{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ABJKH5SXULV4ERHUVLOBGFU5K6","short_pith_number":"pith:ABJKH5SX","canonical_record":{"source":{"id":"1210.4403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-10-16T13:41:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6402595976d7b533cd0cd072526915a32ecfc5844a44f096e53f86a67dcb6587","abstract_canon_sha256":"af8bb93acefe7c2210c48b4b9e648f942569780affd4974abeb96ec3bc822574"},"schema_version":"1.0"},"canonical_sha256":"0052a3f657a2ebc244f4aadc13169d57861fe52276f4f3d31a5480ce70208a45","source":{"kind":"arxiv","id":"1210.4403","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4403","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4403v2","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4403","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"ABJKH5SXULV4","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ABJKH5SXULV4ERHU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ABJKH5SX","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ABJKH5SXULV4ERHUVLOBGFU5K6","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-10-16T13:41:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6402595976d7b533cd0cd072526915a32ecfc5844a44f096e53f86a67dcb6587","abstract_canon_sha256":"af8bb93acefe7c2210c48b4b9e648f942569780affd4974abeb96ec3bc822574"},"schema_version":"1.0"},"canonical_sha256":"0052a3f657a2ebc244f4aadc13169d57861fe52276f4f3d31a5480ce70208a45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:45.865484Z","signature_b64":"Q6HpCbpn5OtHSu3HZ775POdLjm5ZsbeMz0gb8BrM1n+snbuwk257mpUJPy9vkzzxF0vZEVNlXHQwDsgkw7f3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0052a3f657a2ebc244f4aadc13169d57861fe52276f4f3d31a5480ce70208a45","last_reissued_at":"2026-05-18T03:38:45.864630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:45.864630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4403","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":"2026-05-18T03:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ene3vcsRN7NnyJdKZ207mYT2RuUmGTYg5Habj41VN4RvJ1IdFq+5D8pvbni/3CNDEBGumI3ey33M8f+xW3EdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:23:59.942118Z"},"content_sha256":"7af37de5a9ca1325e996d605db670d77ca2e17d3e4bc9cd8b5a56a1b6f0ca2d7","schema_version":"1.0","event_id":"sha256:7af37de5a9ca1325e996d605db670d77ca2e17d3e4bc9cd8b5a56a1b6f0ca2d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ABJKH5SXULV4ERHUVLOBGFU5K6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The refined BPS index from stable pair invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Albrecht Klemm, Jinwon Choi, Sheldon Katz","submitted_at":"2012-10-16T13:41:24Z","abstract_excerpt":"A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi-Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with respect to a C* action on the stable pair moduli space, or alternatively the equivariant index of Nekrasov and Okounkov. This effectively calculates the refined index for M-theory reduced on these Calabi-Yau geometries. Based on physical expectations we propose a product formula for the refined invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local P^1. We explicitly compute "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4403","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":""},"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":"2026-05-18T03:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kMJIdgQh5Yc9nFp5we3RvB9zq+pBx00ylGzz2WNVKZ3zik3lScM7ghx373LGMQrz7PNhgh6J8F2irSvH/CD6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:23:59.942857Z"},"content_sha256":"e08248b0a67f6ef76b9d193da9bffc3b713bb98086d03d2135b3ae24b0538ce7","schema_version":"1.0","event_id":"sha256:e08248b0a67f6ef76b9d193da9bffc3b713bb98086d03d2135b3ae24b0538ce7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABJKH5SXULV4ERHUVLOBGFU5K6/bundle.json","state_url":"https://pith.science/pith/ABJKH5SXULV4ERHUVLOBGFU5K6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABJKH5SXULV4ERHUVLOBGFU5K6/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":"2026-06-08T03:23:59Z","links":{"resolver":"https://pith.science/pith/ABJKH5SXULV4ERHUVLOBGFU5K6","bundle":"https://pith.science/pith/ABJKH5SXULV4ERHUVLOBGFU5K6/bundle.json","state":"https://pith.science/pith/ABJKH5SXULV4ERHUVLOBGFU5K6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABJKH5SXULV4ERHUVLOBGFU5K6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ABJKH5SXULV4ERHUVLOBGFU5K6","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":"af8bb93acefe7c2210c48b4b9e648f942569780affd4974abeb96ec3bc822574","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-10-16T13:41:24Z","title_canon_sha256":"6402595976d7b533cd0cd072526915a32ecfc5844a44f096e53f86a67dcb6587"},"schema_version":"1.0","source":{"id":"1210.4403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4403","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4403v2","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4403","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"ABJKH5SXULV4","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ABJKH5SXULV4ERHU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ABJKH5SX","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:e08248b0a67f6ef76b9d193da9bffc3b713bb98086d03d2135b3ae24b0538ce7","target":"graph","created_at":"2026-05-18T03:38:45Z","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":"A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi-Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with respect to a C* action on the stable pair moduli space, or alternatively the equivariant index of Nekrasov and Okounkov. This effectively calculates the refined index for M-theory reduced on these Calabi-Yau geometries. Based on physical expectations we propose a product formula for the refined invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local P^1. We explicitly compute ","authors_text":"Albrecht Klemm, Jinwon Choi, Sheldon Katz","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-10-16T13:41:24Z","title":"The refined BPS index from stable pair invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4403","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":"sha256:7af37de5a9ca1325e996d605db670d77ca2e17d3e4bc9cd8b5a56a1b6f0ca2d7","target":"record","created_at":"2026-05-18T03:38:45Z","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":"af8bb93acefe7c2210c48b4b9e648f942569780affd4974abeb96ec3bc822574","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-10-16T13:41:24Z","title_canon_sha256":"6402595976d7b533cd0cd072526915a32ecfc5844a44f096e53f86a67dcb6587"},"schema_version":"1.0","source":{"id":"1210.4403","kind":"arxiv","version":2}},"canonical_sha256":"0052a3f657a2ebc244f4aadc13169d57861fe52276f4f3d31a5480ce70208a45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0052a3f657a2ebc244f4aadc13169d57861fe52276f4f3d31a5480ce70208a45","first_computed_at":"2026-05-18T03:38:45.864630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:45.864630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q6HpCbpn5OtHSu3HZ775POdLjm5ZsbeMz0gb8BrM1n+snbuwk257mpUJPy9vkzzxF0vZEVNlXHQwDsgkw7f3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:45.865484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7af37de5a9ca1325e996d605db670d77ca2e17d3e4bc9cd8b5a56a1b6f0ca2d7","sha256:e08248b0a67f6ef76b9d193da9bffc3b713bb98086d03d2135b3ae24b0538ce7"],"state_sha256":"14419a7609e875457192845390a449851c933a1dca5cf38ae022b5c18743af97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q63a80GMfyg63pS7bixBO6IPpMpGmfH5CVQow+ljouY76M6HMIhWyyCig7G6niLd6nJly21Y56iP3qbDT3qvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:23:59.946641Z","bundle_sha256":"6263774029e2138b89e611d8fde1646cc3294d780effb32b01e942e28cbdc82e"}}