{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5XUHAFLWXNCK6QO5HJFTUUTNHB","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":"935e0c6bbf35a132b9b4f7323648e1e01001d19da961d89b9c741f5286302f98","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-11T16:11:16Z","title_canon_sha256":"ce1cc0cabd4660e1f88b4e47ceca9130a7876159fdedfd05c700c40fdf87a270"},"schema_version":"1.0","source":{"id":"1604.03016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03016","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03016v1","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03016","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"5XUHAFLWXNCK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5XUHAFLWXNCK6QO5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5XUHAFLW","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:9ea2ee13d30d24decea9942ab512734074ec36c49581b308517cdb48ee75e9e8","target":"graph","created_at":"2026-05-18T01:16:38Z","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":"We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in their definition of a tropical oriented matroid, induces an action of the hyperplane face monoid of the classical braid arrangement on the arrangement, and hence on a number of interesting related structures. Along the way, we introduce a new characterization of the types (in the sense of Develin and Sturmfels) of points with respect to a tropica","authors_text":"Marianne Johnson, Mark Kambites","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-11T16:11:16Z","title":"Face monoid actions and tropical hyperplane arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03016","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:f76f714d1849a2f277c497b9e0e507a0f26e635888c8c16131767bb5113061db","target":"record","created_at":"2026-05-18T01:16:38Z","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":"935e0c6bbf35a132b9b4f7323648e1e01001d19da961d89b9c741f5286302f98","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-11T16:11:16Z","title_canon_sha256":"ce1cc0cabd4660e1f88b4e47ceca9130a7876159fdedfd05c700c40fdf87a270"},"schema_version":"1.0","source":{"id":"1604.03016","kind":"arxiv","version":1}},"canonical_sha256":"ede8701576bb44af41dd3a4b3a526d386964980f2fc0524ee6324f1240c85aa9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ede8701576bb44af41dd3a4b3a526d386964980f2fc0524ee6324f1240c85aa9","first_computed_at":"2026-05-18T01:16:38.911439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:38.911439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J1gyA0Rd0vX91RLDap/a/EtHEh/RU6ihj8TtDLE5TOKn4jDRW/6jQOddIBHhEuyby+g69QQ1i/kEUbckGHfJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:38.912130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f76f714d1849a2f277c497b9e0e507a0f26e635888c8c16131767bb5113061db","sha256:9ea2ee13d30d24decea9942ab512734074ec36c49581b308517cdb48ee75e9e8"],"state_sha256":"75e989238d2305f6b9adf03c96fe2cbc1240dd7f34ace44d8d520ec6bca3885e"}