{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:VHQFEB5JWHBDGZIVEEQWMLJWBW","short_pith_number":"pith:VHQFEB5J","canonical_record":{"source":{"id":"2212.05408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-11T04:45:25Z","cross_cats_sorted":[],"title_canon_sha256":"c9f3c7fda9646da338d5b1c2a28ee3c3ff979397efc47ace55afbb00a2eb204c","abstract_canon_sha256":"81eba7d01d7e2dba05f99158580174c7e750d2087c9b5360362b6884ee06e028"},"schema_version":"1.0"},"canonical_sha256":"a9e05207a9b1c23365152121662d360db353045e99f4e00e9e981d612e1d4d35","source":{"kind":"arxiv","id":"2212.05408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.05408","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"2212.05408v2","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.05408","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"VHQFEB5JWHBD","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"pith_short_16","alias_value":"VHQFEB5JWHBDGZIV","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"pith_short_8","alias_value":"VHQFEB5J","created_at":"2026-07-05T06:08:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:VHQFEB5JWHBDGZIVEEQWMLJWBW","target":"record","payload":{"canonical_record":{"source":{"id":"2212.05408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-11T04:45:25Z","cross_cats_sorted":[],"title_canon_sha256":"c9f3c7fda9646da338d5b1c2a28ee3c3ff979397efc47ace55afbb00a2eb204c","abstract_canon_sha256":"81eba7d01d7e2dba05f99158580174c7e750d2087c9b5360362b6884ee06e028"},"schema_version":"1.0"},"canonical_sha256":"a9e05207a9b1c23365152121662d360db353045e99f4e00e9e981d612e1d4d35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:08:15.271481Z","signature_b64":"aGl6pEDigSyzhPOZk0XPgK06ad1KunoMEnvenQH21ZHDysliolCl1Z/BaEyrir49gyKPuYrdKbKY3LLhkfK1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9e05207a9b1c23365152121662d360db353045e99f4e00e9e981d612e1d4d35","last_reissued_at":"2026-07-05T06:08:15.271061Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:08:15.271061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.05408","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":"2026-07-05T06:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6N4YxOo2xV8fYSxLeebWEEm4vHWti00bmUmbf1A+rS2B+xvm9jkJDDhaN/bQwJJW7uluOPva4NejG31d0ctICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T12:22:59.760962Z"},"content_sha256":"69d4d451aaa2995132d5e01bab57a45a2f1de77fdab0afe657becf1435ab58f5","schema_version":"1.0","event_id":"sha256:69d4d451aaa2995132d5e01bab57a45a2f1de77fdab0afe657becf1435ab58f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:VHQFEB5JWHBDGZIVEEQWMLJWBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite $N$ indices and the giant graviton expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"James T. Liu, Neville Joshua Rajappa","submitted_at":"2022-12-11T04:45:25Z","abstract_excerpt":"The superconformal index of $\\mathcal N=4$ super-Yang Mills theory with $U(N)$ gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for the case of a single giant graviton. Here we give similar explicit formulae for an arbitrary number, $m\\ge1$, of giant gravitons. We provide 1/2 and 1/16 BPS index examples up to the order where three giant gravitons contribute and demonstrate that the expansion of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.05408","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/2212.05408/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":"2026-07-05T06:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBCA89AtF3hz+p5RiHR5IMx7OuS35eMoHVFnGVZBKarTRrclruSRXWP1g1OhFMzTqOBjBDfcwFx7e6Iw5zh7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T12:22:59.761457Z"},"content_sha256":"694e7d05cc1d3ee2d786635824fefeb176b84d9a2c03d1e9c2fc14a25a6d3bec","schema_version":"1.0","event_id":"sha256:694e7d05cc1d3ee2d786635824fefeb176b84d9a2c03d1e9c2fc14a25a6d3bec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW/bundle.json","state_url":"https://pith.science/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW/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":"2026-08-01T12:22:59Z","links":{"resolver":"https://pith.science/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW","bundle":"https://pith.science/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW/bundle.json","state":"https://pith.science/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHQFEB5JWHBDGZIVEEQWMLJWBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VHQFEB5JWHBDGZIVEEQWMLJWBW","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":"81eba7d01d7e2dba05f99158580174c7e750d2087c9b5360362b6884ee06e028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-11T04:45:25Z","title_canon_sha256":"c9f3c7fda9646da338d5b1c2a28ee3c3ff979397efc47ace55afbb00a2eb204c"},"schema_version":"1.0","source":{"id":"2212.05408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.05408","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"2212.05408v2","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.05408","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"VHQFEB5JWHBD","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"pith_short_16","alias_value":"VHQFEB5JWHBDGZIV","created_at":"2026-07-05T06:08:15Z"},{"alias_kind":"pith_short_8","alias_value":"VHQFEB5J","created_at":"2026-07-05T06:08:15Z"}],"graph_snapshots":[{"event_id":"sha256:694e7d05cc1d3ee2d786635824fefeb176b84d9a2c03d1e9c2fc14a25a6d3bec","target":"graph","created_at":"2026-07-05T06:08:15Z","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/2212.05408/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The superconformal index of $\\mathcal N=4$ super-Yang Mills theory with $U(N)$ gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for the case of a single giant graviton. Here we give similar explicit formulae for an arbitrary number, $m\\ge1$, of giant gravitons. We provide 1/2 and 1/16 BPS index examples up to the order where three giant gravitons contribute and demonstrate that the expansion of the ","authors_text":"James T. Liu, Neville Joshua Rajappa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-11T04:45:25Z","title":"Finite $N$ indices and the giant graviton expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.05408","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":"sha256:69d4d451aaa2995132d5e01bab57a45a2f1de77fdab0afe657becf1435ab58f5","target":"record","created_at":"2026-07-05T06:08:15Z","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":"81eba7d01d7e2dba05f99158580174c7e750d2087c9b5360362b6884ee06e028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-11T04:45:25Z","title_canon_sha256":"c9f3c7fda9646da338d5b1c2a28ee3c3ff979397efc47ace55afbb00a2eb204c"},"schema_version":"1.0","source":{"id":"2212.05408","kind":"arxiv","version":2}},"canonical_sha256":"a9e05207a9b1c23365152121662d360db353045e99f4e00e9e981d612e1d4d35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9e05207a9b1c23365152121662d360db353045e99f4e00e9e981d612e1d4d35","first_computed_at":"2026-07-05T06:08:15.271061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:08:15.271061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aGl6pEDigSyzhPOZk0XPgK06ad1KunoMEnvenQH21ZHDysliolCl1Z/BaEyrir49gyKPuYrdKbKY3LLhkfK1DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:08:15.271481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.05408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69d4d451aaa2995132d5e01bab57a45a2f1de77fdab0afe657becf1435ab58f5","sha256:694e7d05cc1d3ee2d786635824fefeb176b84d9a2c03d1e9c2fc14a25a6d3bec"],"state_sha256":"cdb1eeb7df0452b7988553123b68fc0cb8c8c4329d8f1d0fb8bbe8907c83dc71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oG3Y9juQXJcwHe1bt2JwEpa68+xJJkCy5+FkKxEjAF5VGuHQ8P4CnfH6z+atkCFGP/5DBvdRo7z7lNtaYPHmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T12:22:59.765912Z","bundle_sha256":"09d77949fa75493634740297f7ef0c34a367d961cc29bd6ca589b7a4b60ee366"}}