{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BK4LCPY6IVWJITSISGHQRS43B4","short_pith_number":"pith:BK4LCPY6","schema_version":"1.0","canonical_sha256":"0ab8b13f1e456c944e48918f08cb9b0f2d516ae720771721d8c14719d3be928a","source":{"kind":"arxiv","id":"1508.04057","version":3},"attestation_state":"computed","paper":{"title":"Degenerations of toric varieties over valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dhruv Ranganathan, Tyler Foster","submitted_at":"2015-08-17T15:24:58Z","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."},"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":"1508.04057","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-17T15:24:58Z","cross_cats_sorted":[],"title_canon_sha256":"fd40833dcb2f59f7b2220049ba6098301c54f1f42dec54b2fd6a0923b3dfee08","abstract_canon_sha256":"8ed45681a023a4f47d60f45d4b3a34fa5ea21abc1e5e1d863d6f20a350fd7ac2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:59.667244Z","signature_b64":"im4XnbGaqx/AKg5ulmNe6Y5WuzWBt5X1DXFeG6PJ9hEs4yUAHCoIEn+66n93wy2Ax+f9GrGV9Ye8WpPGzgflDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ab8b13f1e456c944e48918f08cb9b0f2d516ae720771721d8c14719d3be928a","last_reissued_at":"2026-05-18T00:15:59.666813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:59.666813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degenerations of toric varieties over valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dhruv Ranganathan, Tyler Foster","submitted_at":"2015-08-17T15:24:58Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04057","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1508.04057","created_at":"2026-05-18T00:15:59.666878+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04057v3","created_at":"2026-05-18T00:15:59.666878+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04057","created_at":"2026-05-18T00:15:59.666878+00:00"},{"alias_kind":"pith_short_12","alias_value":"BK4LCPY6IVWJ","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BK4LCPY6IVWJITSI","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BK4LCPY6","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4","json":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4.json","graph_json":"https://pith.science/api/pith-number/BK4LCPY6IVWJITSISGHQRS43B4/graph.json","events_json":"https://pith.science/api/pith-number/BK4LCPY6IVWJITSISGHQRS43B4/events.json","paper":"https://pith.science/paper/BK4LCPY6"},"agent_actions":{"view_html":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4","download_json":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4.json","view_paper":"https://pith.science/paper/BK4LCPY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04057&json=true","fetch_graph":"https://pith.science/api/pith-number/BK4LCPY6IVWJITSISGHQRS43B4/graph.json","fetch_events":"https://pith.science/api/pith-number/BK4LCPY6IVWJITSISGHQRS43B4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4/action/storage_attestation","attest_author":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4/action/author_attestation","sign_citation":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4/action/citation_signature","submit_replication":"https://pith.science/pith/BK4LCPY6IVWJITSISGHQRS43B4/action/replication_record"}},"created_at":"2026-05-18T00:15:59.666878+00:00","updated_at":"2026-05-18T00:15:59.666878+00:00"}