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The corresponding microcanonical sector of the $\\mathcal{N}=4$ superconformal index is obtained by projecting to equal charges, or equivalently by extracting the constant term in the two charge-difference fugacities. We prove that for the large-$N$ multigraviton sector the projected index factorizes exactly as \\[\n  \\mathcal{I}^{\\rm eqQ}_\\infty(x,p)\n  =\\prod_{k\\ge1}(1-p^kx^{3k})(1-p^{-k}x^{3k})\n  \\sum_{n\\ge0}\\mathsf{p}(n)^3x^{6n}, \\] where $\\mathsf{p}(n)$ is the partition function. This factorization gives"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.03735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-04T06:44:40Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"f0e0208fbfa078a592cbf3c8dbb7a0fe3675ee051ffd9f8221af2c58b230d9a7","abstract_canon_sha256":"d53ba4171c28162ec5cc1680f7d5b8e2fa55a3d1eb85d2b3659c4bad72dd432d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:04.473286Z","signature_b64":"RnoBr119VdCNEi919enyyn45/hAdlmV0wf+yUK+A8LISc4fQM2lVQSrZPH7gotSdtjj9U+zid7yxR3uVlEtFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"166a48ef90ff078ffca9e8776211ce50c05017faa42ef0db76291a8291651f04","last_reissued_at":"2026-07-07T02:18:04.472547Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:04.472547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equal-charge projection of the $\\mathcal{N}=4$ index: exact large-$N$ formula and finite-rank $U(3)$ coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Miguel Tierz","submitted_at":"2026-07-04T06:44:40Z","abstract_excerpt":"The equal-charge branch of supersymmetric rotating AdS$_5$ black holes has $Q_1=Q_2=Q_3$. The corresponding microcanonical sector of the $\\mathcal{N}=4$ superconformal index is obtained by projecting to equal charges, or equivalently by extracting the constant term in the two charge-difference fugacities. We prove that for the large-$N$ multigraviton sector the projected index factorizes exactly as \\[\n  \\mathcal{I}^{\\rm eqQ}_\\infty(x,p)\n  =\\prod_{k\\ge1}(1-p^kx^{3k})(1-p^{-k}x^{3k})\n  \\sum_{n\\ge0}\\mathsf{p}(n)^3x^{6n}, \\] where $\\mathsf{p}(n)$ is the partition function. This factorization gives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03735","kind":"arxiv","version":1},"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/2607.03735/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.03735","created_at":"2026-07-07T02:18:04.472662+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.03735v1","created_at":"2026-07-07T02:18:04.472662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03735","created_at":"2026-07-07T02:18:04.472662+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZVER34Q74DY","created_at":"2026-07-07T02:18:04.472662+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZVER34Q74DY77FJ","created_at":"2026-07-07T02:18:04.472662+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZVER34Q","created_at":"2026-07-07T02:18:04.472662+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD","json":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD.json","graph_json":"https://pith.science/api/pith-number/CZVER34Q74DY77FJ5B3WEEOOKD/graph.json","events_json":"https://pith.science/api/pith-number/CZVER34Q74DY77FJ5B3WEEOOKD/events.json","paper":"https://pith.science/paper/CZVER34Q"},"agent_actions":{"view_html":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD","download_json":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD.json","view_paper":"https://pith.science/paper/CZVER34Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.03735&json=true","fetch_graph":"https://pith.science/api/pith-number/CZVER34Q74DY77FJ5B3WEEOOKD/graph.json","fetch_events":"https://pith.science/api/pith-number/CZVER34Q74DY77FJ5B3WEEOOKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD/action/storage_attestation","attest_author":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD/action/author_attestation","sign_citation":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD/action/citation_signature","submit_replication":"https://pith.science/pith/CZVER34Q74DY77FJ5B3WEEOOKD/action/replication_record"}},"created_at":"2026-07-07T02:18:04.472662+00:00","updated_at":"2026-07-07T02:18:04.472662+00:00"}