{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:F7UIXGPMADES7C4WYVUAF4YL5V","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":"9cb8ecae358ce423a02658fd62c707f055433a64bade07148d34763dd227c30d","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-10-28T19:43:08Z","title_canon_sha256":"2b4ee7e6e85c8ac17a301ec9faa81660c908c1ba786644b506ca8f5988d5446b"},"schema_version":"1.0","source":{"id":"hep-th/0310262","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0310262","created_at":"2026-07-04T16:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0310262v3","created_at":"2026-07-04T16:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0310262","created_at":"2026-07-04T16:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"F7UIXGPMADES","created_at":"2026-07-04T16:41:26Z"},{"alias_kind":"pith_short_16","alias_value":"F7UIXGPMADES7C4W","created_at":"2026-07-04T16:41:26Z"},{"alias_kind":"pith_short_8","alias_value":"F7UIXGPM","created_at":"2026-07-04T16:41:26Z"}],"graph_snapshots":[{"event_id":"sha256:d20040ef64404d132664ff476828c764ad258a4c582e575bb49188fb3be694fc","target":"graph","created_at":"2026-07-04T16:41:26Z","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/hep-th/0310262/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge groups (at the conformal point) in terms of the numbers of bifundamentals. We also provide a detailed analysis of four node ","authors_text":"Christopher P. Herzog","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-10-28T19:43:08Z","title":"Exceptional Collections and del Pezzo Gauge Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0310262","kind":"arxiv","version":3},"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":"sha256:45f9578ae049151a5dc1b61cec8f5ed1a13f58c6e7befa24b12c056690a16139","target":"record","created_at":"2026-07-04T16:41:26Z","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":"9cb8ecae358ce423a02658fd62c707f055433a64bade07148d34763dd227c30d","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-10-28T19:43:08Z","title_canon_sha256":"2b4ee7e6e85c8ac17a301ec9faa81660c908c1ba786644b506ca8f5988d5446b"},"schema_version":"1.0","source":{"id":"hep-th/0310262","kind":"arxiv","version":3}},"canonical_sha256":"2fe88b99ec00c92f8b96c56802f30bed78620a8ae0bc0960365a5e450db03549","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fe88b99ec00c92f8b96c56802f30bed78620a8ae0bc0960365a5e450db03549","first_computed_at":"2026-07-04T16:41:26.559235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:41:26.559235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ir3+lOD6woYiR4XdUK8FWRorlMMWJAwr3x6UEMDNp5upDb0dMRoUk7D+khSEYf6NREppXnWYwiFhjhv7Yqo1Aw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:41:26.559598Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0310262","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45f9578ae049151a5dc1b61cec8f5ed1a13f58c6e7befa24b12c056690a16139","sha256:d20040ef64404d132664ff476828c764ad258a4c582e575bb49188fb3be694fc"],"state_sha256":"fd7ee66a948b34ff6a3b5ea02a302827b95841e9938e5f9d20aae3288d66c2a2"}