{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MLJ5TGCYV3A7AGWCPVYIJWVEPD","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":"a338305e627704ac6b3919733b40d0c012af4819b6c66c527e29f49e03c79604","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-18T22:41:44Z","title_canon_sha256":"e125cdf18823ad6bbd7a522038362cd623b5b75153fba7b63aa38678a7dd7465"},"schema_version":"1.0","source":{"id":"1509.05815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05815","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05815v2","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05815","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"MLJ5TGCYV3A7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MLJ5TGCYV3A7AGWC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MLJ5TGCY","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:850f0227675e3d013f84065885c633ef9cf117142bd2447a314dc3f88b54fe5a","target":"graph","created_at":"2026-05-18T01:04:01Z","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 consider the question of when points in tropical affine space uniquely determine a tropical hypersurface. We introduce a notion of multiplicity of points so that this question may be meaningful even if some of the points coincide. We give a geometric/combinatorial way and a tropical linear-algebraic way to approach this question. First, given a fixed hypersurface, we show how one can determine whether points on the hypersurface determine it by looking at a corresponding marking of the dual complex. With a regularity condition on the dual complex and when the number of points is minimal, we ","authors_text":"Drew Johnson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-18T22:41:44Z","title":"Determining Tropical Hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05815","kind":"arxiv","version":2},"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":"sha256:2fa3eb4792d09637a30387e0130a84738d1aaffc047d5d4e7ffa224b109cef59","target":"record","created_at":"2026-05-18T01:04:01Z","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":"a338305e627704ac6b3919733b40d0c012af4819b6c66c527e29f49e03c79604","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-18T22:41:44Z","title_canon_sha256":"e125cdf18823ad6bbd7a522038362cd623b5b75153fba7b63aa38678a7dd7465"},"schema_version":"1.0","source":{"id":"1509.05815","kind":"arxiv","version":2}},"canonical_sha256":"62d3d99858aec1f01ac27d7084daa478e2e8a30a5296e56a83fca9710174df52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62d3d99858aec1f01ac27d7084daa478e2e8a30a5296e56a83fca9710174df52","first_computed_at":"2026-05-18T01:04:01.314851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:01.314851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gcf52akILYDW0cfV2xL8zabn/P2aPT/1OsDJqhKk1wpLr8SvsFsmhDEVhQQ2CqsB7Yv/3qFEgzs3klIqcVZHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:01.315413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fa3eb4792d09637a30387e0130a84738d1aaffc047d5d4e7ffa224b109cef59","sha256:850f0227675e3d013f84065885c633ef9cf117142bd2447a314dc3f88b54fe5a"],"state_sha256":"44d6f33cd37a21d930dd904118747af5a1b7fca982c6b2bb8b880834b94a11e8"}