{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L4UGMGJKQAZSHFTBJ2YHW4PHY2","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":"aee084e9d1190071548ba62a7d2c0016be9b5100a4bb54f159999cbeb662896d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-15T18:14:18Z","title_canon_sha256":"c895911d6c7d9ad17cb47dfadea6cb77046786fbffac268f90124bba8a1b4260"},"schema_version":"1.0","source":{"id":"1410.4152","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4152","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4152v3","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4152","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"L4UGMGJKQAZS","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4UGMGJKQAZSHFTB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4UGMGJK","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:a3a540330fbec5c29d8c5c1355fe64af3d13ff4307fa27db01ea5fc4c428d5b3","target":"graph","created_at":"2026-05-18T00:50:40Z","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 whether a given tropical curve $\\Gamma$ in $\\mathbb{R}^n$ can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented by $\\Gamma$. We give an affirmative answer to this question for a large class of tropical curves that includes all trivalent tropical curves, but also many tropical curves of higher valence. We then deduce that for every metric graph $G$ with rational edge lengths there exists a smooth algebraic curve in a toric variety whose analytification has skeleton $G$, and the corresponding tropicalization is faithful. Ou","authors_text":"Jennifer Park, Lorenzo Fantini, Man-Wai Cheung, Martin Ulirsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-15T18:14:18Z","title":"Faithful realizability of tropical curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4152","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":"sha256:37fafe174e2ba3ab52eb3a8eb9ddb338b832934b49ddb487957b75025cd7ac0b","target":"record","created_at":"2026-05-18T00:50:40Z","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":"aee084e9d1190071548ba62a7d2c0016be9b5100a4bb54f159999cbeb662896d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-15T18:14:18Z","title_canon_sha256":"c895911d6c7d9ad17cb47dfadea6cb77046786fbffac268f90124bba8a1b4260"},"schema_version":"1.0","source":{"id":"1410.4152","kind":"arxiv","version":3}},"canonical_sha256":"5f2866192a80332396614eb07b71e7c68e7d17aef850fc587e6bb3d40e8237db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f2866192a80332396614eb07b71e7c68e7d17aef850fc587e6bb3d40e8237db","first_computed_at":"2026-05-18T00:50:40.656685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:40.656685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bsHDX8SGjymu5lig30CToRnwF3mf/24Gvw+402B/aqYRebw7mE10UENCR8m87rwXttjbgk22zqxsqshyshhDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:40.657408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4152","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37fafe174e2ba3ab52eb3a8eb9ddb338b832934b49ddb487957b75025cd7ac0b","sha256:a3a540330fbec5c29d8c5c1355fe64af3d13ff4307fa27db01ea5fc4c428d5b3"],"state_sha256":"fbbaabe08598556b73f5c56640ae3776f80e3afa58d0bcb9bd409a79118fe284"}