{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:STC6IR4OAISNLEWZNTCGHLJS23","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":"729dd7172934c3f32b266763c069053309e2f0ad98e91dcca8178ea3d544dc75","cross_cats_sorted":["cs.CC","math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-04-30T14:52:31Z","title_canon_sha256":"04c0f75e38b439f107caf1019ff1c4e2095d4a166fac181842236d5b8f5807fd"},"schema_version":"1.0","source":{"id":"2504.21708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.21708","created_at":"2026-07-05T10:56:28Z"},{"alias_kind":"arxiv_version","alias_value":"2504.21708v1","created_at":"2026-07-05T10:56:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.21708","created_at":"2026-07-05T10:56:28Z"},{"alias_kind":"pith_short_12","alias_value":"STC6IR4OAISN","created_at":"2026-07-05T10:56:28Z"},{"alias_kind":"pith_short_16","alias_value":"STC6IR4OAISNLEWZ","created_at":"2026-07-05T10:56:28Z"},{"alias_kind":"pith_short_8","alias_value":"STC6IR4O","created_at":"2026-07-05T10:56:28Z"}],"graph_snapshots":[{"event_id":"sha256:8faf6a7d132175bd79d0f0fe6b6e28f33c4e357144f73216ba23d58a728f48f9","target":"graph","created_at":"2026-07-05T10:56:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.21708/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{R} = \\mathbb{K}[x_1, \\dots, x_n]$ be a multivariate polynomial ring over a field $\\mathbb{K}$ of characteristic 0. Consider $n$ algebraically independent elements $g_1, \\dots, g_n$ in $\\mathcal{R}$. Let $\\mathcal{S}$ denote the subring of $\\mathcal{R}$ generated by $g_1, \\dots, g_n$, and let $h$ be an element of $\\mathcal{S}$. Then, there exists a unique element ${f} \\in \\mathbb{K}[u_1, \\dots, u_n]$ such that $h = f(g_1, \\dots, g_n)$.\n  In this paper, we provide an algorithm for computing ${f}$, given $h$ and $g_1, \\dots, g_n$. The complexity of our algorithm is linear in the siz","authors_text":"Thi Xuan Vu","cross_cats":["cs.CC","math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-04-30T14:52:31Z","title":"Computing Polynomial Representation in Subrings of Multivariate Polynomial Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.21708","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":"sha256:6c1c007d5ad2865098fc8b6e85c59b68e717d6ec2f9a1c3e70d04b8f535cebdf","target":"record","created_at":"2026-07-05T10:56:28Z","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":"729dd7172934c3f32b266763c069053309e2f0ad98e91dcca8178ea3d544dc75","cross_cats_sorted":["cs.CC","math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-04-30T14:52:31Z","title_canon_sha256":"04c0f75e38b439f107caf1019ff1c4e2095d4a166fac181842236d5b8f5807fd"},"schema_version":"1.0","source":{"id":"2504.21708","kind":"arxiv","version":1}},"canonical_sha256":"94c5e4478e0224d592d96cc463ad32d6f94f62b225969d0e5cf9fd60058f8c71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94c5e4478e0224d592d96cc463ad32d6f94f62b225969d0e5cf9fd60058f8c71","first_computed_at":"2026-07-05T10:56:28.521991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:56:28.521991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UvJriMcU08R3/iDkrCOTEUjMTYaaMd1JY7xKHppKDP9oGhohDWSTm/4BoZNR9IjrcqNLbVbOghrHnE2tj6u1AA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:56:28.522402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.21708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c1c007d5ad2865098fc8b6e85c59b68e717d6ec2f9a1c3e70d04b8f535cebdf","sha256:8faf6a7d132175bd79d0f0fe6b6e28f33c4e357144f73216ba23d58a728f48f9"],"state_sha256":"12be5954420ac961eb8ad24ee5e70ff88272639eea5cb818aaf20f5e3615f8c7"}