{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2UAPYYAAEXQWM5RI2INH5CVXVM","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":"c0070fbf8b95b4c5b4e72d4935f09ca7f467d3ce8aab1bfb337642d2b5121de3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-13T00:01:04Z","title_canon_sha256":"e90fc2dc3bcfa52b57fa58f5b2f531991d8c2221f4e3efa552fb43401a649e96"},"schema_version":"1.0","source":{"id":"1509.03787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03787","created_at":"2026-05-18T01:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03787v1","created_at":"2026-05-18T01:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03787","created_at":"2026-05-18T01:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"2UAPYYAAEXQW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2UAPYYAAEXQWM5RI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2UAPYYAA","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:38a2b0679e042d4f8982830871d5e495b54329fdc984bb7f9d9150e4c50f6fbe","target":"graph","created_at":"2026-05-18T01:33:14Z","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":"Classical Hopf manifolds are compact complex manifolds whose universal covering is $\\mathbb{C}^d \\setminus \\{0\\}$. We investigate the tropical analogues of Hopf manifolds, and relate their geometry to tropical contracting germs. To do this we develop a procedure called monomialization which transforms non-degenerate tropical germs into morphisms, up to tropical modification. A link is provided between tropical Hopf manifolds and the analytification of Hopf manifolds over a non-archimedean field. We conclude by computing the tropical Picard group and $(p,q)$-homology groups.","authors_text":"Kristin Shaw, Matteo Ruggiero","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-13T00:01:04Z","title":"Tropical Hopf manifolds and contracting germs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03787","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":"sha256:5c01a5407e7f674a722509800033701f4765abbfef44aae3b6c79cdf2c0fe73e","target":"record","created_at":"2026-05-18T01:33:14Z","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":"c0070fbf8b95b4c5b4e72d4935f09ca7f467d3ce8aab1bfb337642d2b5121de3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-13T00:01:04Z","title_canon_sha256":"e90fc2dc3bcfa52b57fa58f5b2f531991d8c2221f4e3efa552fb43401a649e96"},"schema_version":"1.0","source":{"id":"1509.03787","kind":"arxiv","version":1}},"canonical_sha256":"d500fc600025e1667628d21a7e8ab7ab3d781950ba008e03b22befb2b6928b6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d500fc600025e1667628d21a7e8ab7ab3d781950ba008e03b22befb2b6928b6b","first_computed_at":"2026-05-18T01:33:14.543082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:14.543082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/0QY5SpxV2ZXBgk+vEUMIOqu1DAJA3Vmu/EfQBXWBrqrIDRVKUiDxkaDs/0X/e6C5HDKX5yky10GXKAp/s+NDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:14.543678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c01a5407e7f674a722509800033701f4765abbfef44aae3b6c79cdf2c0fe73e","sha256:38a2b0679e042d4f8982830871d5e495b54329fdc984bb7f9d9150e4c50f6fbe"],"state_sha256":"0763d8809db633b91af104e946f13e899451310ac14848c697bf5a769adf2e9a"}