{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FZQO2TWRF5CCRBJOPWAIALLJGA","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":"62d1273b2ef9e88796fe975f9f44595af9f68fdec308f9d98955bc9023af595f","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-11T12:38:34Z","title_canon_sha256":"b894d9b7faeb4ea0132a4457d8e31f41dca0e9632a37d652e27504a536bbebdb"},"schema_version":"1.0","source":{"id":"2203.05883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.05883","created_at":"2026-07-05T07:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"2203.05883v2","created_at":"2026-07-05T07:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.05883","created_at":"2026-07-05T07:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"FZQO2TWRF5CC","created_at":"2026-07-05T07:02:24Z"},{"alias_kind":"pith_short_16","alias_value":"FZQO2TWRF5CCRBJO","created_at":"2026-07-05T07:02:24Z"},{"alias_kind":"pith_short_8","alias_value":"FZQO2TWR","created_at":"2026-07-05T07:02:24Z"}],"graph_snapshots":[{"event_id":"sha256:03933e93e888d8d0d1e960aabe4a9edec3904d0350b2f956b0cc3c1ed82f7782","target":"graph","created_at":"2026-07-05T07:02:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.05883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The moduli space $\\overline{\\mathcal{M}}_{0,n}$ of $n$ pointed stable curves of genus $0$ admits an action of the symmetric group $S_n$ by permuting the marked points. We provide a closed formula for the character of the $S_n$-action on the cohomology of $\\overline{\\mathcal{M}}_{0,n}$. This is achieved by studying wall crossings of the moduli spaces of quasimaps which provide us with a new inductive construction of $\\overline{\\mathcal{M}}_{0,n}$, equivariant with respect to the symmetric group action. Moreover we prove that $H^{2k}(\\overline{\\mathcal{M}}_{0,n})$ for $k\\le 3$ and $H^{2k}(\\overl","authors_text":"Donggun Lee, Jinwon Choi, Young-Hoon Kiem","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-11T12:38:34Z","title":"Representations on the cohomology of $\\overline{\\mathcal{M}}_{0,n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.05883","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":"sha256:4b9b0bc66713ee1a877c9474fc1d6f6c20d3b5f7872c497c48d51b6742f900e8","target":"record","created_at":"2026-07-05T07:02:24Z","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":"62d1273b2ef9e88796fe975f9f44595af9f68fdec308f9d98955bc9023af595f","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-11T12:38:34Z","title_canon_sha256":"b894d9b7faeb4ea0132a4457d8e31f41dca0e9632a37d652e27504a536bbebdb"},"schema_version":"1.0","source":{"id":"2203.05883","kind":"arxiv","version":2}},"canonical_sha256":"2e60ed4ed12f4428852e7d80802d69302d048cd91ad47d731d0f4afa08957f64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e60ed4ed12f4428852e7d80802d69302d048cd91ad47d731d0f4afa08957f64","first_computed_at":"2026-07-05T07:02:24.612447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:02:24.612447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PrifxiXqnSccIbSA1GoNpEQiaoBJsop0mPTKtOqUBgDRapLl64QtvQC93c9Doox4ACIBEVCuJKc8Tqp61hJcCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:02:24.612860Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.05883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b9b0bc66713ee1a877c9474fc1d6f6c20d3b5f7872c497c48d51b6742f900e8","sha256:03933e93e888d8d0d1e960aabe4a9edec3904d0350b2f956b0cc3c1ed82f7782"],"state_sha256":"f2587b87065fc2cbab513863528bed656458441895ba34dc2877929bef9d0201"}