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By a construction of Marc Krasner, each valued field gives rise to a stringent hyperfield.\n  We show that if $H$ is a stringent skew hyperfield, then the vectors of any weak matroid over $H$ are orthogonal to its covectors, and we deduce that weak matroids over $H$ are strong matroids over $H$. Also, we present ve"},"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":"1908.03420","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T11:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"9614b74fcfea9cbf7c7c736478b8a89bd174e54a4b702e30c87efa7195b6e10b","abstract_canon_sha256":"989de21092f506dd43b63e9fc9d211ad1ab1c3be46f1ac7e1ca0011eb0ae6034"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:50:35.851792Z","signature_b64":"w4y+SKBgiLBJRrGze7KyvdNxcanxuTibBWB0MFXZIhYHO0lBe4SUOUzDmNKsCCNctpQKovtTCy4adlo+epaTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"704e978742318eff021abc26dc4f55dbe59515170bbb6922bd09ea01a74b3f53","last_reissued_at":"2026-07-05T05:50:35.851371Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:50:35.851371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfect matroids over hyperfields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Bowler, Rudi Pendavingh","submitted_at":"2019-08-09T11:43:12Z","abstract_excerpt":"We investigate valuated matroids with an additional algebraic structure on their residue matroids. 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