{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P47GG324RLKSBRQ5RIW2GUMVHS","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":"e085a25cf190f8f9844778f5fe090369e98a195a322dbb3800fe6ef0feee8665","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-21T15:28:17Z","title_canon_sha256":"5602937239d4c6a96bb69ed2cae59fa3a5583c5fb77f003f6b8620fd96d95990"},"schema_version":"1.0","source":{"id":"1503.06309","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06309","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06309v3","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06309","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"P47GG324RLKS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P47GG324RLKSBRQ5","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P47GG324","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:2983164412dbd3d5e177a34ce9f6b5dcf82c98af1ac6f7ad94923921ad0e094f","target":"graph","created_at":"2026-05-18T02:19:52Z","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":"Let $\\mathcal{M}(d,\\chi)$ be the moduli stack of stable sheaves of rank 0, Euler characteristic $\\chi$ and first Chern class $dH~(d>0)$, with $H$ the hyperplane class in $\\mathbb{P}^2$. We compute the $A$-valued motivic measure $\\mu_A(\\mathcal{M}(d,\\chi))$ of $\\mathcal{M}(d,\\chi)$ and get explicit formula in codimension $D:=\\rho_d-1$, where $\\rho_d$ is $d-1$ for $d=p$ or $2p$ with $p$ prime, and $7$ otherwise. As a corollary, we get the last $2(D+1)$ Betti numbers of the moduli scheme $M(d,\\chi)$ when $d$ is coprime to $\\chi$.","authors_text":"Yao Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-21T15:28:17Z","title":"Motivic measures of the moduli spaces of pure sheaves on $\\mathbb{P}^2$ with all degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06309","kind":"arxiv","version":3},"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":"sha256:4ec215ce7e0cf23b9e0232246cd767b38b1e57d95fd09367c5c4383cc66a2efd","target":"record","created_at":"2026-05-18T02:19:52Z","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":"e085a25cf190f8f9844778f5fe090369e98a195a322dbb3800fe6ef0feee8665","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-21T15:28:17Z","title_canon_sha256":"5602937239d4c6a96bb69ed2cae59fa3a5583c5fb77f003f6b8620fd96d95990"},"schema_version":"1.0","source":{"id":"1503.06309","kind":"arxiv","version":3}},"canonical_sha256":"7f3e636f5c8ad520c61d8a2da351953c976bab43034a4269f3d865c4ff8bdf3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f3e636f5c8ad520c61d8a2da351953c976bab43034a4269f3d865c4ff8bdf3f","first_computed_at":"2026-05-18T02:19:52.168624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:52.168624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucU+6Zwej91eIs2Z+DTt9QvMfOL7fWujGfE1zPPtP5jfUb6PnUVhdObL1fEVoWyX2rVJMNKZoR6o9BSAaIIsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:52.169148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06309","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ec215ce7e0cf23b9e0232246cd767b38b1e57d95fd09367c5c4383cc66a2efd","sha256:2983164412dbd3d5e177a34ce9f6b5dcf82c98af1ac6f7ad94923921ad0e094f"],"state_sha256":"0b272c0e450f78d87a6b80386b397442994bda25ca5fdc7fdde7c7104ccc3e4a"}