{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RLQ6OYFDZOIGICVD2DRMRNENCG","short_pith_number":"pith:RLQ6OYFD","schema_version":"1.0","canonical_sha256":"8ae1e760a3cb90640aa3d0e2c8b48d11aae1acbe90c8b9f7099f45378edbbfcf","source":{"kind":"arxiv","id":"1204.6154","version":2},"attestation_state":"computed","paper":{"title":"Local Tropicalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dmitry Stepanov, Patrick Popescu-Pampu","submitted_at":"2012-04-27T09:21:26Z","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 "},"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":"1204.6154","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-27T09:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"03e9e45eee7728b2166dea7ddbd3694fefd4575e82167598b9751f01b18e27d3","abstract_canon_sha256":"cf073e61d8731c309eee44e4ce41b26d915f710f322a917d94f761e4dca62b70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:15.904136Z","signature_b64":"5XxxE6IKluVr9G/4BeesQHNDnqUETVfOJLk+FgMMvANwtzWfD0d3KXXfhPC+XoE1dMawT+Va8obwb9Hs6Wi2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ae1e760a3cb90640aa3d0e2c8b48d11aae1acbe90c8b9f7099f45378edbbfcf","last_reissued_at":"2026-05-18T02:21:15.903532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:15.903532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Tropicalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dmitry Stepanov, Patrick Popescu-Pampu","submitted_at":"2012-04-27T09:21:26Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6154","kind":"arxiv","version":2},"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":"1204.6154","created_at":"2026-05-18T02:21:15.903608+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.6154v2","created_at":"2026-05-18T02:21:15.903608+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6154","created_at":"2026-05-18T02:21:15.903608+00:00"},{"alias_kind":"pith_short_12","alias_value":"RLQ6OYFDZOIG","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RLQ6OYFDZOIGICVD","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RLQ6OYFD","created_at":"2026-05-18T12:27:20.899486+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/RLQ6OYFDZOIGICVD2DRMRNENCG","json":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG.json","graph_json":"https://pith.science/api/pith-number/RLQ6OYFDZOIGICVD2DRMRNENCG/graph.json","events_json":"https://pith.science/api/pith-number/RLQ6OYFDZOIGICVD2DRMRNENCG/events.json","paper":"https://pith.science/paper/RLQ6OYFD"},"agent_actions":{"view_html":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG","download_json":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG.json","view_paper":"https://pith.science/paper/RLQ6OYFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.6154&json=true","fetch_graph":"https://pith.science/api/pith-number/RLQ6OYFDZOIGICVD2DRMRNENCG/graph.json","fetch_events":"https://pith.science/api/pith-number/RLQ6OYFDZOIGICVD2DRMRNENCG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/action/storage_attestation","attest_author":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/action/author_attestation","sign_citation":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/action/citation_signature","submit_replication":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/action/replication_record"}},"created_at":"2026-05-18T02:21:15.903608+00:00","updated_at":"2026-05-18T02:21:15.903608+00:00"}