{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RLQ6OYFDZOIGICVD2DRMRNENCG","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":"cf073e61d8731c309eee44e4ce41b26d915f710f322a917d94f761e4dca62b70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-27T09:21:26Z","title_canon_sha256":"03e9e45eee7728b2166dea7ddbd3694fefd4575e82167598b9751f01b18e27d3"},"schema_version":"1.0","source":{"id":"1204.6154","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6154","created_at":"2026-05-18T02:21:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6154v2","created_at":"2026-05-18T02:21:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6154","created_at":"2026-05-18T02:21:15Z"},{"alias_kind":"pith_short_12","alias_value":"RLQ6OYFDZOIG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RLQ6OYFDZOIGICVD","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RLQ6OYFD","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:0a3d45ca552212ba4d00a01909555632c3b28d2c0c04f0ac3e646d63545e72bf","target":"graph","created_at":"2026-05-18T02:21:15Z","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":"In this paper we propose a general functorial definition of the operation of \\emph{local tropicalization} in commutative algebra. Let $R$ be a commutative ring, $\\Gamma$ a finitely generated subsemigroup of a lattice, $\\gamma : \\Gamma \\rightarrow R/ R^*$ a morphism of semigroups, and $\\V(R)$ the topological space of valuations on $R$ taking values in $\\R \\cup \\infty$. Then we may \\emph{tropicalize} with respect to $\\gamma$ any subset $\\W$ of the space of valuations $\\V(R)$. By definition, we get a subset of a rational polyhedral cone canonically associated to $\\Gamma$, enriched with strata at ","authors_text":"Dmitry Stepanov, Patrick Popescu-Pampu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-27T09:21:26Z","title":"Local Tropicalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6154","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":"sha256:50c71e764275f89055069138b3ea0f6e5941a1aad6c4185f46e1ccbf9272b6fb","target":"record","created_at":"2026-05-18T02:21:15Z","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":"cf073e61d8731c309eee44e4ce41b26d915f710f322a917d94f761e4dca62b70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-27T09:21:26Z","title_canon_sha256":"03e9e45eee7728b2166dea7ddbd3694fefd4575e82167598b9751f01b18e27d3"},"schema_version":"1.0","source":{"id":"1204.6154","kind":"arxiv","version":2}},"canonical_sha256":"8ae1e760a3cb90640aa3d0e2c8b48d11aae1acbe90c8b9f7099f45378edbbfcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae1e760a3cb90640aa3d0e2c8b48d11aae1acbe90c8b9f7099f45378edbbfcf","first_computed_at":"2026-05-18T02:21:15.903532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:15.903532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5XxxE6IKluVr9G/4BeesQHNDnqUETVfOJLk+FgMMvANwtzWfD0d3KXXfhPC+XoE1dMawT+Va8obwb9Hs6Wi2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:15.904136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6154","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50c71e764275f89055069138b3ea0f6e5941a1aad6c4185f46e1ccbf9272b6fb","sha256:0a3d45ca552212ba4d00a01909555632c3b28d2c0c04f0ac3e646d63545e72bf"],"state_sha256":"51071acced1609282a4909eaf51c96eadd50cad8f46aa0b5f64206c16c382fb1"}