{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WAI352XCWUBAEMR7VYOBMEWFKJ","short_pith_number":"pith:WAI352XC","schema_version":"1.0","canonical_sha256":"b011beeae2b50202323fae1c1612c5524580ba9498b206a401d0cb1ae622c082","source":{"kind":"arxiv","id":"1707.01026","version":2},"attestation_state":"computed","paper":{"title":"Polyhedra and parameter spaces for matroids over valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Alex Fink, Luca Moci","submitted_at":"2017-07-04T14:59:34Z","abstract_excerpt":"In this paper we address two of the major foundational questions in the theory of matroids over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of the base polytope for matroids. Second, we describe a parameter space for matroids over a valuation ring, which turns out to be a tropical version of the Bott-Samelson varieties for the full flag variety. Thus a matroid over a valuation ring is a sequence of flags of tropical linear spaces a.k.a. valuated matroids."},"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":"1707.01026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-04T14:59:34Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9a5b72eaaec79e54faf670d4e8f582af76f40e8bdacce39624018cc76573d312","abstract_canon_sha256":"ec201e539e2e56f988d6fb5de75989655c18c5857fabf38f0b847f186a654891"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:50.212894Z","signature_b64":"+DvQTVHUmpMyY0SAke4kBXg6C97NNyFHZzpsw/kbHcwq82vd+ztYjZdqNMRNkwSxLMcoHlVzhIW49mXIC79rBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b011beeae2b50202323fae1c1612c5524580ba9498b206a401d0cb1ae622c082","last_reissued_at":"2026-05-18T00:38:50.212199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:50.212199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polyhedra and parameter spaces for matroids over valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Alex Fink, Luca Moci","submitted_at":"2017-07-04T14:59:34Z","abstract_excerpt":"In this paper we address two of the major foundational questions in the theory of matroids over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of the base polytope for matroids. Second, we describe a parameter space for matroids over a valuation ring, which turns out to be a tropical version of the Bott-Samelson varieties for the full flag variety. Thus a matroid over a valuation ring is a sequence of flags of tropical linear spaces a.k.a. valuated matroids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01026","kind":"arxiv","version":2},"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":"1707.01026","created_at":"2026-05-18T00:38:50.212328+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01026v2","created_at":"2026-05-18T00:38:50.212328+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01026","created_at":"2026-05-18T00:38:50.212328+00:00"},{"alias_kind":"pith_short_12","alias_value":"WAI352XCWUBA","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WAI352XCWUBAEMR7","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WAI352XC","created_at":"2026-05-18T12:31:53.515858+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/WAI352XCWUBAEMR7VYOBMEWFKJ","json":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ.json","graph_json":"https://pith.science/api/pith-number/WAI352XCWUBAEMR7VYOBMEWFKJ/graph.json","events_json":"https://pith.science/api/pith-number/WAI352XCWUBAEMR7VYOBMEWFKJ/events.json","paper":"https://pith.science/paper/WAI352XC"},"agent_actions":{"view_html":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ","download_json":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ.json","view_paper":"https://pith.science/paper/WAI352XC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01026&json=true","fetch_graph":"https://pith.science/api/pith-number/WAI352XCWUBAEMR7VYOBMEWFKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/WAI352XCWUBAEMR7VYOBMEWFKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ/action/storage_attestation","attest_author":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ/action/author_attestation","sign_citation":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ/action/citation_signature","submit_replication":"https://pith.science/pith/WAI352XCWUBAEMR7VYOBMEWFKJ/action/replication_record"}},"created_at":"2026-05-18T00:38:50.212328+00:00","updated_at":"2026-05-18T00:38:50.212328+00:00"}