{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:O4TVLEHQ445ZJ2LXD3PEBALV7R","short_pith_number":"pith:O4TVLEHQ","canonical_record":{"source":{"id":"2202.06897","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-14T17:42:53Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"title_canon_sha256":"c39303b60d351b32a71287a5cffe2fdff226d0cfc7741eaa39289ef7ee0494a1","abstract_canon_sha256":"46772084f4aa9b4e33c09c1cf92c9020fb9304b6e6b30fbb1865fb538c2fbd52"},"schema_version":"1.0"},"canonical_sha256":"77275590f0e73b94e9771ede408175fc5cfe5482b3ca7b9d08bc0d2e2bd136c1","source":{"kind":"arxiv","id":"2202.06897","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.06897","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"2202.06897v2","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06897","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"O4TVLEHQ445Z","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"pith_short_16","alias_value":"O4TVLEHQ445ZJ2LX","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"pith_short_8","alias_value":"O4TVLEHQ","created_at":"2026-07-05T05:44:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:O4TVLEHQ445ZJ2LXD3PEBALV7R","target":"record","payload":{"canonical_record":{"source":{"id":"2202.06897","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-14T17:42:53Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"title_canon_sha256":"c39303b60d351b32a71287a5cffe2fdff226d0cfc7741eaa39289ef7ee0494a1","abstract_canon_sha256":"46772084f4aa9b4e33c09c1cf92c9020fb9304b6e6b30fbb1865fb538c2fbd52"},"schema_version":"1.0"},"canonical_sha256":"77275590f0e73b94e9771ede408175fc5cfe5482b3ca7b9d08bc0d2e2bd136c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:44:37.390429Z","signature_b64":"7AlODJvwWIWzwpLJbDkrnYqtz1bciEz41jKKZcD5VtuozfLXg7YPpSjQbmbrlK5bMSpIQCw1bG7T/J096z6JAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77275590f0e73b94e9771ede408175fc5cfe5482b3ca7b9d08bc0d2e2bd136c1","last_reissued_at":"2026-07-05T05:44:37.389884Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:44:37.389884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.06897","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":"2026-07-05T05:44:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4+gw2+F+/xuVVm1O158E2z/Dka/M54rQziJgbCdWYltBruhytWa6LntCtARCQn55kh/4k2QAaMeQVWGVIHCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:51:31.653730Z"},"content_sha256":"b77371cfb3d2dfd187a499d6c7200907b204299f97aa1b15f1ea7ebeb56827ca","schema_version":"1.0","event_id":"sha256:b77371cfb3d2dfd187a499d6c7200907b204299f97aa1b15f1ea7ebeb56827ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:O4TVLEHQ445ZJ2LXD3PEBALV7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unitary matrix models, free fermion ensembles, and the giant graviton expansion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"primary_cat":"hep-th","authors_text":"Sameer Murthy","submitted_at":"2022-02-14T17:42:53Z","abstract_excerpt":"We consider a class of matrix integrals over the unitary group $U(N)$ with an infinite set of couplings characterized by a series $f(q)=\\sum_{n \\ge 1} a_n q^n$, with $a_n \\in \\mathbb{Z}$. Such integrals arise in physics as the partition functions of free four-dimensional gauge theories on $S^3$ and, in particular, as the superconformal index of super Yang-Mills theory. We show that any such model can be expressed in terms of a system of free fermions in an ensemble parameterized by the infinite set of couplings. Integrating out the fermions in a given quantum state leads to a convergent