{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RLQ6OYFDZOIGICVD2DRMRNENCG","short_pith_number":"pith:RLQ6OYFD","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"},"canonical_sha256":"8ae1e760a3cb90640aa3d0e2c8b48d11aae1acbe90c8b9f7099f45378edbbfcf","source":{"kind":"arxiv","id":"1204.6154","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RLQ6OYFDZOIGICVD2DRMRNENCG","target":"record","payload":{"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"},"canonical_sha256":"8ae1e760a3cb90640aa3d0e2c8b48d11aae1acbe90c8b9f7099f45378edbbfcf","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"},"source_kind":"arxiv","source_id":"1204.6154","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCW8zCr4XMdaJKtjDAEHjZFRbD0NilXHicgQKiM9ajhHPSg9H7OFQPr5f8t4zWvnnmczjiy/ezXag3Q5Hhb/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:22:23.771386Z"},"content_sha256":"50c71e764275f89055069138b3ea0f6e5941a1aad6c4185f46e1ccbf9272b6fb","schema_version":"1.0","event_id":"sha256:50c71e764275f89055069138b3ea0f6e5941a1aad6c4185f46e1ccbf9272b6fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RLQ6OYFDZOIGICVD2DRMRNENCG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqNXdTnKzwkFwtjLJJ3zGd8ZkwKoGLY0adUatDUc+06f2s3U7yEdGB88n3R6N4e9KTASGw+7nNxr3dJLSBhQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:22:23.771745Z"},"content_sha256":"0a3d45ca552212ba4d00a01909555632c3b28d2c0c04f0ac3e646d63545e72bf","schema_version":"1.0","event_id":"sha256:0a3d45ca552212ba4d00a01909555632c3b28d2c0c04f0ac3e646d63545e72bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/bundle.json","state_url":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T09:22:23Z","links":{"resolver":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG","bundle":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/bundle.json","state":"https://pith.science/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLQ6OYFDZOIGICVD2DRMRNENCG/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r0uNhTy6ZSOQchTHfwCJ9REB8J6lAD9RVMLpai1VeS6SGu5jdbgJwFlJ0x5pqmqKY52By8ErLIEHumzIcbOgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:22:23.773726Z","bundle_sha256":"a1df9623922125503b4ee7e7bc25cdf2cbdbde2992d1af8ca474f369a645ac5a"}}