{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2HMTUGTCPHSUZBDGHDOOIV4NUQ","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":"50fe9423e605575e7447cbe9aab8f9a110aa447e1f5e71d35a4547b503bc6445","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-06T08:14:36Z","title_canon_sha256":"64dfec2494c44ab2d7f3193637c454ac92a30f7764e376a6f8bbcf164f693146"},"schema_version":"1.0","source":{"id":"1802.01838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01838","created_at":"2026-05-18T00:24:21Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01838v1","created_at":"2026-05-18T00:24:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01838","created_at":"2026-05-18T00:24:21Z"},{"alias_kind":"pith_short_12","alias_value":"2HMTUGTCPHSU","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2HMTUGTCPHSUZBDG","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2HMTUGTC","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:de1226b4ba3518b8aa69efb769bbd6d2de52e5a69c10738e86cbefa92b25c8ee","target":"graph","created_at":"2026-05-18T00:24:21Z","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":"In this paper, we classify singular real plane tropical curves by means of subdivisions of Newton polytopes. First, we introduce signed Bergman fans (generalizing positive Bergman fans from [AKW06]) that describe real tropicalizations of real linear spaces ([Tab15]). Then, we establish a duality of real plane tropical curves and signed regular subdivisions of the Newton polytope and explore the combinatorics. We define a signed secondary fan that parametrizes real tropical Laurent polynomials and study the subset providing singular real plane tropical curves. A cone of the signed secondary fan","authors_text":"Christian J\\\"urgens","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-06T08:14:36Z","title":"Real Tropical Singularities and Bergman Fans"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01838","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":"sha256:37c645c471b62a1cc7ee938794f1d0724f3bf735cb8a11937c55835e3ad10a64","target":"record","created_at":"2026-05-18T00:24:21Z","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":"50fe9423e605575e7447cbe9aab8f9a110aa447e1f5e71d35a4547b503bc6445","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-06T08:14:36Z","title_canon_sha256":"64dfec2494c44ab2d7f3193637c454ac92a30f7764e376a6f8bbcf164f693146"},"schema_version":"1.0","source":{"id":"1802.01838","kind":"arxiv","version":1}},"canonical_sha256":"d1d93a1a6279e54c846638dce4578da4174a72f061ddb680a669b64b6c596c6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1d93a1a6279e54c846638dce4578da4174a72f061ddb680a669b64b6c596c6f","first_computed_at":"2026-05-18T00:24:21.130800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:21.130800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5BmZoFwt5hvbKKCjEqQX00b3CpBYLTJ+3CTu1vS134vql0qw6XqXrL27d9GgNly4euMmcmziVjxi3E1EWqENAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:21.131213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37c645c471b62a1cc7ee938794f1d0724f3bf735cb8a11937c55835e3ad10a64","sha256:de1226b4ba3518b8aa69efb769bbd6d2de52e5a69c10738e86cbefa92b25c8ee"],"state_sha256":"3807057f67ad6da55cfb3cf9574139d1fdebc3e57fe9a79560e11b7453abcb03"}