{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:2OQI7DRRYTVG3H6B2PNSMOQVD4","short_pith_number":"pith:2OQI7DRR","canonical_record":{"source":{"id":"hep-th/0611346","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-11-30T16:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"9b405ea16ac956079c57ca74ccc00c5a64a7e1f6583433a44abc5be51c47bcac","abstract_canon_sha256":"7fef5ab1ea2d42fc63f42739848781b027671fc4f36a95494d50656206b7dcc1"},"schema_version":"1.0"},"canonical_sha256":"d3a08f8e31c4ea6d9fc1d3db263a151f1ba2ce84d109568bc6915c8d3a7b18a1","source":{"kind":"arxiv","id":"hep-th/0611346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0611346","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0611346v1","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0611346","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"2OQI7DRRYTVG","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"2OQI7DRRYTVG3H6B","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"2OQI7DRR","created_at":"2026-07-04T15:34:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:2OQI7DRRYTVG3H6B2PNSMOQVD4","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0611346","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-11-30T16:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"9b405ea16ac956079c57ca74ccc00c5a64a7e1f6583433a44abc5be51c47bcac","abstract_canon_sha256":"7fef5ab1ea2d42fc63f42739848781b027671fc4f36a95494d50656206b7dcc1"},"schema_version":"1.0"},"canonical_sha256":"d3a08f8e31c4ea6d9fc1d3db263a151f1ba2ce84d109568bc6915c8d3a7b18a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:34:28.279883Z","signature_b64":"37x4OEyrOqTpuxmOmvaqiflY/8oAczM8kgQcLqT80XJaIluI4ceW9xdps3YoBtnvblNts2unNzky2LY9HXCqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3a08f8e31c4ea6d9fc1d3db263a151f1ba2ce84d109568bc6915c8d3a7b18a1","last_reissued_at":"2026-07-04T15:34:28.279504Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:34:28.279504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0611346","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":"2026-07-04T15:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2WDOhIkLIO179POWB5tyabku1EPnOB85gIGm2s7CDU3yBekDPAmblq0wsWyysz8ZHZ6tx/hbescxNcuK3hHSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:26:18.417582Z"},"content_sha256":"065209b39c20bd6c8e10ff87efa2466301080dc29c000e7296a5c4004a3e2389","schema_version":"1.0","event_id":"sha256:065209b39c20bd6c8e10ff87efa2466301080dc29c000e7296a5c4004a3e2389"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:2OQI7DRRYTVG3H6B2PNSMOQVD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amihay Hanany, Christian Romelsberger","submitted_at":"2006-11-30T16:58:38Z","abstract_excerpt":"This note is presenting the generating functions which count the BPS operators in the chiral ring of a N=2 quiver gauge theory that lives on N D3 branes probing an ALE singularity. The difficulty in this computation arises from the fact that this quiver gauge theory has a moduli space of vacua that splits into many branches -- the Higgs, the Coulomb and mixed branches. As a result there can be operators which explore those different branches and the counting gets complicated by having to deal with such operators while avoiding over or under counting. The solution to this problem turns out to b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0611346","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/hep-th/0611346/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":"2026-07-04T15:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eX9nMFw0x+re7smmCkxK3k20/RJ3dk0LLEP9RJtVpevXK2HIqF0feuqLqVQwcaZyyzykVjVZYtwnTsyQknHaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:26:18.417952Z"},"content_sha256":"435f76e796742d2edfb0b7c97d7a417c948c5fc697322e80c7b5a5144e7e2039","schema_version":"1.0","event_id":"sha256:435f76e796742d2edfb0b7c97d7a417c948c5fc697322e80c7b5a5144e7e2039"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4/bundle.json","state_url":"https://pith.science/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4/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":"2026-08-14T08:26:18Z","links":{"resolver":"https://pith.science/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4","bundle":"https://pith.science/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4/bundle.json","state":"https://pith.science/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2OQI7DRRYTVG3H6B2PNSMOQVD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:2OQI7DRRYTVG3H6B2PNSMOQVD4","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":"7fef5ab1ea2d42fc63f42739848781b027671fc4f36a95494d50656206b7dcc1","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2006-11-30T16:58:38Z","title_canon_sha256":"9b405ea16ac956079c57ca74ccc00c5a64a7e1f6583433a44abc5be51c47bcac"},"schema_version":"1.0","source":{"id":"hep-th/0611346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0611346","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0611346v1","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0611346","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"2OQI7DRRYTVG","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"2OQI7DRRYTVG3H6B","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"2OQI7DRR","created_at":"2026-07-04T15:34:28Z"}],"graph_snapshots":[{"event_id":"sha256:435f76e796742d2edfb0b7c97d7a417c948c5fc697322e80c7b5a5144e7e2039","target":"graph","created_at":"2026-07-04T15:34:28Z","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/hep-th/0611346/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note is presenting the generating functions which count the BPS operators in the chiral ring of a N=2 quiver gauge theory that lives on N D3 branes probing an ALE singularity. The difficulty in this computation arises from the fact that this quiver gauge theory has a moduli space of vacua that splits into many branches -- the Higgs, the Coulomb and mixed branches. As a result there can be operators which explore those different branches and the counting gets complicated by having to deal with such operators while avoiding over or under counting. The solution to this problem turns out to b","authors_text":"Amihay Hanany, Christian Romelsberger","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-11-30T16:58:38Z","title":"Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0611346","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":"sha256:065209b39c20bd6c8e10ff87efa2466301080dc29c000e7296a5c4004a3e2389","target":"record","created_at":"2026-07-04T15:34:28Z","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":"7fef5ab1ea2d42fc63f42739848781b027671fc4f36a95494d50656206b7dcc1","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2006-11-30T16:58:38Z","title_canon_sha256":"9b405ea16ac956079c57ca74ccc00c5a64a7e1f6583433a44abc5be51c47bcac"},"schema_version":"1.0","source":{"id":"hep-th/0611346","kind":"arxiv","version":1}},"canonical_sha256":"d3a08f8e31c4ea6d9fc1d3db263a151f1ba2ce84d109568bc6915c8d3a7b18a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3a08f8e31c4ea6d9fc1d3db263a151f1ba2ce84d109568bc6915c8d3a7b18a1","first_computed_at":"2026-07-04T15:34:28.279504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:34:28.279504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"37x4OEyrOqTpuxmOmvaqiflY/8oAczM8kgQcLqT80XJaIluI4ceW9xdps3YoBtnvblNts2unNzky2LY9HXCqAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:34:28.279883Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0611346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065209b39c20bd6c8e10ff87efa2466301080dc29c000e7296a5c4004a3e2389","sha256:435f76e796742d2edfb0b7c97d7a417c948c5fc697322e80c7b5a5144e7e2039"],"state_sha256":"b91fb4d457a6a9dd497c8c51213620293b019ed6443f85133efc19a2926e3b84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+afZqXT1ORAW/lU1HOwaoeTOseGRDQEaeSLYi49DNeVJVlbb5qyvx/FM+K4wI8ANbJYbzDiezKtYYLOLny8tDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:26:18.421178Z","bundle_sha256":"51eb400b0647f14164e1b9157eb972633e22d3a750eaaaddc9b3e36ef45767c4"}}