{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KBRTTNKUXVCJTABCPDO6XSSIJE","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":"8880189e3c14dc9bf0b0a036965bf3a8b945ec66ed3100acf85ceba0105c4868","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T23:29:28Z","title_canon_sha256":"e4cbe8ebdd0b6e4e52c48a9bf874a97b3de5f52698471eb884000af1178c368c"},"schema_version":"1.0","source":{"id":"1709.10198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10198","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10198v1","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10198","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"KBRTTNKUXVCJ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KBRTTNKUXVCJTABC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KBRTTNKU","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:1a16cfb5a121ecef8b03c5c59627986346284707109ae2646be294d614a22259","target":"graph","created_at":"2026-05-18T00:33:58Z","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":"Doran, Jensen and Giansiracusa showed a bijection between homogeneous elements in the Cox ring of $\\overline{M}_{0,n}$ not divisible by any exceptional divisor section, and weighted pure-dimensional simplicial complexes satisfying a zero-tension condition. Motivated by the study of the monoid of effective divisors, the pseudoeffective cone and the Cox ring of $\\overline{M}_{0,n}$, we point out a simplification of the zero-tension condition and study the space of balanced complexes. We give examples of irreducible elements in the monoid of effective divisors of $\\overline{M}_{0,n}$ for large $n","authors_text":"Elijah Gunther, Jos\\'e Luis Gonz\\'alez, Olivia Zhang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T23:29:28Z","title":"Balanced complexes and effective divisors on $\\overline{M}_{0,n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10198","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":"sha256:27b6f1802f743aea293eec17e62398e185cc3217d87b53a6ff742496599a2b53","target":"record","created_at":"2026-05-18T00:33:58Z","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":"8880189e3c14dc9bf0b0a036965bf3a8b945ec66ed3100acf85ceba0105c4868","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T23:29:28Z","title_canon_sha256":"e4cbe8ebdd0b6e4e52c48a9bf874a97b3de5f52698471eb884000af1178c368c"},"schema_version":"1.0","source":{"id":"1709.10198","kind":"arxiv","version":1}},"canonical_sha256":"506339b554bd4499802278ddebca4849143fd25c30e1e7eae5ab6a98b79a9bc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"506339b554bd4499802278ddebca4849143fd25c30e1e7eae5ab6a98b79a9bc7","first_computed_at":"2026-05-18T00:33:58.175702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:58.175702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GDgL8rs4SSneye6p7iGI3d8V6XSck+qHNLFp/xjjqIRUKmjPOReaaNNL2sJRb6w7K8XkLp+e9gLn8YwlEa0xBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:58.176384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27b6f1802f743aea293eec17e62398e185cc3217d87b53a6ff742496599a2b53","sha256:1a16cfb5a121ecef8b03c5c59627986346284707109ae2646be294d614a22259"],"state_sha256":"2a6c1caa5bb033e1c8a519cfc76a0bdc07b42519260e03575ece73bc91340bf0"}