{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:OGW6OK56BEWRPXGM2BGRR2MB5Y","short_pith_number":"pith:OGW6OK56","canonical_record":{"source":{"id":"2210.17551","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-31T17:59:59Z","cross_cats_sorted":[],"title_canon_sha256":"4cf529b69d5681f1931b01ce1aeb43c0badd83d84fb208fe00ea47a77dd415eb","abstract_canon_sha256":"f53ab60517f1c60d05703349eff0dc878264813e0d62a09bbd5a731e6d276e8a"},"schema_version":"1.0"},"canonical_sha256":"71ade72bbe092d17dcccd04d18e981ee20dce92a37b25e18602b4663a25db7c2","source":{"kind":"arxiv","id":"2210.17551","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.17551","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"2210.17551v3","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.17551","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"OGW6OK56BEWR","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"pith_short_16","alias_value":"OGW6OK56BEWRPXGM","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"pith_short_8","alias_value":"OGW6OK56","created_at":"2026-07-05T06:42:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:OGW6OK56BEWRPXGM2BGRR2MB5Y","target":"record","payload":{"canonical_record":{"source":{"id":"2210.17551","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-31T17:59:59Z","cross_cats_sorted":[],"title_canon_sha256":"4cf529b69d5681f1931b01ce1aeb43c0badd83d84fb208fe00ea47a77dd415eb","abstract_canon_sha256":"f53ab60517f1c60d05703349eff0dc878264813e0d62a09bbd5a731e6d276e8a"},"schema_version":"1.0"},"canonical_sha256":"71ade72bbe092d17dcccd04d18e981ee20dce92a37b25e18602b4663a25db7c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:42:40.601404Z","signature_b64":"4e4t3h7yf4i4ZOvZWHXnq9t6X/pOSfiPeflBBTy3LO+sw62w/hax+TX4g9eaPJU0zGVqTbniKbcbxH+RsMT+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71ade72bbe092d17dcccd04d18e981ee20dce92a37b25e18602b4663a25db7c2","last_reissued_at":"2026-07-05T06:42:40.600887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:42:40.600887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.17551","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fna101t6JBmsFgFXtwnZgX4J1U7JEvQtrSblWGETVjbf74lvLiEICXrB9C24tFpyQgRmerOJ2lkjVn2MaBDcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:30:26.169705Z"},"content_sha256":"7d4b527b6fbf79dbdb7ae1661ff628dbe5a4c86388c02d2b5225573facf2a98c","schema_version":"1.0","event_id":"sha256:7d4b527b6fbf79dbdb7ae1661ff628dbe5a4c86388c02d2b5225573facf2a98c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:OGW6OK56BEWRPXGM2BGRR2MB5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular factorization of superconformal indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Sam van Leuven, Vishnu Jejjala, Wei Li, Yang Lei","submitted_at":"2022-10-31T17:59:59Z","abstract_excerpt":"Superconformal indices of four-dimensional $\\mathcal{N}=1$ gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an $SL(3,\\mathbb{Z})$ and $SL(2,\\mathbb{Z})\\ltimes \\mathbb{Z}^2$ transformation. The former corresponds to a gluing transformation and the latter to an overall large diffeomorphism, both associated with a Heegaard splitting of the underlying geometry. The extension to more general transformations leads us to argue that a given index can be factorized in terms of a family of holomorphic blocks parametrized by m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.17551","kind":"arxiv","version":3},"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/2210.17551/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":"2026-07-05T06:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3YZvlJ+NVwd3FezblH+iifczImX9FcKDVZOCEh2mkx8+S5npVWe/dF7GX1VhmEjMNSvXZOykaURHufM7eDvJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:30:26.170277Z"},"content_sha256":"06baa7ac6071801483e427a4e7a56927f76eee76ad27fb1ab7a71f6b8fcea6ec","schema_version":"1.0","event_id":"sha256:06baa7ac6071801483e427a4e7a56927f76eee76ad27fb1ab7a71f6b8fcea6ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y/bundle.json","state_url":"https://pith.science/