{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GWPPB3LRBPSU4XYLX5KMYSERV2","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":"1b99dc1bc363b10fb7655a3668da2bd9e8cebbd257cf402b87321b71ec60c37b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-07T19:58:05Z","title_canon_sha256":"9fac3f699b3054c1c8332e4c8a44fbd46ce040a9a5f3cc2b6b66ea5f15469f5b"},"schema_version":"1.0","source":{"id":"1606.02282","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02282","created_at":"2026-05-18T00:20:40Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02282v2","created_at":"2026-05-18T00:20:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02282","created_at":"2026-05-18T00:20:40Z"},{"alias_kind":"pith_short_12","alias_value":"GWPPB3LRBPSU","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GWPPB3LRBPSU4XYL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GWPPB3LR","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:369f11bd461af5fd4c1044e322dba78e279e479dd1fae96b0b083f30810f845d","target":"graph","created_at":"2026-05-18T00:20:40Z","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 the behavior of theta characteristics on an algebraic curve under the specialization map to a tropical curve. We show that each effective theta characteristic on the tropical curve is the specialization of $2^{g-1}$ even theta characteristics and $2^{g-1}$ odd theta characteristics. We then study the relationship between unramified double covers of a tropical curve and its theta characteristics, and use this to define the tropical Prym variety.","authors_text":"David Jensen, Yoav Len","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-07T19:58:05Z","title":"Tropicalization of theta characteristics, double covers, and Prym varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02282","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":"sha256:26b320107ea6cc5c9c3ce6656187f9eb66a259202974f75020e7ed6e21e98b08","target":"record","created_at":"2026-05-18T00:20:40Z","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":"1b99dc1bc363b10fb7655a3668da2bd9e8cebbd257cf402b87321b71ec60c37b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-07T19:58:05Z","title_canon_sha256":"9fac3f699b3054c1c8332e4c8a44fbd46ce040a9a5f3cc2b6b66ea5f15469f5b"},"schema_version":"1.0","source":{"id":"1606.02282","kind":"arxiv","version":2}},"canonical_sha256":"359ef0ed710be54e5f0bbf54cc4891ae833d71707f1e0cdc1cfd73ee1520b4a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"359ef0ed710be54e5f0bbf54cc4891ae833d71707f1e0cdc1cfd73ee1520b4a7","first_computed_at":"2026-05-18T00:20:40.197955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:40.197955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ruy/BY9dkEtTsMNi69L8wOLtYSELwhYTCkJqempNtiLtnnlP0OOa9YjCBGZT2CItHVRjos8Xs6hKHWVcnHdcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:40.198649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02282","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26b320107ea6cc5c9c3ce6656187f9eb66a259202974f75020e7ed6e21e98b08","sha256:369f11bd461af5fd4c1044e322dba78e279e479dd1fae96b0b083f30810f845d"],"state_sha256":"19ec34d5e0218d0df07bcced58e0c72a2a484f29baf1f578609247e61eb13375"}