{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:PP6KVS5N5FTCBXUZTZB3WZHS44","short_pith_number":"pith:PP6KVS5N","canonical_record":{"source":{"id":"0810.5072","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-10-28T17:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"f0f5b93c639f4fd1cc1f125673272aa6b305d13729a4d8f6e2731713729c552c","abstract_canon_sha256":"a70103079a5ac4fe1e74ea70ddd050c2f18337b68ef1ee86f4adb03d56078878"},"schema_version":"1.0"},"canonical_sha256":"7bfcaacbade96620de999e43bb64f2e70df7a53e5070b37e7772a625ebd400a4","source":{"kind":"arxiv","id":"0810.5072","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.5072","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"0810.5072v2","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.5072","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"PP6KVS5N5FTC","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"pith_short_16","alias_value":"PP6KVS5N5FTCBXUZ","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"pith_short_8","alias_value":"PP6KVS5N","created_at":"2026-07-04T15:54:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:PP6KVS5N5FTCBXUZTZB3WZHS44","target":"record","payload":{"canonical_record":{"source":{"id":"0810.5072","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-10-28T17:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"f0f5b93c639f4fd1cc1f125673272aa6b305d13729a4d8f6e2731713729c552c","abstract_canon_sha256":"a70103079a5ac4fe1e74ea70ddd050c2f18337b68ef1ee86f4adb03d56078878"},"schema_version":"1.0"},"canonical_sha256":"7bfcaacbade96620de999e43bb64f2e70df7a53e5070b37e7772a625ebd400a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:54:16.421051Z","signature_b64":"YNo3oC/ONKfDP6kiVr/jlMc+6ghwkN1l2A84fzs8pdk3StnV3RDxojUUZUIDkn1d9R7YJRikZ2LUAA8zqVmNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfcaacbade96620de999e43bb64f2e70df7a53e5070b37e7772a625ebd400a4","last_reissued_at":"2026-07-04T15:54:16.420643Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:54:16.420643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.5072","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pGmtw6LgYJhIU2JtZKNFJQFOIQhwesCOazwKdXFVd2KhQgZIfqf4sGF1JIyI9HJfB0qoQPNopSfdR8JRzXdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T18:33:46.223469Z"},"content_sha256":"438dca45d91833bb0b5d6ef071f169d90a39fa268da24c5003d957fbbd92897c","schema_version":"1.0","event_id":"sha256:438dca45d91833bb0b5d6ef071f169d90a39fa268da24c5003d957fbbd92897c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:PP6KVS5N5FTCBXUZTZB3WZHS44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Daniel L. Jafferis, Wu-yen Chuang","submitted_at":"2008-10-28T17:50:17Z","abstract_excerpt":"In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kaehler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers.\n  The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.5072","kind":"arxiv","version":2},"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/0810.5072/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":"2026-07-04T15:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xQY5iaP8A2rxldum9g4/pFG9KBdpMoQwlJ8cirWnLo1nol8KOtj6PFdJ3WXtXJfzBUrTqudAy/G9tVY/fZ+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T18:33:46.224196Z"},"content_sha256":"fee9757f43b7fab490e1c5b5a30ec6d428e308d100e1f2aac74ed4b9c821af93","schema_version":"1.0","event_id":"sha256:fee9757f43b7fab490e1c5b5a30ec6d428e308d100e1f2aac74ed4b9c821af93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PP6KVS5N5FTCBXUZTZB3WZHS44/bundle.json","state_url":"https://pith.science/pith/PP6KVS5N5FTCBXUZTZB3WZHS44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PP6KVS5N5FTCBXUZTZB3WZHS44/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":"2026-07-31T18:33:46Z","links":{"resolver":"https://pith.science/pith/PP6KVS5N5FTCBXUZTZB3WZHS44","bundle":"https://pith.science/pith/PP6KVS5N5FTCBXUZTZB3WZHS44/bundle.json","state":"https://pith.science/pith/PP6KVS5N5FTCBXUZTZB3WZHS44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PP6KVS5N5FTCBXUZTZB3WZHS44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:PP6KVS5N5FTCBXUZTZB3WZHS44","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":"a70103079a5ac4fe1e74ea70ddd050c2f18337b68ef1ee86f4adb03d56078878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-10-28T17:50:17Z","title_canon_sha256":"f0f5b93c639f4fd1cc1f125673272aa6b305d13729a4d8f6e2731713729c552c"},"schema_version":"1.0","source":{"id":"0810.5072","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.5072","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"0810.5072v2","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.5072","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"PP6KVS5N5FTC","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"pith_short_16","alias_value":"PP6KVS5N5FTCBXUZ","created_at":"2026-07-04T15:54:16Z"},{"alias_kind":"pith_short_8","alias_value":"PP6KVS5N","created_at":"2026-07-04T15:54:16Z"}],"graph_snapshots":[{"event_id":"sha256:fee9757f43b7fab490e1c5b5a30ec6d428e308d100e1f2aac74ed4b9c821af93","target":"graph","created_at":"2026-07-04T15:54:16Z","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/0810.5072/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kaehler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers.\n  The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the o","authors_text":"Daniel L. Jafferis, Wu-yen Chuang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-10-28T17:50:17Z","title":"Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.5072","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":"sha256:438dca45d91833bb0b5d6ef071f169d90a39fa268da24c5003d957fbbd92897c","target":"record","created_at":"2026-07-04T15:54:16Z","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":"a70103079a5ac4fe1e74ea70ddd050c2f18337b68ef1ee86f4adb03d56078878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-10-28T17:50:17Z","title_canon_sha256":"f0f5b93c639f4fd1cc1f125673272aa6b305d13729a4d8f6e2731713729c552c"},"schema_version":"1.0","source":{"id":"0810.5072","kind":"arxiv","version":2}},"canonical_sha256":"7bfcaacbade96620de999e43bb64f2e70df7a53e5070b37e7772a625ebd400a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bfcaacbade96620de999e43bb64f2e70df7a53e5070b37e7772a625ebd400a4","first_computed_at":"2026-07-04T15:54:16.420643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:54:16.420643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNo3oC/ONKfDP6kiVr/jlMc+6ghwkN1l2A84fzs8pdk3StnV3RDxojUUZUIDkn1d9R7YJRikZ2LUAA8zqVmNBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:54:16.421051Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.5072","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:438dca45d91833bb0b5d6ef071f169d90a39fa268da24c5003d957fbbd92897c","sha256:fee9757f43b7fab490e1c5b5a30ec6d428e308d100e1f2aac74ed4b9c821af93"],"state_sha256":"b4d6523f68b54572186a8a4ab47875d05400d795ec86935841e80ef4797a2451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3DsZIt1x+nPAbCqDo1wRJ3MouO+/h7TtHAAPMi0xyip+iqTrA5lADqYejieI5GKNLQaV+1I9f/VXlHwoSomaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T18:33:46.230556Z","bundle_sha256":"675c9d6bfb49aa7473a9160ebc064377bea7d014e8237c4b197991aa611b5235"}}