{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:4OZ5I6TVQOLKYGAD4HTJ5E4ECY","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":"c188bee91b784bb3de2e59f3cdd4fd5f4eb8c5d354df7199df9d233ccf213fcf","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AG","submitted_at":"2001-05-24T15:20:13Z","title_canon_sha256":"2fb577d7f5b4bbaca04a7b34b8677a2080e4b92148b8207fcd5972b1f5ca5914"},"schema_version":"1.0","source":{"id":"math/0105198","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0105198","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0105198v2","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0105198","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"4OZ5I6TVQOLK","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"4OZ5I6TVQOLKYGAD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"4OZ5I6TV","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:c3c992e3d42886c8c2f2f25b5ec352d2cae6cb0b01ee4d7210a37114591f584d","target":"graph","created_at":"2026-05-18T01:05:37Z","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 introduce a class of combinatorial hypersurfaces in the complex projective space. They are submanifolds of codimension~2 in $\\C P^n$ and are topologically \"glued\" out of algebraic hypersurfaces in $(\\C^*)^n$. Our construction can be viewed as a version of the Viro gluing theorem, relating topology of algebraic hypersurfaces to the combinatorics of subdivisions of convex lattice polytopes. If a subdivision is convex, then according to the Viro theorem a combinatorial hypersurface is isotopic to an algebraic one. We study combinatorial hypersurfaces resulting from non-convex subdivisions of c","authors_text":"Eugenii Shustin, Ilia Itenberg","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-05-24T15:20:13Z","title":"Viro theorem and topology of real and complex combinatorial hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105198","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:d73365ccc636e6fc72f19c8daa8f0345aba602fd6dfa6f455c92a73e0c2910f1","target":"record","created_at":"2026-05-18T01:05:37Z","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":"c188bee91b784bb3de2e59f3cdd4fd5f4eb8c5d354df7199df9d233ccf213fcf","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AG","submitted_at":"2001-05-24T15:20:13Z","title_canon_sha256":"2fb577d7f5b4bbaca04a7b34b8677a2080e4b92148b8207fcd5972b1f5ca5914"},"schema_version":"1.0","source":{"id":"math/0105198","kind":"arxiv","version":2}},"canonical_sha256":"e3b3d47a758396ac1803e1e69e9384162d9f31235cb3823d2686f2ab0d9f851d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3b3d47a758396ac1803e1e69e9384162d9f31235cb3823d2686f2ab0d9f851d","first_computed_at":"2026-05-18T01:05:37.777026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.777026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kYvM6mbHA2/9R/rNxcSydZ7TGr3VacjrKvuue0mhCNcexs+IVkdIYZanJ0bjiYc/pO8k9A2t10HlK4jR0SB7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.777694Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0105198","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d73365ccc636e6fc72f19c8daa8f0345aba602fd6dfa6f455c92a73e0c2910f1","sha256:c3c992e3d42886c8c2f2f25b5ec352d2cae6cb0b01ee4d7210a37114591f584d"],"state_sha256":"df3ad24ed3ed2a21759cec8834eed81b9aa8aa0ea52f81b3a7b5c2508dcab3d2"}