{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TEIGLNUHZPWY7VQTYBB56RXXHM","short_pith_number":"pith:TEIGLNUH","canonical_record":{"source":{"id":"1311.7476","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-29T07:49:44Z","cross_cats_sorted":[],"title_canon_sha256":"59ed26713d1e8cdb43729ee180f2211ff2a780c6856edd089c77df051c4fa017","abstract_canon_sha256":"2bcbc4913251fb0ae878c8099f5d92ff90c907da945451489f4d83e9060b2616"},"schema_version":"1.0"},"canonical_sha256":"991065b687cbed8fd613c043df46f73b24fefa3f8e14ade1c5df8accaf07859e","source":{"kind":"arxiv","id":"1311.7476","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7476","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7476v4","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7476","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"TEIGLNUHZPWY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TEIGLNUHZPWY7VQT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TEIGLNUH","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TEIGLNUHZPWY7VQTYBB56RXXHM","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7476","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-29T07:49:44Z","cross_cats_sorted":[],"title_canon_sha256":"59ed26713d1e8cdb43729ee180f2211ff2a780c6856edd089c77df051c4fa017","abstract_canon_sha256":"2bcbc4913251fb0ae878c8099f5d92ff90c907da945451489f4d83e9060b2616"},"schema_version":"1.0"},"canonical_sha256":"991065b687cbed8fd613c043df46f73b24fefa3f8e14ade1c5df8accaf07859e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.349281Z","signature_b64":"9EB0VzlMI+VHavjvM4SNSF9RD1g61r2XyVaiXQdd4CTSclDz7+mJpWgmwpKpN0Ura+vlZWzNuoK0lgTEx3OrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"991065b687cbed8fd613c043df46f73b24fefa3f8e14ade1c5df8accaf07859e","last_reissued_at":"2026-05-18T01:21:45.348438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.348438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7476","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gVCUZQmhKuzbp9Ycd+BoXJ0FwXcvzJyjygksKZtJxF/JBW8x8XMVuJspp+Xzn+2mwIiROlh24bR+yF1DNoNdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:28:42.374627Z"},"content_sha256":"47c08fa7c2bd7aa2db89658bd7b1547914334e14612039ed8de520559a760cea","schema_version":"1.0","event_id":"sha256:47c08fa7c2bd7aa2db89658bd7b1547914334e14612039ed8de520559a760cea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TEIGLNUHZPWY7VQTYBB56RXXHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flops and the S-duality conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yukinobu Toda","submitted_at":"2013-11-29T07:49:44Z","abstract_excerpt":"We prove the transformation formula of Donaldson-Thomas (DT) invariants counting two dimensional torsion sheaves on Calabi-Yau 3-folds under flops. The error term is described by the Dedekind eta function and the Jacobi theta function, and our result gives evidence of a 3-fold version of Vafa-Witten's S-duality conjecture. As an application, we prove a blow-up formula of DT type invariants on the total spaces of canonical line bundles on smooth projective surfaces. It gives an analogue of the similar blow-up formula in the original S-duality conjecture by Yoshioka, Li-Qin and G\\\"ottsche."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7476","kind":"arxiv","version":4},"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":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hObgetYNIasoUWU/izsB4Ym0fyzIzXFQdAWa9Lokia37LtZU7YUBXYUBJxa0COqAbscwwd563a43zVneclFcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:28:42.374974Z"},"content_sha256":"fb6530252e639208824b9e1264c4819bbacdf1108ebcf3997135e6de050877e7","schema_version":"1.0","event_id":"sha256:fb6530252e639208824b9e1264c4819bbacdf1108ebcf3997135e6de050877e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEIGLNUHZPWY7VQTYBB56RXXHM/bundle.json","state_url":"https://pith.science/pith/TEIGLNUHZPWY7VQTYBB56RXXHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEIGLNUHZPWY7VQTYBB56RXXHM/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":"2026-06-06T16:28:42Z","links":{"resolver":"https://pith.science/pith/TEIGLNUHZPWY7VQTYBB56RXXHM","bundle":"https://pith.science/pith/TEIGLNUHZPWY7VQTYBB56RXXHM/bundle.json","state":"https://pith.science/pith/TEIGLNUHZPWY7VQTYBB56RXXHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEIGLNUHZPWY7VQTYBB56RXXHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TEIGLNUHZPWY7VQTYBB56RXXHM","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":"2bcbc4913251fb0ae878c8099f5d92ff90c907da945451489f4d83e9060b2616","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-29T07:49:44Z","title_canon_sha256":"59ed26713d1e8cdb43729ee180f2211ff2a780c6856edd089c77df051c4fa017"},"schema_version":"1.0","source":{"id":"1311.7476","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7476","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7476v4","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7476","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"TEIGLNUHZPWY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TEIGLNUHZPWY7VQT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TEIGLNUH","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:fb6530252e639208824b9e1264c4819bbacdf1108ebcf3997135e6de050877e7","target":"graph","created_at":"2026-05-18T01:21:45Z","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":"We prove the transformation formula of Donaldson-Thomas (DT) invariants counting two dimensional torsion sheaves on Calabi-Yau 3-folds under flops. The error term is described by the Dedekind eta function and the Jacobi theta function, and our result gives evidence of a 3-fold version of Vafa-Witten's S-duality conjecture. As an application, we prove a blow-up formula of DT type invariants on the total spaces of canonical line bundles on smooth projective surfaces. It gives an analogue of the similar blow-up formula in the original S-duality conjecture by Yoshioka, Li-Qin and G\\\"ottsche.","authors_text":"Yukinobu Toda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-29T07:49:44Z","title":"Flops and the S-duality conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7476","kind":"arxiv","version":4},"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":"sha256:47c08fa7c2bd7aa2db89658bd7b1547914334e14612039ed8de520559a760cea","target":"record","created_at":"2026-05-18T01:21:45Z","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":"2bcbc4913251fb0ae878c8099f5d92ff90c907da945451489f4d83e9060b2616","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-29T07:49:44Z","title_canon_sha256":"59ed26713d1e8cdb43729ee180f2211ff2a780c6856edd089c77df051c4fa017"},"schema_version":"1.0","source":{"id":"1311.7476","kind":"arxiv","version":4}},"canonical_sha256":"991065b687cbed8fd613c043df46f73b24fefa3f8e14ade1c5df8accaf07859e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"991065b687cbed8fd613c043df46f73b24fefa3f8e14ade1c5df8accaf07859e","first_computed_at":"2026-05-18T01:21:45.348438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:45.348438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9EB0VzlMI+VHavjvM4SNSF9RD1g61r2XyVaiXQdd4CTSclDz7+mJpWgmwpKpN0Ura+vlZWzNuoK0lgTEx3OrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:45.349281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7476","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47c08fa7c2bd7aa2db89658bd7b1547914334e14612039ed8de520559a760cea","sha256:fb6530252e639208824b9e1264c4819bbacdf1108ebcf3997135e6de050877e7"],"state_sha256":"9b74a3fbd12773432ecbfd461017fe00e5d3bc0366542286faf209fd4ad12f38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IXL+BpvtElabFLFJezFxD9u4rgywzoRFHv+6h2sCj1SFsmWqZjrcfrE1DcObUWODqTExaW+HLRqXrKlEyhlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:28:42.376938Z","bundle_sha256":"885962ce4d7261a1c7051a2fc4f47127708f9c9e6d703794bb209351c30c1af0"}}