{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XATEN4NS4Y3WL3WMOAFC5OBFO2","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":"710d1aa0dda5458a0540f25972272957e10c4d4eb6e51c0df802f94f6f45a5cd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T19:38:57Z","title_canon_sha256":"946d6a658f6c0292990cdda411f490ad88f0af7d37e8a1a782f4f6d78d53c7cd"},"schema_version":"1.0","source":{"id":"2408.12703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12703","created_at":"2026-07-05T08:58:28Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12703v1","created_at":"2026-07-05T08:58:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12703","created_at":"2026-07-05T08:58:28Z"},{"alias_kind":"pith_short_12","alias_value":"XATEN4NS4Y3W","created_at":"2026-07-05T08:58:28Z"},{"alias_kind":"pith_short_16","alias_value":"XATEN4NS4Y3WL3WM","created_at":"2026-07-05T08:58:28Z"},{"alias_kind":"pith_short_8","alias_value":"XATEN4NS","created_at":"2026-07-05T08:58:28Z"}],"graph_snapshots":[{"event_id":"sha256:b5e20433ff5a2fc7bf50c81291bcec6ec5ec2449a234876579471d74aaf225a4","target":"graph","created_at":"2026-07-05T08:58:28Z","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/2408.12703/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting formula in $\\mathcal{N}=4$ theories involving the Weyl denominator formula of a Borcherds-Kac-Moody Lie algebra. A general form of the generating function is suggested based on the Lie algebra associated to the adjacency matrix of the BPS quiver whenever the BPS spectrum of the $\\mathcal{N}=2$ theory admits such a description. This proposal is tested for the B","authors_text":"Daniel Bryan, Murad Alim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T19:38:57Z","title":"Generating functions for $\\mathcal{N}=2$ BPS structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12703","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":"sha256:370ece7ad1ec973ae6c52ce4faa965bdc77a0b90e0669f8763281e388d879bf2","target":"record","created_at":"2026-07-05T08:58:28Z","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":"710d1aa0dda5458a0540f25972272957e10c4d4eb6e51c0df802f94f6f45a5cd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T19:38:57Z","title_canon_sha256":"946d6a658f6c0292990cdda411f490ad88f0af7d37e8a1a782f4f6d78d53c7cd"},"schema_version":"1.0","source":{"id":"2408.12703","kind":"arxiv","version":1}},"canonical_sha256":"b82646f1b2e63765eecc700a2eb82576bbc04a85f3fd42b6e7e455dc3bcae1d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b82646f1b2e63765eecc700a2eb82576bbc04a85f3fd42b6e7e455dc3bcae1d3","first_computed_at":"2026-07-05T08:58:28.828486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:28.828486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WS0E2XrWAshh5ZQ0r69LMWPtnZBUQiBi0P7VSKNb9UeUBn5Opx0Nh1aBIcp9uf8hJpPTGfiEcDwqfoteKw1bDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:28.828941Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.12703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:370ece7ad1ec973ae6c52ce4faa965bdc77a0b90e0669f8763281e388d879bf2","sha256:b5e20433ff5a2fc7bf50c81291bcec6ec5ec2449a234876579471d74aaf225a4"],"state_sha256":"f1411583d9e1e53a187cabde729ee27c3407c4f64b0caea66b5df0c3620fceed"}