{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4JGFG4ZK7J2J3Y55BO7RADPOLU","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":"a9cd749f1394e22f940e1a82d798e2463a5fdb7c522e0d2d2b9e8cdcb7118318","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T18:13:47Z","title_canon_sha256":"2103847c8aed67521fcf4d308d4d77c27ad03294c5c7b74431930d23be14bcf6"},"schema_version":"1.0","source":{"id":"1901.08032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08032","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08032v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08032","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"4JGFG4ZK7J2J","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4JGFG4ZK7J2J3Y55","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4JGFG4ZK","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:eac86004a6ec27345a888ebd9b0217bb7c6a6f86f3d3a82be6e989d382c99841","target":"graph","created_at":"2026-05-17T23:55:39Z","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":"This paper lays out a foundation for a theory of supertropical algebraic geometry, relying on commutative $\\nu$-algebra. To this end, the paper introduces $\\mathfrak{q}$-congruences, carried over $\\nu$-semirings, whose distinguished ghost and tangible clusters allow both quotienting and localization. Utilizing these clusters, $\\mathfrak{g}$-prime, $\\mathfrak{g}$-radical, and maximal $\\mathfrak{q}$-congruences are naturally defined, satisfying the classical relations among analogous ideals. Thus, a foundation of systematic theory of commutative $\\nu$-algebra is laid. In this framework, the unde","authors_text":"Zur Izhakian","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T18:13:47Z","title":"Commutative $\\nu$-algebra and supertropical algebraic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08032","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":"sha256:23331de3ded0c8307cd22521d3ebf461d633ea229bdb2fe0b5f0707ff6a3363c","target":"record","created_at":"2026-05-17T23:55:39Z","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":"a9cd749f1394e22f940e1a82d798e2463a5fdb7c522e0d2d2b9e8cdcb7118318","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T18:13:47Z","title_canon_sha256":"2103847c8aed67521fcf4d308d4d77c27ad03294c5c7b74431930d23be14bcf6"},"schema_version":"1.0","source":{"id":"1901.08032","kind":"arxiv","version":1}},"canonical_sha256":"e24c53732afa749de3bd0bbf100dee5d06d256d451a9715b0bd9f4db59267db8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e24c53732afa749de3bd0bbf100dee5d06d256d451a9715b0bd9f4db59267db8","first_computed_at":"2026-05-17T23:55:39.287540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:39.287540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l/gIJqsGZdO2MW7lcXyoxFndW44ZG+mP7Hnlvu6zeoFp3AKd7VBD1SzH7cvTJoSQLBmYSTSzdvx7qz01zMJLDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:39.287918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.08032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23331de3ded0c8307cd22521d3ebf461d633ea229bdb2fe0b5f0707ff6a3363c","sha256:eac86004a6ec27345a888ebd9b0217bb7c6a6f86f3d3a82be6e989d382c99841"],"state_sha256":"2b5c7e2c1d02eedcf5b3a061f019e75a73a94edf47e6ed806aa6a10ad953a566"}