{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CHEM4LFZSD6HQR6PTWP5GMYN5Q","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":"92e2e2112c7f3acd8e2556d858566f1cee6aa5cecc6849a776656cbea63e95dd","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-24T07:12:19Z","title_canon_sha256":"4ffc6734b172254f3220208a92b06555671a4fa801215fec3447aefac25f9308"},"schema_version":"1.0","source":{"id":"2109.11773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11773","created_at":"2026-07-05T05:02:39Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11773v2","created_at":"2026-07-05T05:02:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11773","created_at":"2026-07-05T05:02:39Z"},{"alias_kind":"pith_short_12","alias_value":"CHEM4LFZSD6H","created_at":"2026-07-05T05:02:39Z"},{"alias_kind":"pith_short_16","alias_value":"CHEM4LFZSD6HQR6P","created_at":"2026-07-05T05:02:39Z"},{"alias_kind":"pith_short_8","alias_value":"CHEM4LFZ","created_at":"2026-07-05T05:02:39Z"}],"graph_snapshots":[{"event_id":"sha256:50b837ebf7c649f450b78599f1b7a822ce0eccc36dd62ba292fca91dfbeca715","target":"graph","created_at":"2026-07-05T05:02:39Z","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/2109.11773/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the \"box-counting\" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas theory and Pandharipande-Thomas theory) are equal up to a factor of MacMahon's generating function for plane partitions. The main tools in our proof are a Desnanot-Jacobi-type condensation identity, and a novel application of the tripartite double-dimer model of Kenyon-Wilson.","authors_text":"Benjamin Young, Gautam Webb, Helen Jenne","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-24T07:12:19Z","title":"Double-dimer condensation and the PT-DT correspondence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11773","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":"sha256:0719132e10125e4f8cba3d026a0e228f7b8808a92b41aa4956b2bb059194faa0","target":"record","created_at":"2026-07-05T05:02:39Z","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":"92e2e2112c7f3acd8e2556d858566f1cee6aa5cecc6849a776656cbea63e95dd","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-24T07:12:19Z","title_canon_sha256":"4ffc6734b172254f3220208a92b06555671a4fa801215fec3447aefac25f9308"},"schema_version":"1.0","source":{"id":"2109.11773","kind":"arxiv","version":2}},"canonical_sha256":"11c8ce2cb990fc7847cf9d9fd3330dec2fcbc5f2db27fa3080e9ce7aa7ba933c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11c8ce2cb990fc7847cf9d9fd3330dec2fcbc5f2db27fa3080e9ce7aa7ba933c","first_computed_at":"2026-07-05T05:02:39.562365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:39.562365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DzB2tQMzhVN39Ccz671oRzHHKkgMZhzJXG/8D3QRfXn56DkK98NlhcFv6xNVPDTxjVmF8GOLwZDRsKEkjjy4AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:39.562724Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0719132e10125e4f8cba3d026a0e228f7b8808a92b41aa4956b2bb059194faa0","sha256:50b837ebf7c649f450b78599f1b7a822ce0eccc36dd62ba292fca91dfbeca715"],"state_sha256":"ffeff9da4c0ecd5ba085889a2fb03c1c6002c42ce857ef9c99099fa79c5f924d"}