{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:WHXEGUGY2YQZVTOKFZG2BGVUV5","short_pith_number":"pith:WHXEGUGY","canonical_record":{"source":{"id":"0706.1660","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-06-12T10:57:39Z","cross_cats_sorted":[],"title_canon_sha256":"f71b1880a5a7f999c9aa7daa1f2b4c88a58ec6e5b1685e322cc79f70b962c489","abstract_canon_sha256":"7bb5a9e8cc0e6dd85a46e1d026460b9dfbeb6ab382620bd7289796c3a344e51e"},"schema_version":"1.0"},"canonical_sha256":"b1ee4350d8d6219acdca2e4da09ab4af5a5f34c2a3b940e9939ad0f438baa04b","source":{"kind":"arxiv","id":"0706.1660","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.1660","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"0706.1660v1","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1660","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"WHXEGUGY2YQZ","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"pith_short_16","alias_value":"WHXEGUGY2YQZVTOK","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"pith_short_8","alias_value":"WHXEGUGY","created_at":"2026-07-04T15:18:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:WHXEGUGY2YQZVTOKFZG2BGVUV5","target":"record","payload":{"canonical_record":{"source":{"id":"0706.1660","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-06-12T10:57:39Z","cross_cats_sorted":[],"title_canon_sha256":"f71b1880a5a7f999c9aa7daa1f2b4c88a58ec6e5b1685e322cc79f70b962c489","abstract_canon_sha256":"7bb5a9e8cc0e6dd85a46e1d026460b9dfbeb6ab382620bd7289796c3a344e51e"},"schema_version":"1.0"},"canonical_sha256":"b1ee4350d8d6219acdca2e4da09ab4af5a5f34c2a3b940e9939ad0f438baa04b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:18:41.746026Z","signature_b64":"G7ezdMDnEZxreOsJRZLyYXwCiN0bLmejvUBOsUASu8BrI0azZIAJ+Xvv6YV1IFH+RY3o8/q/9pHjZxiTT/4DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1ee4350d8d6219acdca2e4da09ab4af5a5f34c2a3b940e9939ad0f438baa04b","last_reissued_at":"2026-07-04T15:18:41.745639Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:18:41.745639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.1660","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kqbRpyHBfNAfv7diaTXaVvAdyyzitBhhIBzeVoVk++bhjIF9eB7cerdPreDNb8U9FDmFphVcY9ViMj7pTmrYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T04:50:08.548270Z"},"content_sha256":"c98e44b14c37b5068f00af653e79c83a62ec1d2aec3f73be2b30153f62e7c7b8","schema_version":"1.0","event_id":"sha256:c98e44b14c37b5068f00af653e79c83a62ec1d2aec3f73be2b30153f62e7c7b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:WHXEGUGY2YQZVTOKFZG2BGVUV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brane Tilings","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Kristian D. Kennaway","submitted_at":"2007-06-12T10:57:39Z","abstract_excerpt":"We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the world-volume of a stack of D3-branes placed at the tip of a toric Calabi-Yau cone, at an ``orbifold point'' in Kaehler moduli space. These provide an infinite class of four-dimensional N=1 superconformal field theories which may be studied in the context of the AdS/CFT correspondence. It is now understood that these gauge theories are completely specified by certain two-dimensional torus graphs, called brane tilings, and the combinatorics "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1660","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0706.1660/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKe/AArcnh5sN4ZIyr9Xjt5xjUhdrsODc6NT1kawrK1pKqS7rSD2CcioQSik8hStQdY6JD5JvGpR6w4C3ekFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T04:50:08.548568Z"},"content_sha256":"28656f11d5d4d89f44b6588b099abf5604421e0bbeb9637109c998486fee3e91","schema_version":"1.0","event_id":"sha256:28656f11d5d4d89f44b6588b099abf5604421e0bbeb9637109c998486fee3e91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5/bundle.json","state_url":"https://pith.science/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-01T04:50:08Z","links":{"resolver":"https://pith.science/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5","bundle":"https://pith.science/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5/bundle.json","state":"https://pith.science/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHXEGUGY2YQZVTOKFZG2BGVUV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WHXEGUGY2YQZVTOKFZG2BGVUV5","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":"7bb5a9e8cc0e6dd85a46e1d026460b9dfbeb6ab382620bd7289796c3a344e51e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2007-06-12T10:57:39Z","title_canon_sha256":"f71b1880a5a7f999c9aa7daa1f2b4c88a58ec6e5b1685e322cc79f70b962c489"},"schema_version":"1.0","source":{"id":"0706.1660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.1660","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"0706.1660v1","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1660","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"WHXEGUGY2YQZ","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"pith_short_16","alias_value":"WHXEGUGY2YQZVTOK","created_at":"2026-07-04T15:18:41Z"},{"alias_kind":"pith_short_8","alias_value":"WHXEGUGY","created_at":"2026-07-04T15:18:41Z"}],"graph_snapshots":[{"event_id":"sha256:28656f11d5d4d89f44b6588b099abf5604421e0bbeb9637109c998486fee3e91","target":"graph","created_at":"2026-07-04T15:18:41Z","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/0706.1660/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the world-volume of a stack of D3-branes placed at the tip of a toric Calabi-Yau cone, at an ``orbifold point'' in Kaehler moduli space. These provide an infinite class of four-dimensional N=1 superconformal field theories which may be studied in the context of the AdS/CFT correspondence. It is now understood that these gauge theories are completely specified by certain two-dimensional torus graphs, called brane tilings, and the combinatorics ","authors_text":"Kristian D. Kennaway","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-06-12T10:57:39Z","title":"Brane Tilings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1660","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:c98e44b14c37b5068f00af653e79c83a62ec1d2aec3f73be2b30153f62e7c7b8","target":"record","created_at":"2026-07-04T15:18:41Z","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":"7bb5a9e8cc0e6dd85a46e1d026460b9dfbeb6ab382620bd7289796c3a344e51e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2007-06-12T10:57:39Z","title_canon_sha256":"f71b1880a5a7f999c9aa7daa1f2b4c88a58ec6e5b1685e322cc79f70b962c489"},"schema_version":"1.0","source":{"id":"0706.1660","kind":"arxiv","version":1}},"canonical_sha256":"b1ee4350d8d6219acdca2e4da09ab4af5a5f34c2a3b940e9939ad0f438baa04b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1ee4350d8d6219acdca2e4da09ab4af5a5f34c2a3b940e9939ad0f438baa04b","first_computed_at":"2026-07-04T15:18:41.745639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:18:41.745639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G7ezdMDnEZxreOsJRZLyYXwCiN0bLmejvUBOsUASu8BrI0azZIAJ+Xvv6YV1IFH+RY3o8/q/9pHjZxiTT/4DAw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:18:41.746026Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.1660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c98e44b14c37b5068f00af653e79c83a62ec1d2aec3f73be2b30153f62e7c7b8","sha256:28656f11d5d4d89f44b6588b099abf5604421e0bbeb9637109c998486fee3e91"],"state_sha256":"32758fc2834f639a43eece6853caad7729e2b5e6d9beca24d262cf6fabc49e11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xgGiQi/37JIpzwtNMaP00NQMcqJqmvkcmCbk1c/iaH5AO3CZhR+Ucjm/kb03Mz0L12zVZ4s32ANwdQDJfb9ZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T04:50:08.550959Z","bundle_sha256":"43e4daa1d9fb9283411555bfa989481e29f1705b45523b742796886f1fa38f6b"}}