{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6NCYF4JICHL3ITV4RMDIQD6HUH","short_pith_number":"pith:6NCYF4JI","schema_version":"1.0","canonical_sha256":"f34582f12811d7b44ebc8b06880fc7a1da0cf2f97921f7ad3502d7ad5ed2f407","source":{"kind":"arxiv","id":"2606.22819","version":1},"attestation_state":"computed","paper":{"title":"Connectivity for slice-projections of connected polymatroids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xian'an Jin, Xiaxia Guan","submitted_at":"2026-06-22T03:51:01Z","abstract_excerpt":"It is well-known that deleting or contracting any element of a connected matroid always yields at least one connected minor. However, for a connected polymatroid, only two such elements can be guaranteed, proved by Hall in 2013. This note investigates the connectivity properties of slice-projections of connected polymatroids, which includes deletion and contraction. We establish that for any element of a connected polymatroid, at least one of its two consecutive slice-projections is connected. We also obtain that the $j$-th slice-projection from the top of a polymatroid and $j$-th slice-projec"},"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":"2606.22819","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-22T03:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"8b81e56da060735ea73a8a5ad04aa2cbd5ac13719c4f9416c465b6063872ae4c","abstract_canon_sha256":"e03e520a7d21009af52f041db904e918f1fc5509943274996e694e92a7a96601"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:14:00.311731Z","signature_b64":"AAVMhsQdtFwDhKNAjjcoLbH2h5b3GbHNZe05YN54COnpg5RnIriF+44sFXF7hO+Wvi/T/qiYHPa5ZBnb11ebBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f34582f12811d7b44ebc8b06880fc7a1da0cf2f97921f7ad3502d7ad5ed2f407","last_reissued_at":"2026-06-23T02:14:00.311349Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:14:00.311349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectivity for slice-projections of connected polymatroids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xian'an Jin, Xiaxia Guan","submitted_at":"2026-06-22T03:51:01Z","abstract_excerpt":"It is well-known that deleting or contracting any element of a connected matroid always yields at least one connected minor. However, for a connected polymatroid, only two such elements can be guaranteed, proved by Hall in 2013. This note investigates the connectivity properties of slice-projections of connected polymatroids, which includes deletion and contraction. We establish that for any element of a connected polymatroid, at least one of its two consecutive slice-projections is connected. We also obtain that the $j$-th slice-projection from the top of a polymatroid and $j$-th slice-projec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22819","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22819/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.22819","created_at":"2026-06-23T02:14:00.311408+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22819v1","created_at":"2026-06-23T02:14:00.311408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22819","created_at":"2026-06-23T02:14:00.311408+00:00"},{"alias_kind":"pith_short_12","alias_value":"6NCYF4JICHL3","created_at":"2026-06-23T02:14:00.311408+00:00"},{"alias_kind":"pith_short_16","alias_value":"6NCYF4JICHL3ITV4","created_at":"2026-06-23T02:14:00.311408+00:00"},{"alias_kind":"pith_short_8","alias_value":"6NCYF4JI","created_at":"2026-06-23T02:14:00.311408+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/6NCYF4JICHL3ITV4RMDIQD6HUH","json":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH.json","graph_json":"https://pith.science/api/pith-number/6NCYF4JICHL3ITV4RMDIQD6HUH/graph.json","events_json":"https://pith.science/api/pith-number/6NCYF4JICHL3ITV4RMDIQD6HUH/events.json","paper":"https://pith.science/paper/6NCYF4JI"},"agent_actions":{"view_html":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH","download_json":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH.json","view_paper":"https://pith.science/paper/6NCYF4JI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22819&json=true","fetch_graph":"https://pith.science/api/pith-number/6NCYF4JICHL3ITV4RMDIQD6HUH/graph.json","fetch_events":"https://pith.science/api/pith-number/6NCYF4JICHL3ITV4RMDIQD6HUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH/action/storage_attestation","attest_author":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH/action/author_attestation","sign_citation":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH/action/citation_signature","submit_replication":"https://pith.science/pith/6NCYF4JICHL3ITV4RMDIQD6HUH/action/replication_record"}},"created_at":"2026-06-23T02:14:00.311408+00:00","updated_at":"2026-06-23T02:14:00.311408+00:00"}