expans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06897","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/2202.06897/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":"2026-07-05T05:44:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrlEASu5wu9I9dF74Tn6yUHiXlL5E+/VL14D73pxWtBgFYRYan+SYw341/op9do7IRvVK8Ys3h9nJf0z7vr2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:51:31.654619Z"},"content_sha256":"bad945f71ffcce3d098f74760cec1c0a18df4721aa7aef8fa5276f0491fe49e7","schema_version":"1.0","event_id":"sha256:bad945f71ffcce3d098f74760cec1c0a18df4721aa7aef8fa5276f0491fe49e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R/bundle.json","state_url":"https://pith.science/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R/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":"2026-08-04T10:51:31Z","links":{"resolver":"https://pith.science/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R","bundle":"https://pith.science/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R/bundle.json","state":"https://pith.science/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4TVLEHQ445ZJ2LXD3PEBALV7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:O4TVLEHQ445ZJ2LXD3PEBALV7R","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":"46772084f4aa9b4e33c09c1cf92c9020fb9304b6e6b30fbb1865fb538c2fbd52","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-14T17:42:53Z","title_canon_sha256":"c39303b60d351b32a71287a5cffe2fdff226d0cfc7741eaa39289ef7ee0494a1"},"schema_version":"1.0","source":{"id":"2202.06897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.06897","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"2202.06897v2","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06897","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"O4TVLEHQ445Z","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"pith_short_16","alias_value":"O4TVLEHQ445ZJ2LX","created_at":"2026-07-05T05:44:37Z"},{"alias_kind":"pith_short_8","alias_value":"O4TVLEHQ","created_at":"2026-07-05T05:44:37Z"}],"graph_snapshots":[{"event_id":"sha256:bad945f71ffcce3d098f74760cec1c0a18df4721aa7aef8fa5276f0491fe49e7","target":"graph","created_at":"2026-07-05T05:44:37Z","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/2202.06897/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a class of matrix integrals over the unitary group $U(N)$ with an infinite set of couplings characterized by a series $f(q)=\\sum_{n \\ge 1} a_n q^n$, with $a_n \\in \\mathbb{Z}$. Such integrals arise in physics as the partition functions of free four-dimensional gauge theories on $S^3$ and, in particular, as the superconformal index of super Yang-Mills theory. We show that any such model can be expressed in terms of a system of free fermions in an ensemble parameterized by the infinite set of couplings. Integrating out the fermions in a given quantum state leads to a convergent expans","authors_text":"Sameer Murthy","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-14T17:42:53Z","title":"Unitary matrix models, free fermion ensembles, and the giant graviton expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06897","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:b77371cfb3d2dfd187a499d6c7200907b204299f97aa1b15f1ea7ebeb56827ca","target":"record","created_at":"2026-07-05T05:44:37Z","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":"46772084f4aa9b4e33c09c1cf92c9020fb9304b6e6b30fbb1865fb538c2fbd52","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-14T17:42:53Z","title_canon_sha256":"c39303b60d351b32a71287a5cffe2fdff226d0cfc7741eaa39289ef7ee0494a1"},"schema_version":"1.0","source":{"id":"2202.06897","kind":"arxiv","version":2}},"canonical_sha256":"77275590f0e73b94e9771ede408175fc5cfe5482b3ca7b9d08bc0d2e2bd136c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77275590f0e73b94e9771ede408175fc5cfe5482b3ca7b9d08bc0d2e2bd136c1","first_computed_at":"2026-07-05T05:44:37.389884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:44:37.389884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7AlODJvwWIWzwpLJbDkrnYqtz1bciEz41jKKZcD5VtuozfLXg7YPpSjQbmbrlK5bMSpIQCw1bG7T/J096z6JAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:44:37.390429Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.06897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b77371cfb3d2dfd187a499d6c7200907b204299f97aa1b15f1ea7ebeb56827ca","sha256:bad945f71ffcce3d098f74760cec1c0a18df4721aa7aef8fa5276f0491fe49e7"],"state_sha256":"a24ef32665db94ae28158208475f9fb23581ad12b47b5c645d7bc1f647c9a1d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2z55wTSh5qQ1xLBJ+lMLD3u6l4vF1kU+KShWUbmMRG6vV2oI85Cv2hBmibHDETpa6IZMsn4ap9OnUq28fG/TBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T10:51:31.660585Z","bundle_sha256":"5f6b0d583dea0f3ac13c0a3f127b80ad9cb136b1efb9df0bbdba9be14807c338"}}