"},{"alias_kind":"pith_short_16","alias_value":"QO2HIRB7RP6KLANH","created_at":"2026-07-05T06:48:53.206174+00:00"},{"alias_kind":"pith_short_8","alias_value":"QO2HIRB7","created_at":"2026-07-05T06:48:53.206174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2506.06851","citing_title":"Weakly separated self-affine carpets","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK","json":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK.json","graph_json":"https://pith.science/api/pith-number/QO2HIRB7RP6KLANHEM66OAM4QK/graph.json","events_json":"https://pith.science/api/pith-number/QO2HIRB7RP6KLANHEM66OAM4QK/events.json","paper":"https://pith.science/paper/QO2HIRB7"},"agent_actions":{"view_html":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK","download_json":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK.json","view_paper":"https://pith.science/paper/QO2HIRB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.03985&json=true","fetch_graph":"https://pith.science/api/pith-number/QO2HIRB7RP6KLANHEM66OAM4QK/graph.json","fetch_events":"https://pith.science/api/pith-number/QO2HIRB7RP6KLANHEM66OAM4QK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK/action/storage_attestation","attest_author":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK/action/author_attestation","sign_citation":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK/action/citation_signature","submit_replication":"https://pith.science/pith/QO2HIRB7RP6KLANHEM66OAM4QK/action/replication_record"}},"created_at":"2026-07-05T06:48:53.206174+00:00","updated_at":"2026-07-05T06:48:53.206174+00:00"}