{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:V2HGILR65YFUMHXWZD4MWGT2ST","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":"7a7b4dfe191c738ed596cc9d3663bc85a45311eacddaa481b20e0a9c2dbd4127","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2006-10-18T06:37:36Z","title_canon_sha256":"f54c0d827f86be846a4f7710a93ead5cfea2fe1bf13e3f72bdd5699370995a76"},"schema_version":"1.0","source":{"id":"hep-th/0610204","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0610204","created_at":"2026-05-18T00:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0610204v2","created_at":"2026-05-18T00:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0610204","created_at":"2026-05-18T00:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"V2HGILR65YFU","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"V2HGILR65YFUMHXW","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"V2HGILR6","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:d8478a4254c284a1a9228e699bcff8fb6062ecb2ecd1222dc156864d6a7aac41","target":"graph","created_at":"2026-05-18T00:35:53Z","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":"We propose a brane configuration for the (2+1)d, $\\mathcal{N}=2$ superconformal theories (CFT$_3$) arising from M2-branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M-theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT$_4$. The fundamental fields of the CFT$_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and bary","authors_text":"Sangmin Lee","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-10-18T06:37:36Z","title":"Superconformal field theories from crystal lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0610204","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":"sha256:44518f543ad872d78bf3db93e5526da76ac3d923e39617d9f54be911280a24bc","target":"record","created_at":"2026-05-18T00:35:53Z","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":"7a7b4dfe191c738ed596cc9d3663bc85a45311eacddaa481b20e0a9c2dbd4127","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2006-10-18T06:37:36Z","title_canon_sha256":"f54c0d827f86be846a4f7710a93ead5cfea2fe1bf13e3f72bdd5699370995a76"},"schema_version":"1.0","source":{"id":"hep-th/0610204","kind":"arxiv","version":2}},"canonical_sha256":"ae8e642e3eee0b461ef6c8f8cb1a7a94df0cc76fb39b5f6f9024dd23bbd52004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae8e642e3eee0b461ef6c8f8cb1a7a94df0cc76fb39b5f6f9024dd23bbd52004","first_computed_at":"2026-05-18T00:35:53.962607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:53.962607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fe2pUc0MxF7X+Qbiw+sg2yk+prag91qC9URhdUayNpy0Ci1lpaodfRb+90MBjyflSIrOUNfomQmdx5vEb8e/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:53.962984Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0610204","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44518f543ad872d78bf3db93e5526da76ac3d923e39617d9f54be911280a24bc","sha256:d8478a4254c284a1a9228e699bcff8fb6062ecb2ecd1222dc156864d6a7aac41"],"state_sha256":"d1312bee33e9fa432645916165cf21608d30ef489489e481cfcdb14b742350ad"}