{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EMPJ36WPM2JQX6PTUUZEUZO6DW","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":"98c634361f68030c74ba24b986e67b970219b78a6e91177983e23f46c32dcf50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-16T16:15:22Z","title_canon_sha256":"09804a5d48fb04f5062a21a795d00f043bc9daa809861788bf326aa1cfb7f367"},"schema_version":"1.0","source":{"id":"1304.4508","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4508","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4508v3","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4508","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"EMPJ36WPM2JQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EMPJ36WPM2JQX6PT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EMPJ36WP","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:1810db8929e4d62148440b186224fb00eafe4785d8c7c2a770137b2a70adde61","target":"graph","created_at":"2026-05-18T01:30:55Z","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 $f:U\\to{\\mathbb A}^1$ be a regular function on a smooth scheme $U$ over a field $\\mathbb K$. Pantev, Toen, Vaquie and Vezzosi (arXiv:1111.3209, arXiv:1109.5213) define the \"derived critical locus\" Crit$(f)$, an example of a new class of spaces in derived algebraic geometry, which they call \"$-1$-shifted symplectic derived schemes\".\n  They show that intersections of algebraic Lagrangians in a smooth symplectic $\\mathbb K$-scheme, and stable moduli schemes of coherent sheaves on a Calabi-Yau 3-fold over $\\mathbb K$, are also $-1$-shifted symplectic derived schemes. Thus, their theory may hav","authors_text":"Dominic Joyce","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-16T16:15:22Z","title":"A classical model for derived critical loci"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4508","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":"sha256:73ecc105d3f650a24a0ff073dc8e0d32d2384272ad41934f560e9bfd61ce9dc2","target":"record","created_at":"2026-05-18T01:30:55Z","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":"98c634361f68030c74ba24b986e67b970219b78a6e91177983e23f46c32dcf50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-16T16:15:22Z","title_canon_sha256":"09804a5d48fb04f5062a21a795d00f043bc9daa809861788bf326aa1cfb7f367"},"schema_version":"1.0","source":{"id":"1304.4508","kind":"arxiv","version":3}},"canonical_sha256":"231e9dfacf66930bf9f3a5324a65de1da8223353d68ffad8f296e31aeb04706f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"231e9dfacf66930bf9f3a5324a65de1da8223353d68ffad8f296e31aeb04706f","first_computed_at":"2026-05-18T01:30:55.680999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:55.680999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ngHaG2cgV2OWtvBxRBx8Xk4UGeTOELW4V3KFQdPVEak0DeaoeBc5ChrTtQNfvXWIkuBTGhJ9MAi7ivqAGzHMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:55.681619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4508","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73ecc105d3f650a24a0ff073dc8e0d32d2384272ad41934f560e9bfd61ce9dc2","sha256:1810db8929e4d62148440b186224fb00eafe4785d8c7c2a770137b2a70adde61"],"state_sha256":"b42e74e1d6a71e6b9090e836c929506fa8d9b9ae5f9b4344010b415a9109577a"}