{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OTJSEJ6AS5KLADZAE2UHME5EPC","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":"4b2c2460e2c3341ae0dbbf1cf2cc96d019bd8ea38da28fdaedf29a894783ce42","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-06T13:58:35Z","title_canon_sha256":"4d6b20fefcb7bca3670006e46ac6dea58030d7215d9a41bceeba56b6336fe650"},"schema_version":"1.0","source":{"id":"1112.1278","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1278","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1278v3","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1278","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"pith_short_12","alias_value":"OTJSEJ6AS5KL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OTJSEJ6AS5KLADZA","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OTJSEJ6A","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:43ca5ea0e6ab958acf0dcd26e43dd0085a64e2a2f14cdb10271232c4b282e4d1","target":"graph","created_at":"2026-05-18T02:21:27Z","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":"The Dressian Dr(k,n) parametrizes all tropical linear spaces, and it carries a natural fan structure as a subfan of the secondaryfan of the hypersimplex \\Delta(k,n). We explore the combinatorics of the rays of Dr(k,n), that is, the most degenerate tropical planes, for arbitrary k and n. This is related to a new rigidity concept for configurations of n-k points in the tropical (k-1)-torus. Additional conditions are given for k=3. On the way, we compute the entire fan Dr(3,8).","authors_text":"David Speyer, Michael Joswig, Sven Herrmann","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-06T13:58:35Z","title":"Dressians, Tropical Grassmannians, and Their Rays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1278","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:a4c0c38e12ceeddc369b9968197cb74b216d044ae574810566d4a04f79a4c1fe","target":"record","created_at":"2026-05-18T02:21:27Z","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":"4b2c2460e2c3341ae0dbbf1cf2cc96d019bd8ea38da28fdaedf29a894783ce42","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-06T13:58:35Z","title_canon_sha256":"4d6b20fefcb7bca3670006e46ac6dea58030d7215d9a41bceeba56b6336fe650"},"schema_version":"1.0","source":{"id":"1112.1278","kind":"arxiv","version":3}},"canonical_sha256":"74d32227c09754b00f2026a87613a478ad46983ac57bbf92edb8dd218f093246","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74d32227c09754b00f2026a87613a478ad46983ac57bbf92edb8dd218f093246","first_computed_at":"2026-05-18T02:21:27.808817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:27.808817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d3F1qtHlg1RtW64YKOu4XNGkie7avwLIbyN/4m9AlS28W1/0NCMB3tYVjVSGf9y9Yjhc5xb+Zi6Rch90RSlgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:27.809586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1278","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4c0c38e12ceeddc369b9968197cb74b216d044ae574810566d4a04f79a4c1fe","sha256:43ca5ea0e6ab958acf0dcd26e43dd0085a64e2a2f14cdb10271232c4b282e4d1"],"state_sha256":"e2163f5f97e6bddc7833f556c0bf232572d45388c255e3e0d5293b15b3f6232e"}