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Letting A(P) be the Ehrhart ring of P=conv(V), we are able to show that if A is the clutter matrix of a uniform, unmixed MFMC clutter C, then C is an Ehrhart clutter and in this case we provide sharp bounds on the Castelnuovo-Mumford regularity of A(P). Motivated by the Conforti-Cornuejols conjecture on packing problems, we conjecture that if C is both ideal and the clique clutter of a perfect graph, then C has the MFMC pro"},"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":"0902.1354","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-02-09T01:31:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"13e89f80186bc45885091c1903ce761f7df0c5fd4b56459b9f665fd82e80e5b2","abstract_canon_sha256":"482bbba802cddd017a9125c32a5fcf8fa2ee4730661e463dea418a1df9b0c17f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:11.620817Z","signature_b64":"Q+UM3Ht1fTiACptbyJIRWFwkh8BLAHZ4LwcHrLIlHBR5SvdLR19AMiqSKwh1QA3QSr9az6dwlfXZvTKX06GDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c94cc31252c870c49d8a68a728987330b376f7158eab400a4d7eec7e9b0cf19c","last_reissued_at":"2026-05-18T04:25:11.620194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:11.620194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ehrhart clutters: Regularity and Max-Flow Min-Cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Edwin O'Shea, Jose Martinez-Bernal, Rafael H. 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