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Function $\\Gamma$ is compatible with the cut-norm $\\|\\cdot \\|_\\Box$, in the sense that graphons close in cut-norm have similar $\\Gamma $-values. Here we show the converse, by proving that every graphon $w$ can be approximated by a Robinson graphon $R_w$ so that $\\|w-R_w\\|_\\Box$ is bound"},"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":"2005.05253","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2020-05-11T16:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"4e7764af24a6ffb1b780bccde89a9678c38b7cba32620a96aa33ec2ceb1882a6","abstract_canon_sha256":"5ca1a96fcc8d8021e02c262042a6b0232a4602845cf5d565905039e97cc2a6fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:04.956517Z","signature_b64":"jOGhwIlAbZWWeldvDbo0VrQutpJkz1Lu221mAsx7hfQxbVI4Cwc0FizFd1RRjgnWZD0YiCXZPaPKRFFtC+tCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54ca395d35cc5b6b80a21a473b22de28b6d37084cabe53e60cb80747b40a5604","last_reissued_at":"2026-07-05T08:36:04.956011Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:04.956011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph sequences sampled from Robinson graphons","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeannette Janssen, Mahya Ghandehari","submitted_at":"2020-05-11T16:47:55Z","abstract_excerpt":"The function $\\Gamma$ on the space of graphons, introduced in [CGH$^+$15], aims to measure the extent to which a graphon $w$ exhibits the Robinson property: for all $x<y<z$, $w(x,z)\\leq \\min\\{ w(x,y),w(y,z)\\}$. 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