{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:WOCDYUS6MASSXCEAATOHMO75PS","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":"54316626d54417a2da3af6b389ae1f7435d1a30514e6b39e5a5cd48337e7c488","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-06-30T15:16:33Z","title_canon_sha256":"bee4ef81efb1b1f598e910c74eba4852dea4c94dd8777e4d304dcbcad720f806"},"schema_version":"1.0","source":{"id":"2006.16885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16885","created_at":"2026-07-05T04:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16885v2","created_at":"2026-07-05T04:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16885","created_at":"2026-07-05T04:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"WOCDYUS6MASS","created_at":"2026-07-05T04:26:31Z"},{"alias_kind":"pith_short_16","alias_value":"WOCDYUS6MASSXCEA","created_at":"2026-07-05T04:26:31Z"},{"alias_kind":"pith_short_8","alias_value":"WOCDYUS6","created_at":"2026-07-05T04:26:31Z"}],"graph_snapshots":[{"event_id":"sha256:45ed69f789f87305d39ab251310b9342aeae7db3531ea722da2e95d01b5f03f5","target":"graph","created_at":"2026-07-05T04:26:31Z","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/2006.16885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We state two conjectures that together allow one to describe the set of smoothing components of a Gorenstein toric affine 3-fold in terms of a combinatorially defined and easily studied set of Laurent polynomials called 0-mutable polynomials. We explain the origin of the conjectures in mirror symmetry and present some of the evidence.","authors_text":"Alessio Corti, Andrea Petracci, Matej Filip","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-06-30T15:16:33Z","title":"Mirror Symmetry and smoothing Gorenstein toric affine 3-folds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16885","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":"sha256:0b10b657d1a380d18758c0a45bc5173f996cb59760ceeb6ee5ff402f814eb16b","target":"record","created_at":"2026-07-05T04:26:31Z","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":"54316626d54417a2da3af6b389ae1f7435d1a30514e6b39e5a5cd48337e7c488","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-06-30T15:16:33Z","title_canon_sha256":"bee4ef81efb1b1f598e910c74eba4852dea4c94dd8777e4d304dcbcad720f806"},"schema_version":"1.0","source":{"id":"2006.16885","kind":"arxiv","version":2}},"canonical_sha256":"b3843c525e60252b888004dc763bfd7c92d9bc97a195d55bc251438b416a5cc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3843c525e60252b888004dc763bfd7c92d9bc97a195d55bc251438b416a5cc1","first_computed_at":"2026-07-05T04:26:31.777370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:26:31.777370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQGICCl4auO9Vs9jCxnvl3yBvdiHTok51JvbnE7P4rRmEaz8S7egzN35yuTiaRWxXYxwq1T3A/QIZPH7LILRBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:26:31.777791Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.16885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b10b657d1a380d18758c0a45bc5173f996cb59760ceeb6ee5ff402f814eb16b","sha256:45ed69f789f87305d39ab251310b9342aeae7db3531ea722da2e95d01b5f03f5"],"state_sha256":"66116963607e63e136fd1be38608ea5c433507766d50f784e9e002b4d5085437"}