{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ORNMVS2TZHHB5XI2AYMAIKVO45","short_pith_number":"pith:ORNMVS2T","schema_version":"1.0","canonical_sha256":"745acacb53c9ce1edd1a0618042aaee77524c7d0ed101ad833fd9ded7cd9ba24","source":{"kind":"arxiv","id":"1806.11374","version":1},"attestation_state":"computed","paper":{"title":"Inhomogeneous Partition Regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Leader, Paul A. Russell","submitted_at":"2018-06-29T12:18:32Z","abstract_excerpt":"We say that the system of equations $Ax=b$, where $A$ is an integer matrix and $b$ is a (non-zero) integer vector, is partition regular if whenever the integers are finitely coloured there is a monochromatic vector $x$ with $Ax=b$. Rado proved that the system $Ax=b$ is partition regular if and only if it has a constant solution. Byszewski and Krawczyk asked if this remains true when the integers are replaced by a general ring $R$. Our aim in this note is to answer this question in the affirmative. The main ingredient is a new `direct' proof of Rado's result."},"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":"1806.11374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-29T12:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"26ca379e9634d979bf2c52fb2c5e617b542d50fbda44e7bb8b496e963b50abbb","abstract_canon_sha256":"9afb7565ccdd5fff85793acf7c91ad1c66abeed4ed9a5a0d3f69fa1bdf20b22a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:02.072498Z","signature_b64":"u6NPPw3e8EE3wEdE5SAxp21BiR7DPepV8L3tVHDjyMkKtshigsPP67hWKsWcm5IgYIdn1AI72+4WeAVorkJzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"745acacb53c9ce1edd1a0618042aaee77524c7d0ed101ad833fd9ded7cd9ba24","last_reissued_at":"2026-05-18T00:12:02.071938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:02.071938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inhomogeneous Partition Regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Leader, Paul A. Russell","submitted_at":"2018-06-29T12:18:32Z","abstract_excerpt":"We say that the system of equations $Ax=b$, where $A$ is an integer matrix and $b$ is a (non-zero) integer vector, is partition regular if whenever the integers are finitely coloured there is a monochromatic vector $x$ with $Ax=b$. Rado proved that the system $Ax=b$ is partition regular if and only if it has a constant solution. Byszewski and Krawczyk asked if this remains true when the integers are replaced by a general ring $R$. Our aim in this note is to answer this question in the affirmative. The main ingredient is a new `direct' proof of Rado's result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11374","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":"1806.11374","created_at":"2026-05-18T00:12:02.072019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.11374v1","created_at":"2026-05-18T00:12:02.072019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11374","created_at":"2026-05-18T00:12:02.072019+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORNMVS2TZHHB","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORNMVS2TZHHB5XI2","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORNMVS2T","created_at":"2026-05-18T12:32:43.782077+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/ORNMVS2TZHHB5XI2AYMAIKVO45","json":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45.json","graph_json":"https://pith.science/api/pith-number/ORNMVS2TZHHB5XI2AYMAIKVO45/graph.json","events_json":"https://pith.science/api/pith-number/ORNMVS2TZHHB5XI2AYMAIKVO45/events.json","paper":"https://pith.science/paper/ORNMVS2T"},"agent_actions":{"view_html":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45","download_json":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45.json","view_paper":"https://pith.science/paper/ORNMVS2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.11374&json=true","fetch_graph":"https://pith.science/api/pith-number/ORNMVS2TZHHB5XI2AYMAIKVO45/graph.json","fetch_events":"https://pith.science/api/pith-number/ORNMVS2TZHHB5XI2AYMAIKVO45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45/action/storage_attestation","attest_author":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45/action/author_attestation","sign_citation":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45/action/citation_signature","submit_replication":"https://pith.science/pith/ORNMVS2TZHHB5XI2AYMAIKVO45/action/replication_record"}},"created_at":"2026-05-18T00:12:02.072019+00:00","updated_at":"2026-05-18T00:12:02.072019+00:00"}