{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:AM5P3DS2YXWBOXD3UK24F3X3YS","short_pith_number":"pith:AM5P3DS2","schema_version":"1.0","canonical_sha256":"033afd8e5ac5ec175c7ba2b5c2eefbc4ab3e3d26065ef71d2cc3bc3451614a22","source":{"kind":"arxiv","id":"2505.24027","version":1},"attestation_state":"computed","paper":{"title":"A proof of the Fields Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Andy Wilson, Brendon Rhoades, Satoshi Murai","submitted_at":"2025-05-29T22:00:09Z","abstract_excerpt":"The {\\em superspace ring} of rank $n$ is the algebra $\\Omega_n$ of differential forms on affine $n$-space. The algebra $\\Omega_n$ is bigraded with respect to polynomial and exterior degree and carries a natural action of the symmetric group $\\mathfrak{S}_n$. Modding out by $\\mathfrak{S}_n$-invariants with vanishing constant term yields the {\\em superspace coinvariant ring} $SR_n$. We prove that, as an ungraded $\\mathfrak{S}_n$-module, the space $SR_n$ is isomorphic to the sign-twisted permutation action of $\\mathfrak{S}_n$ on ordered set partitions of $\\{1,\\dots,n\\}$. We refine this result by "},"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":"2505.24027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-29T22:00:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"84ddb34d49711e5229643f694b8662f818a68aa17e0462942d74deec8a830da2","abstract_canon_sha256":"7c33915f279b6b2288fa6d0f80cc4a290d1c51de0a421ea1e9aa1545ad891f4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:40.361755Z","signature_b64":"0++Pfhjumpe+XJyfp+FI+Ddkhitj7bWxac7LiJIen5QvHcO19JIJiWgG3wSZVKZxPQLykdkz77xRkFJqzasrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"033afd8e5ac5ec175c7ba2b5c2eefbc4ab3e3d26065ef71d2cc3bc3451614a22","last_reissued_at":"2026-07-05T11:12:40.361283Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:40.361283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A proof of the Fields Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Andy Wilson, Brendon Rhoades, Satoshi Murai","submitted_at":"2025-05-29T22:00:09Z","abstract_excerpt":"The {\\em superspace ring} of rank $n$ is the algebra $\\Omega_n$ of differential forms on affine $n$-space. The algebra $\\Omega_n$ is bigraded with respect to polynomial and exterior degree and carries a natural action of the symmetric group $\\mathfrak{S}_n$. Modding out by $\\mathfrak{S}_n$-invariants with vanishing constant term yields the {\\em superspace coinvariant ring} $SR_n$. We prove that, as an ungraded $\\mathfrak{S}_n$-module, the space $SR_n$ is isomorphic to the sign-twisted permutation action of $\\mathfrak{S}_n$ on ordered set partitions of $\\{1,\\dots,n\\}$. We refine this result by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.24027","created_at":"2026-07-05T11:12:40.361359+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.24027v1","created_at":"2026-07-05T11:12:40.361359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24027","created_at":"2026-07-05T11:12:40.361359+00:00"},{"alias_kind":"pith_short_12","alias_value":"AM5P3DS2YXWB","created_at":"2026-07-05T11:12:40.361359+00:00"},{"alias_kind":"pith_short_16","alias_value":"AM5P3DS2YXWBOXD3","created_at":"2026-07-05T11:12:40.361359+00:00"},{"alias_kind":"pith_short_8","alias_value":"AM5P3DS2","created_at":"2026-07-05T11:12:40.361359+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11549","citing_title":"Superspace coinvariants and inverse systems for $GL_n(\\mathbb{F}_q)$","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30977","citing_title":"Superspace coinvariants for wreath products","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS","json":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS.json","graph_json":"https://pith.science/api/pith-number/AM5P3DS2YXWBOXD3UK24F3X3YS/graph.json","events_json":"https://pith.science/api/pith-number/AM5P3DS2YXWBOXD3UK24F3X3YS/events.json","paper":"https://pith.science/paper/AM5P3DS2"},"agent_actions":{"view_html":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS","download_json":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS.json","view_paper":"https://pith.science/paper/AM5P3DS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.24027&json=true","fetch_graph":"https://pith.science/api/pith-number/AM5P3DS2YXWBOXD3UK24F3X3YS/graph.json","fetch_events":"https://pith.science/api/pith-number/AM5P3DS2YXWBOXD3UK24F3X3YS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS/action/storage_attestation","attest_author":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS/action/author_attestation","sign_citation":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS/action/citation_signature","submit_replication":"https://pith.science/pith/AM5P3DS2YXWBOXD3UK24F3X3YS/action/replication_record"}},"created_at":"2026-07-05T11:12:40.361359+00:00","updated_at":"2026-07-05T11:12:40.361359+00:00"}