{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q76LLQTNDNPMKS5SRP55BA7TWP","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":"4a9db20dda56da8210c919bb23a49f0d483c848f70898ae103be7bae501cdf5a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-02T21:03:50Z","title_canon_sha256":"88052675da1d3d36cfc1ea637a5f91b4f73d3bbe52b27436bea11dd9bbb86ee9"},"schema_version":"1.0","source":{"id":"1504.00690","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00690","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00690v2","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00690","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"Q76LLQTNDNPM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q76LLQTNDNPMKS5S","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q76LLQTN","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:13e36d6895b0dc7de1ad93cbbbab8cb8a38c21601fe01e2b20a05e950bf033fe","target":"graph","created_at":"2026-05-18T00:21:00Z","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 $({\\bf X},\\omega_{\\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\\rm vdim}_{\\mathbb C}{\\bf X}=n\\in\\mathbb Z$, and $X_{\\rm an}$ the underlying complex analytic topological space. We prove that $X_{\\rm an}$ can be given the structure of a derived smooth manifold ${\\bf X}_{\\rm dm}$, of real virtual dimension ${\\rm vdim}_{\\mathbb R}{\\bf X}_{\\rm dm}=n$. This ${\\bf X}_{\\rm dm}$ is not canonical, but is independent of choices up to bordisms fixing the underlying topolog","authors_text":"Dennis Borisov, Dominic Joyce","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-02T21:03:50Z","title":"Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00690","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:ba480a6740b3eca72b7ef60367b00510dbdb81d3d3c7c5af05143a97595956e6","target":"record","created_at":"2026-05-18T00:21:00Z","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":"4a9db20dda56da8210c919bb23a49f0d483c848f70898ae103be7bae501cdf5a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-02T21:03:50Z","title_canon_sha256":"88052675da1d3d36cfc1ea637a5f91b4f73d3bbe52b27436bea11dd9bbb86ee9"},"schema_version":"1.0","source":{"id":"1504.00690","kind":"arxiv","version":2}},"canonical_sha256":"87fcb5c26d1b5ec54bb28bfbd083f3b3c09340406f9b3306f27d96679c09d89e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87fcb5c26d1b5ec54bb28bfbd083f3b3c09340406f9b3306f27d96679c09d89e","first_computed_at":"2026-05-18T00:21:00.521949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:00.521949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W28cnPGJFasym0Ptfz+KEVGqwdI2/Q0SDOCQMNOFx4b6a8lgGJi9xSxiJFPq9/EYmw0exH9MRD8hbAyqy8wZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:00.522574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00690","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba480a6740b3eca72b7ef60367b00510dbdb81d3d3c7c5af05143a97595956e6","sha256:13e36d6895b0dc7de1ad93cbbbab8cb8a38c21601fe01e2b20a05e950bf033fe"],"state_sha256":"1a284ac0dbbc74cd0da7f6377e99ca271207caae7e11c6b659d6d0ee07362bb0"}