{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:Z3HLTYFTJXMC47IWPFAVOPPMS3","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":"1d8a5b96296a02629ff51d2f3de95cd224d3b0ba1e7fa761d6ab061f7470aa8a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CO","submitted_at":"2006-05-22T23:38:02Z","title_canon_sha256":"f6299e3ed3393d51007cf5b42f8b093e57e79f1caa82423b920bc8a79d293307"},"schema_version":"1.0","source":{"id":"math/0605598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605598","created_at":"2026-07-04T14:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605598v1","created_at":"2026-07-04T14:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605598","created_at":"2026-07-04T14:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"Z3HLTYFTJXMC","created_at":"2026-07-04T14:55:05Z"},{"alias_kind":"pith_short_16","alias_value":"Z3HLTYFTJXMC47IW","created_at":"2026-07-04T14:55:05Z"},{"alias_kind":"pith_short_8","alias_value":"Z3HLTYFT","created_at":"2026-07-04T14:55:05Z"}],"graph_snapshots":[{"event_id":"sha256:3ace715b7424e2116c9f5c44731368b91af818eef7d37ba649b1a2c949f28183","target":"graph","created_at":"2026-07-04T14:55:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0605598/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the line arrangement that results from intersecting d complete flags in C^n. We give a combinatorial description of the matroid T_{n,d} that keeps track of the linear dependence relations among these lines. We prove that the bases of the matroid T_{n,3} characterize the triangles with holes which can be tiled with unit rhombi. More generally, we provide evidence for a conjectural connection between the matroid T_{n,d}, the triangulations of the product of simplices Delta_{n-1} x \\Delta_{d-1}, and the arrangements of d tropical hyperplanes in tropical (n-1)-space. Our work provid","authors_text":"Federico Ardila, Sara Billey","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2006-05-22T23:38:02Z","title":"Flag arrangements and triangulations of products of simplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605598","kind":"arxiv","version":1},"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:c8dfd34d2579c0e05a9acd8e716df730dcb9348abedaf406fee22869bab8c1ec","target":"record","created_at":"2026-07-04T14:55:05Z","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":"1d8a5b96296a02629ff51d2f3de95cd224d3b0ba1e7fa761d6ab061f7470aa8a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CO","submitted_at":"2006-05-22T23:38:02Z","title_canon_sha256":"f6299e3ed3393d51007cf5b42f8b093e57e79f1caa82423b920bc8a79d293307"},"schema_version":"1.0","source":{"id":"math/0605598","kind":"arxiv","version":1}},"canonical_sha256":"ceceb9e0b34dd82e7d167941573dec96e0d37c2d6eae29fc17f14287646cdf17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceceb9e0b34dd82e7d167941573dec96e0d37c2d6eae29fc17f14287646cdf17","first_computed_at":"2026-07-04T14:55:05.739441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:55:05.739441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAEDePVcCK0nX+fBrsIu1nZ+KKkhoTfP1+do7qDPNgHMm/Gj+LyhqOL5WDtrT79DJ4/oXoU221ylMOWOHbC6BA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:55:05.739825Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8dfd34d2579c0e05a9acd8e716df730dcb9348abedaf406fee22869bab8c1ec","sha256:3ace715b7424e2116c9f5c44731368b91af818eef7d37ba649b1a2c949f28183"],"state_sha256":"6d619e1b5cbbc55782ff73fddabdfaf51b0a888f6fea4bce6578566e2d3e33b9"}