{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WKX7XXNNTLVO3GVRD572FGSBLE","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":"199717f854dfbb480b0e98352da770748565dbd1eed4629a79579624904e9a82","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-14T04:26:11Z","title_canon_sha256":"20db005a46bec897543f0f134cf1fd0286a49ca5b9424ac0ab2bc812cc5ef5d0"},"schema_version":"1.0","source":{"id":"1212.3391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3391","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3391v1","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3391","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"WKX7XXNNTLVO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WKX7XXNNTLVO3GVR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WKX7XXNN","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:765a75a9dd81fba3545556e67a2193fbe85a7c0ea447e44d1ffeaa36983c4908","target":"graph","created_at":"2026-05-18T03:38:24Z","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":"For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number field admits a globally minimal presentation.","authors_text":"Lucien Szpiro, Michael Tepper, Phillip Williams","cross_cats":["math.AG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-14T04:26:11Z","title":"Semi-stable Reduction Implies Minimality of the Resultant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3391","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:da4dfaa5405564c09f66cfd6878201ef4d17129a9035d41adf6d0d58307150fb","target":"record","created_at":"2026-05-18T03:38:24Z","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":"199717f854dfbb480b0e98352da770748565dbd1eed4629a79579624904e9a82","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-14T04:26:11Z","title_canon_sha256":"20db005a46bec897543f0f134cf1fd0286a49ca5b9424ac0ab2bc812cc5ef5d0"},"schema_version":"1.0","source":{"id":"1212.3391","kind":"arxiv","version":1}},"canonical_sha256":"b2affbddad9aeaed9ab11f7fa29a415903755df02055325269f3045dddf4513a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2affbddad9aeaed9ab11f7fa29a415903755df02055325269f3045dddf4513a","first_computed_at":"2026-05-18T03:38:24.781908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:24.781908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSbnlSnjm8aiyd31irk0a4BuVH0qYG+w9ODQV25LN6IGX/5Xay//F4TV0DDbTbYjU1WT/8dl53WOmrEfcjhfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:24.782449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da4dfaa5405564c09f66cfd6878201ef4d17129a9035d41adf6d0d58307150fb","sha256:765a75a9dd81fba3545556e67a2193fbe85a7c0ea447e44d1ffeaa36983c4908"],"state_sha256":"e00e99f37d00abb9db56146bb77d0172eccf7d0fbaa1c803b6a36a598adb9b21"}