{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:S6Q3MNUGNORCSMC5I4POU7J5ZH","short_pith_number":"pith:S6Q3MNUG","schema_version":"1.0","canonical_sha256":"97a1b636866ba229305d471eea7d3dc9f319f89eb56b3bc329d4ddc9dc534e39","source":{"kind":"arxiv","id":"1707.06727","version":1},"attestation_state":"computed","paper":{"title":"An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carrie Rutherford, Robin Whitty","submitted_at":"2017-07-21T00:47:28Z","abstract_excerpt":"A fundamental theorem of matroid theory establishes that a transversal matroid is representable over fields of any characteristic. It was proved in 1970 by Piff and Welsh: their proof is elegant and concise and, moveover, constructive. However it is far from being algorithmic, in terms of suggesting a step-by-step procedure for deriving a collection of vectors over a given base field representing the transversal matroid induced by a given set system. In this note we recast Piff and Welsh's proof in algorithmic form."},"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":"1707.06727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-21T00:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"7b73979ab5ca7541956d282f62ec65009fc04904befb1ad0a83b2b68f767b96b","abstract_canon_sha256":"ea7586faa133ccdde125b68ab28d553eb7c330370cdf380c504a578a72444c65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.849706Z","signature_b64":"kCmEetI+r7bCYYYFIH8P/2AE8kC9JxbqyvhEq1MDoXA8L1mnUkW7oP6+LbkLHUBYnlTxAKDXha73fyV4Rbm9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97a1b636866ba229305d471eea7d3dc9f319f89eb56b3bc329d4ddc9dc534e39","last_reissued_at":"2026-05-18T00:39:51.849109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.849109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carrie Rutherford, Robin Whitty","submitted_at":"2017-07-21T00:47:28Z","abstract_excerpt":"A fundamental theorem of matroid theory establishes that a transversal matroid is representable over fields of any characteristic. It was proved in 1970 by Piff and Welsh: their proof is elegant and concise and, moveover, constructive. However it is far from being algorithmic, in terms of suggesting a step-by-step procedure for deriving a collection of vectors over a given base field representing the transversal matroid induced by a given set system. In this note we recast Piff and Welsh's proof in algorithmic form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06727","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":""},"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":"1707.06727","created_at":"2026-05-18T00:39:51.849221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06727v1","created_at":"2026-05-18T00:39:51.849221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06727","created_at":"2026-05-18T00:39:51.849221+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6Q3MNUGNORC","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6Q3MNUGNORCSMC5","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6Q3MNUG","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH","json":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH.json","graph_json":"https://pith.science/api/pith-number/S6Q3MNUGNORCSMC5I4POU7J5ZH/graph.json","events_json":"https://pith.science/api/pith-number/S6Q3MNUGNORCSMC5I4POU7J5ZH/events.json","paper":"https://pith.science/paper/S6Q3MNUG"},"agent_actions":{"view_html":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH","download_json":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH.json","view_paper":"https://pith.science/paper/S6Q3MNUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06727&json=true","fetch_graph":"https://pith.science/api/pith-number/S6Q3MNUGNORCSMC5I4POU7J5ZH/graph.json","fetch_events":"https://pith.science/api/pith-number/S6Q3MNUGNORCSMC5I4POU7J5ZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH/action/storage_attestation","attest_author":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH/action/author_attestation","sign_citation":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH/action/citation_signature","submit_replication":"https://pith.science/pith/S6Q3MNUGNORCSMC5I4POU7J5ZH/action/replication_record"}},"created_at":"2026-05-18T00:39:51.849221+00:00","updated_at":"2026-05-18T00:39:51.849221+00:00"}