{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BK4LCPY6IVWJITSISGHQRS43B4","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":"8ed45681a023a4f47d60f45d4b3a34fa5ea21abc1e5e1d863d6f20a350fd7ac2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-17T15:24:58Z","title_canon_sha256":"fd40833dcb2f59f7b2220049ba6098301c54f1f42dec54b2fd6a0923b3dfee08"},"schema_version":"1.0","source":{"id":"1508.04057","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04057","created_at":"2026-05-18T00:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04057v3","created_at":"2026-05-18T00:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04057","created_at":"2026-05-18T00:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"BK4LCPY6IVWJ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BK4LCPY6IVWJITSI","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BK4LCPY6","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:defbd56b9303cfcb422483e7a5090520ef077341f327c1fbed7d7f6844c9e9c1","target":"graph","created_at":"2026-05-18T00:15:59Z","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 develop a theory of multi-stage degenerations of toric varieties over finite rank valuation rings, extending the Mumford--Gubler theory in rank one. Such degenerations are constructed from fan-like structures over totally ordered abelian groups of finite rank. Our main theorem describes the geometry of successive special fibers in the degeneration in terms of the polyhedral geometry of a system of recession complexes associated to the fan.","authors_text":"Dhruv Ranganathan, Tyler Foster","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-17T15:24:58Z","title":"Degenerations of toric varieties over valuation rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04057","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":"sha256:336368cfec28ec1e41a6c4a63cf26086faf41877fab93a30ba277f594952c13d","target":"record","created_at":"2026-05-18T00:15:59Z","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":"8ed45681a023a4f47d60f45d4b3a34fa5ea21abc1e5e1d863d6f20a350fd7ac2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-17T15:24:58Z","title_canon_sha256":"fd40833dcb2f59f7b2220049ba6098301c54f1f42dec54b2fd6a0923b3dfee08"},"schema_version":"1.0","source":{"id":"1508.04057","kind":"arxiv","version":3}},"canonical_sha256":"0ab8b13f1e456c944e48918f08cb9b0f2d516ae720771721d8c14719d3be928a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ab8b13f1e456c944e48918f08cb9b0f2d516ae720771721d8c14719d3be928a","first_computed_at":"2026-05-18T00:15:59.666813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:59.666813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"im4XnbGaqx/AKg5ulmNe6Y5WuzWBt5X1DXFeG6PJ9hEs4yUAHCoIEn+66n93wy2Ax+f9GrGV9Ye8WpPGzgflDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:59.667244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04057","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:336368cfec28ec1e41a6c4a63cf26086faf41877fab93a30ba277f594952c13d","sha256:defbd56b9303cfcb422483e7a5090520ef077341f327c1fbed7d7f6844c9e9c1"],"state_sha256":"116224d91a629a43a6a75a1e35b1c4713bfda253c640b34cd8609759ea9b63b4"}