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Here we characterize all $3$-self-affine convex quadrangles, obtaining $5$ one-parameter families and $13$ singular examples of affine types. This way we reduce the quest for all $n$-self-affine convex quadrangles to the open case $n=4$.\n  In addition, we show that there are $n$-self-affine non-convex quadrangles for all $n \\ge 3$, but not for"},"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":"2502.15521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-21T15:22:50Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"1d6d2859c3524f16ca76a352f28f5eec57e39f3f1db7f95d11b3b407d2b58eb1","abstract_canon_sha256":"d4729e2f8f98cc9643318bf27b7f4af1378ff472a50468cb8f682d864c280c9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:02.412959Z","signature_b64":"KeaJmGPxVjCiPCGx0nqZnH5IRn8e0wSp0wZC59+MfFXMQSl8dg7GPdGjJ+p+Y3poUT2L7hNvIqXGOnyaCGzLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5926b1f65cc7e7149e95fb4a3c661d2b57be7c432e217038a754482ef55307a5","last_reissued_at":"2026-05-25T02:01:02.412271Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:02.412271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-affine quadrangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Christian Richter, Felix Zimmermann","submitted_at":"2025-02-21T15:22:50Z","abstract_excerpt":"A quadrangle in the Euclidean plane is called $n$-self-affine if it has a dissection into $n$ affine images of itself. 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