{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:II37SOUI7VIQPQRGFMWKSNOL4E","short_pith_number":"pith:II37SOUI","schema_version":"1.0","canonical_sha256":"4237f93a88fd5107c2262b2ca935cbe11f98d5d445920be4c8e7ad47d667989a","source":{"kind":"arxiv","id":"1904.01913","version":2},"attestation_state":"computed","paper":{"title":"A Polymatroid Approach to Generalized Weights of Rank Metric Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Sudhir R. Ghorpade, Trygve Johnsen","submitted_at":"2019-04-03T11:00:14Z","abstract_excerpt":"We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martinez-Penas and Matsumoto for relative generalized rank weights are derived as a consequence."},"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":"1904.01913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-03T11:00:14Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"c29052fd86b32e221492a197042ad5b5271037d2051e9398f00db419b39f5879","abstract_canon_sha256":"b531bf1c139a846cb9101c1139903012c45935744b093643f4fb76862c47b504"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:03.880107Z","signature_b64":"v0eLv5oFVquZH4PzV/pW0fY7nd6UWiiNOc9BubitqLmtd5vcoIevvmGjNy6mjsU9vvfG3bMLeuWYgPkd25j7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4237f93a88fd5107c2262b2ca935cbe11f98d5d445920be4c8e7ad47d667989a","last_reissued_at":"2026-05-17T23:45:03.879518Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:03.879518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Polymatroid Approach to Generalized Weights of Rank Metric Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Sudhir R. Ghorpade, Trygve Johnsen","submitted_at":"2019-04-03T11:00:14Z","abstract_excerpt":"We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martinez-Penas and Matsumoto for relative generalized rank weights are derived as a consequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01913","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":"1904.01913","created_at":"2026-05-17T23:45:03.879602+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.01913v2","created_at":"2026-05-17T23:45:03.879602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01913","created_at":"2026-05-17T23:45:03.879602+00:00"},{"alias_kind":"pith_short_12","alias_value":"II37SOUI7VIQ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"II37SOUI7VIQPQRG","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"II37SOUI","created_at":"2026-05-18T12:33:18.533446+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/II37SOUI7VIQPQRGFMWKSNOL4E","json":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E.json","graph_json":"https://pith.science/api/pith-number/II37SOUI7VIQPQRGFMWKSNOL4E/graph.json","events_json":"https://pith.science/api/pith-number/II37SOUI7VIQPQRGFMWKSNOL4E/events.json","paper":"https://pith.science/paper/II37SOUI"},"agent_actions":{"view_html":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E","download_json":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E.json","view_paper":"https://pith.science/paper/II37SOUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.01913&json=true","fetch_graph":"https://pith.science/api/pith-number/II37SOUI7VIQPQRGFMWKSNOL4E/graph.json","fetch_events":"https://pith.science/api/pith-number/II37SOUI7VIQPQRGFMWKSNOL4E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E/action/storage_attestation","attest_author":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E/action/author_attestation","sign_citation":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E/action/citation_signature","submit_replication":"https://pith.science/pith/II37SOUI7VIQPQRGFMWKSNOL4E/action/replication_record"}},"created_at":"2026-05-17T23:45:03.879602+00:00","updated_at":"2026-05-17T23:45:03.879602+00:00"}