{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CZV7Z3YJMHGIBZ4W6Q2NAOVUDC","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":"e48cb2a420f6399f38bb3476a4a2b476d4dfdbfa7f2527bb5f31254bdd19ecbc","cross_cats_sorted":["math-ph","math.AG","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-03T22:24:01Z","title_canon_sha256":"2b5b673d971a8e10146df5905eaee56c79384f74a58d96f435df1422e3ed61b4"},"schema_version":"1.0","source":{"id":"2607.03617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03617","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03617v1","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03617","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"CZV7Z3YJMHGI","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"CZV7Z3YJMHGIBZ4W","created_at":"2026-07-07T02:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"CZV7Z3YJ","created_at":"2026-07-07T02:17:57Z"}],"graph_snapshots":[{"event_id":"sha256:13226794ad42e46e0d4bb8f97015482e99937697574ac1bad4f92e9e7c33e595","target":"graph","created_at":"2026-07-07T02:17:57Z","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/2607.03617/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive new exact formulae for elliptic genera in two spacetime dimensions with $\\mathcal{N}\\ge 2$ supercharges, as well as their one- and zero-dimensional counterparts (for Witten indices and matrix-model partition functions). Our results are written as a discrete sum over geometric/combinatorial structures of crystals introduced previously by the authors. The contribution from each crystal may be expressed in terms of the boundary data of a finite substructure of the crystal called the molecules. Our results provide vast generalisations of the celebrated Nekrasov partition function enumera","authors_text":"Jiakang Bao, Masahito Yamazaki","cross_cats":["math-ph","math.AG","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-03T22:24:01Z","title":"Quiver BPS Indices from Crystal Profiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03617","kind":"arxiv","version":1},"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":"sha256:5c88a1144a20fc36cacf9f373d85bc6c1030726ce06736bbfcae3586421fb891","target":"record","created_at":"2026-07-07T02:17:57Z","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":"e48cb2a420f6399f38bb3476a4a2b476d4dfdbfa7f2527bb5f31254bdd19ecbc","cross_cats_sorted":["math-ph","math.AG","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-03T22:24:01Z","title_canon_sha256":"2b5b673d971a8e10146df5905eaee56c79384f74a58d96f435df1422e3ed61b4"},"schema_version":"1.0","source":{"id":"2607.03617","kind":"arxiv","version":1}},"canonical_sha256":"166bfcef0961cc80e796f434d03ab418922a84f334e0f56cedd524cfae1ba3e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"166bfcef0961cc80e796f434d03ab418922a84f334e0f56cedd524cfae1ba3e5","first_computed_at":"2026-07-07T02:17:57.636845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:57.636845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LvHFUAC7FpujQzwpl7R+rNF0wdY5MsRhdGjK+SMQKX4AECHqV/mp2Iz0v25X8h5/5oaHCgNV7FUrkxFXYyn9DQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:57.637596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c88a1144a20fc36cacf9f373d85bc6c1030726ce06736bbfcae3586421fb891","sha256:13226794ad42e46e0d4bb8f97015482e99937697574ac1bad4f92e9e7c33e595"],"state_sha256":"aecdf8c839b9fb1c8db4b44841120b6c74a263f99fbb34619ffcae1c13d5a070"}