{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:D4SXPRE3VHXEVCEFS5YOE77BFR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cce85b6a122a57108f5d3629e81ab1d3a3693e12594d4224229977efccd8ea04","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-19T13:25:38Z","title_canon_sha256":"0d860570bdd8b28f61bf6422e50c9c357c8acbb8874bc5cdb51bd441606906a1"},"schema_version":"1.0","source":{"id":"0902.3362","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.3362","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"0902.3362v3","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.3362","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"D4SXPRE3VHXE","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"D4SXPRE3VHXEVCEF","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"D4SXPRE3","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:a878ce0e19865239eddfeaadabcc0c40504bc5eb2d5d00e88abcc37537965662","target":"graph","created_at":"2026-05-18T04:36:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For the ordered set $[n]$ of $n$ elements, we consider the class $\\Bscr_n$ of bases $B$ of tropical Pl\\\"ucker functions on $2^{[n]}$ such that $B$ can be obtained by a series of mutations (flips) from the basis formed by the intervals in $[n]$. We show that these bases are representable by special wiring diagrams and by certain arrangements generalizing rhombus tilings on the $n$-zonogon. Based on the generalized tiling representation, we then prove that each weakly separated set-system in $2^{[n]}$ having maximum possible size belongs to $\\Bscr_n$, thus answering affirmatively a conjecture du","authors_text":"Alexander V. Karzanov, Gleb A. Koshevoy, Vladimir I. Danilov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-19T13:25:38Z","title":"Pl\\\"ucker environments, wiring and tiling diagrams, and weakly separated set-systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3362","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6f48d4a1335d5ee0925440fa63b497e68d1544ed8e17e643a3f44e012f3f2f0c","target":"record","created_at":"2026-05-18T04:36:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cce85b6a122a57108f5d3629e81ab1d3a3693e12594d4224229977efccd8ea04","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-19T13:25:38Z","title_canon_sha256":"0d860570bdd8b28f61bf6422e50c9c357c8acbb8874bc5cdb51bd441606906a1"},"schema_version":"1.0","source":{"id":"0902.3362","kind":"arxiv","version":3}},"canonical_sha256":"1f2577c49ba9ee4a88859770e27fe12c5d5ff5b67dabe3aa93f29976c8588058","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f2577c49ba9ee4a88859770e27fe12c5d5ff5b67dabe3aa93f29976c8588058","first_computed_at":"2026-05-18T04:36:08.988835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:08.988835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W5cm2oTnQlnufVNgG5f0yfbLy/Zs2RLwhVGtyfGQI0NxTnYuOjFkYycEBlcfjz5qYjB7TWP8qPVkR1HK+OC/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:08.989454Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.3362","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f48d4a1335d5ee0925440fa63b497e68d1544ed8e17e643a3f44e012f3f2f0c","sha256:a878ce0e19865239eddfeaadabcc0c40504bc5eb2d5d00e88abcc37537965662"],"state_sha256":"0622a62ff0e662ae1ae78316a5327bc05f130a5821679ec214403251b9636a99"}