{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TGQ3ZNFUTC4Q5AFNS6UZYZF6RU","short_pith_number":"pith:TGQ3ZNFU","schema_version":"1.0","canonical_sha256":"99a1bcb4b498b90e80ad97a99c64be8d250c7c6b530690571368f06d38f8bcfb","source":{"kind":"arxiv","id":"2310.08313","version":1},"attestation_state":"computed","paper":{"title":"Real phase structures on tropical manifolds and patchworks in higher codimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Arthur Renaudineau, Johannes Rau, Kris Shaw","submitted_at":"2023-10-12T13:20:31Z","abstract_excerpt":"This paper generalises the homeomorphism theorem behind Viro's combinatorial patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical geometry. We first define the patchwork of a polyhedral space equipped with a real phase structure. When the polyhedral subspace is tropically non-singular, we show that the patchwork is a topological manifold. When a non-singular tropical variety appears as a tropical limit of a real analytic family, we show that the real part of a fibre of the family near the tropical limit is homeomorphic to the patchwork.\n  Finally we extend t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.08313","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-10-12T13:20:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3882558c61382680c6696e1ac4d96ff55f1bb16659aba9dd79e4cc2c7f55da06","abstract_canon_sha256":"56114f1c5f5f9251c145dd395d4eab9343a7efed85238866e98d8666bc43e708"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:00:13.900459Z","signature_b64":"vLV7NuCJZkf/nc829syFmY9tVqao80C9AVPA7roAMa3hVtwsedjlOqvfBa8Y/wBe3+RThLb8M9CRJ+t4eF8IAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99a1bcb4b498b90e80ad97a99c64be8d250c7c6b530690571368f06d38f8bcfb","last_reissued_at":"2026-07-05T07:00:13.900054Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:00:13.900054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real phase structures on tropical manifolds and patchworks in higher codimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Arthur Renaudineau, Johannes Rau, Kris Shaw","submitted_at":"2023-10-12T13:20:31Z","abstract_excerpt":"This paper generalises the homeomorphism theorem behind Viro's combinatorial patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical geometry. We first define the patchwork of a polyhedral space equipped with a real phase structure. When the polyhedral subspace is tropically non-singular, we show that the patchwork is a topological manifold. When a non-singular tropical variety appears as a tropical limit of a real analytic family, we show that the real part of a fibre of the family near the tropical limit is homeomorphic to the patchwork.\n  Finally we extend t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.08313","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.08313/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.08313","created_at":"2026-07-05T07:00:13.900114+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.08313v1","created_at":"2026-07-05T07:00:13.900114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.08313","created_at":"2026-07-05T07:00:13.900114+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGQ3ZNFUTC4Q","created_at":"2026-07-05T07:00:13.900114+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGQ3ZNFUTC4Q5AFN","created_at":"2026-07-05T07:00:13.900114+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGQ3ZNFU","created_at":"2026-07-05T07:00:13.900114+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2501.11295","citing_title":"Filtrations of Tope Spaces of Oriented Matroids","ref_index":20,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU","json":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU.json","graph_json":"https://pith.science/api/pith-number/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/graph.json","events_json":"https://pith.science/api/pith-number/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/events.json","paper":"https://pith.science/paper/TGQ3ZNFU"},"agent_actions":{"view_html":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU","download_json":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU.json","view_paper":"https://pith.science/paper/TGQ3ZNFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.08313&json=true","fetch_graph":"https://pith.science/api/pith-number/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/graph.json","fetch_events":"https://pith.science/api/pith-number/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/action/storage_attestation","attest_author":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/action/author_attestation","sign_citation":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/action/citation_signature","submit_replication":"https://pith.science/pith/TGQ3ZNFUTC4Q5AFNS6UZYZF6RU/action/replication_record"}},"created_at":"2026-07-05T07:00:13.900114+00:00","updated_at":"2026-07-05T07:00:13.900114+00:00"}