{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:72DYT3P5ZWFK2TKFVEYSZMLSDK","short_pith_number":"pith:72DYT3P5","canonical_record":{"source":{"id":"0908.1194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-08T21:32:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"03f50ce3e7a1b1b6bf7c93ba0868b9f3ca9ee886f2ece4447881a8f9812bf017","abstract_canon_sha256":"a61b3af14de2d173e13c0c62ba4ee7055d3927299e83bac6dcb5ebe150b52c45"},"schema_version":"1.0"},"canonical_sha256":"fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1","source":{"kind":"arxiv","id":"0908.1194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1194","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1194v1","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1194","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"72DYT3P5ZWFK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"72DYT3P5ZWFK2TKF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"72DYT3P5","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:72DYT3P5ZWFK2TKFVEYSZMLSDK","target":"record","payload":{"canonical_record":{"source":{"id":"0908.1194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-08T21:32:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"03f50ce3e7a1b1b6bf7c93ba0868b9f3ca9ee886f2ece4447881a8f9812bf017","abstract_canon_sha256":"a61b3af14de2d173e13c0c62ba4ee7055d3927299e83bac6dcb5ebe150b52c45"},"schema_version":"1.0"},"canonical_sha256":"fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:23.822017Z","signature_b64":"6A3N+RBs3rv0am8DlADMpS6TsAnF8xCTom8Oxt0DN36DG1p/oJKW7YomATOlu1eZ0tn/rZZZrcfQBerA8gmbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1","last_reissued_at":"2026-05-18T04:18:23.821547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:23.821547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.1194","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":"2026-05-18T04:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"arUNLXunQJBK+Qn/Uw6LaDZX0qSBtrJUYBgEXX4OjwlSEyjnrAogyzHU6EqY5xfpnNLJPIbjI5T7peYLy/e8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:48:36.229738Z"},"content_sha256":"8db55f759cfcbf557829850d135db8405a79864f0a349d90fc9fd9c23f2d54cd","schema_version":"1.0","event_id":"sha256:8db55f759cfcbf557829850d135db8405a79864f0a349d90fc9fd9c23f2d54cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:72DYT3P5ZWFK2TKFVEYSZMLSDK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wall Crossing and M-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Cumrun Vafa, Hirosi Ooguri, Masahito Yamazaki, Mina Aganagic","submitted_at":"2009-08-08T21:32:54Z","abstract_excerpt":"We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi-Yau 3-fold X. When X has no compact 4-cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the Kahler moduli space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1194","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":""},"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":"2026-05-18T04:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AHGJmJkhJ8dK1OdGMdIPBfW7mxVf97i/mSoMM53YgTbYmqhUyys9UFKFpn92pu9Ne/uQou/wgkxihExt6DxUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:48:36.230078Z"},"content_sha256":"0a692b3e52186fffad6362eac9c1a360468a39b7f1c88a86c233e8c9b46f7835","schema_version":"1.0","event_id":"sha256:0a692b3e52186fffad6362eac9c1a360468a39b7f1c88a86c233e8c9b46f7835"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK/bundle.json","state_url":"https://pith.science/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK/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":"2026-05-29T18:48:36Z","links":{"resolver":"https://pith.science/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK","bundle":"https://pith.science/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK/bundle.json","state":"https://pith.science/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72DYT3P5ZWFK2TKFVEYSZMLSDK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:72DYT3P5ZWFK2TKFVEYSZMLSDK","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":"a61b3af14de2d173e13c0c62ba4ee7055d3927299e83bac6dcb5ebe150b52c45","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-08T21:32:54Z","title_canon_sha256":"03f50ce3e7a1b1b6bf7c93ba0868b9f3ca9ee886f2ece4447881a8f9812bf017"},"schema_version":"1.0","source":{"id":"0908.1194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1194","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1194v1","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1194","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"72DYT3P5ZWFK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"72DYT3P5ZWFK2TKF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"72DYT3P5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:0a692b3e52186fffad6362eac9c1a360468a39b7f1c88a86c233e8c9b46f7835","target":"graph","created_at":"2026-05-18T04:18:23Z","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 study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi-Yau 3-fold X. When X has no compact 4-cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the Kahler moduli space.","authors_text":"Cumrun Vafa, Hirosi Ooguri, Masahito Yamazaki, Mina Aganagic","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-08T21:32:54Z","title":"Wall Crossing and M-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1194","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":"sha256:8db55f759cfcbf557829850d135db8405a79864f0a349d90fc9fd9c23f2d54cd","target":"record","created_at":"2026-05-18T04:18:23Z","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":"a61b3af14de2d173e13c0c62ba4ee7055d3927299e83bac6dcb5ebe150b52c45","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-08T21:32:54Z","title_canon_sha256":"03f50ce3e7a1b1b6bf7c93ba0868b9f3ca9ee886f2ece4447881a8f9812bf017"},"schema_version":"1.0","source":{"id":"0908.1194","kind":"arxiv","version":1}},"canonical_sha256":"fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1","first_computed_at":"2026-05-18T04:18:23.821547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:23.821547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6A3N+RBs3rv0am8DlADMpS6TsAnF8xCTom8Oxt0DN36DG1p/oJKW7YomATOlu1eZ0tn/rZZZrcfQBerA8gmbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:23.822017Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8db55f759cfcbf557829850d135db8405a79864f0a349d90fc9fd9c23f2d54cd","sha256:0a692b3e52186fffad6362eac9c1a360468a39b7f1c88a86c233e8c9b46f7835"],"state_sha256":"5b1bd46601afefe54df84936cce514248adedbbba8118f097855a84ce0ead801"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qIgdCWhaB5govAFAy4Y6CSDWPr8WZtb2dj9shh71lqn2rclqv4PkMrKrm8Ql3GjjSF/SQRVb49yD/FG37v33Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:48:36.232120Z","bundle_sha256":"39834c194af6053ab6f912d1fb286c41d0a68866e36b86b8c014cfe6c127e19d"}}