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y/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":"2026-08-04T06:30:26Z","links":{"resolver":"https://pith.science/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y","bundle":"https://pith.science/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y/bundle.json","state":"https://pith.science/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGW6OK56BEWRPXGM2BGRR2MB5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OGW6OK56BEWRPXGM2BGRR2MB5Y","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":"f53ab60517f1c60d05703349eff0dc878264813e0d62a09bbd5a731e6d276e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-31T17:59:59Z","title_canon_sha256":"4cf529b69d5681f1931b01ce1aeb43c0badd83d84fb208fe00ea47a77dd415eb"},"schema_version":"1.0","source":{"id":"2210.17551","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.17551","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"2210.17551v3","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.17551","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"OGW6OK56BEWR","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"pith_short_16","alias_value":"OGW6OK56BEWRPXGM","created_at":"2026-07-05T06:42:40Z"},{"alias_kind":"pith_short_8","alias_value":"OGW6OK56","created_at":"2026-07-05T06:42:40Z"}],"graph_snapshots":[{"event_id":"sha256:06baa7ac6071801483e427a4e7a56927f76eee76ad27fb1ab7a71f6b8fcea6ec","target":"graph","created_at":"2026-07-05T06:42:40Z","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/2210.17551/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Superconformal indices of four-dimensional $\\mathcal{N}=1$ gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an $SL(3,\\mathbb{Z})$ and $SL(2,\\mathbb{Z})\\ltimes \\mathbb{Z}^2$ transformation. The former corresponds to a gluing transformation and the latter to an overall large diffeomorphism, both associated with a Heegaard splitting of the underlying geometry. The extension to more general transformations leads us to argue that a given index can be factorized in terms of a family of holomorphic blocks parametrized by m","authors_text":"Sam van Leuven, Vishnu Jejjala, Wei Li, Yang Lei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-31T17:59:59Z","title":"Modular factorization of superconformal indices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.17551","kind":"arxiv","version":3},"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":"sha256:7d4b527b6fbf79dbdb7ae1661ff628dbe5a4c86388c02d2b5225573facf2a98c","target":"record","created_at":"2026-07-05T06:42:40Z","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":"f53ab60517f1c60d05703349eff0dc878264813e0d62a09bbd5a731e6d276e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-10-31T17:59:59Z","title_canon_sha256":"4cf529b69d5681f1931b01ce1aeb43c0badd83d84fb208fe00ea47a77dd415eb"},"schema_version":"1.0","source":{"id":"2210.17551","kind":"arxiv","version":3}},"canonical_sha256":"71ade72bbe092d17dcccd04d18e981ee20dce92a37b25e18602b4663a25db7c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71ade72bbe092d17dcccd04d18e981ee20dce92a37b25e18602b4663a25db7c2","first_computed_at":"2026-07-05T06:42:40.600887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:42:40.600887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4e4t3h7yf4i4ZOvZWHXnq9t6X/pOSfiPeflBBTy3LO+sw62w/hax+TX4g9eaPJU0zGVqTbniKbcbxH+RsMT+Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T06:42:40.601404Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.17551","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d4b527b6fbf79dbdb7ae1661ff628dbe5a4c86388c02d2b5225573facf2a98c","sha256:06baa7ac6071801483e427a4e7a56927f76eee76ad27fb1ab7a71f6b8fcea6ec"],"state_sha256":"b8ec37f8379e243d7ca259eb62822075223dd08f14dfe76e24f08508a21bfca3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3JK4biES6HMpTne0/zp/TktImzE1daEUynUNcNlv70P1YOFDovMcvCp9ilceKSYrUe7PWjAoWkPUj2dMHZmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:30:26.175166Z","bundle_sha256":"ce2a8123dad1103521a1b3e862331bccbc2900f73724657414cf3487aee35bb6"}}