{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:MVF6CUE3UFMLZKZVOGVDTCCMYU","short_pith_number":"pith:MVF6CUE3","schema_version":"1.0","canonical_sha256":"654be1509ba158bcab3571aa39884cc51b55de7971399790820545e82238d501","source":{"kind":"arxiv","id":"2102.03136","version":1},"attestation_state":"computed","paper":{"title":"Poincar\\'e Series, 3d Gravity and Averages of Rational CFT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Palash Singh, Sunil Mukhi, Viraj Meruliya","submitted_at":"2021-02-05T12:26:50Z","abstract_excerpt":"We investigate the Poincar\\'e approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)$_k$ WZW models provide unitary examples for which the Poincare series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT's sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and al"},"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":"2102.03136","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-02-05T12:26:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"112f1a49dc793cef34f28f6ce4dc3a64bc50b49483c773cba9a0f826adfbbc5e","abstract_canon_sha256":"3e9080827eddff0ad482822d2e5ce0c4737cf7fa0278aab2267a32c4081ad2dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:39:14.088618Z","signature_b64":"7UqeqBfehr40zhOxOxPNWYWCrrZngCQYiUaIX9JbayDzqFDBePkLDdW38fiQhoLntBunO2lYcYssqIVKny4ODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"654be1509ba158bcab3571aa39884cc51b55de7971399790820545e82238d501","last_reissued_at":"2026-07-05T02:39:14.088174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:39:14.088174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e Series, 3d Gravity and Averages of Rational CFT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Palash Singh, Sunil Mukhi, Viraj Meruliya","submitted_at":"2021-02-05T12:26:50Z","abstract_excerpt":"We investigate the Poincar\\'e approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)$_k$ WZW models provide unitary examples for which the Poincare series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT's sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.03136","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/2102.03136/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":"2102.03136","created_at":"2026-07-05T02:39:14.088221+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.03136v1","created_at":"2026-07-05T02:39:14.088221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.03136","created_at":"2026-07-05T02:39:14.088221+00:00"},{"alias_kind":"pith_short_12","alias_value":"MVF6CUE3UFML","created_at":"2026-07-05T02:39:14.088221+00:00"},{"alias_kind":"pith_short_16","alias_value":"MVF6CUE3UFMLZKZV","created_at":"2026-07-05T02:39:14.088221+00:00"},{"alias_kind":"pith_short_8","alias_value":"MVF6CUE3","created_at":"2026-07-05T02:39:14.088221+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2505.03068","citing_title":"M\\\"obius randomness in the Hartle-Hawking state","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12590","citing_title":"A solvable model of 3d quantum gravity","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01072","citing_title":"Reconstructing conformal field theoretical compositions with Transformers","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU","json":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU.json","graph_json":"https://pith.science/api/pith-number/MVF6CUE3UFMLZKZVOGVDTCCMYU/graph.json","events_json":"https://pith.science/api/pith-number/MVF6CUE3UFMLZKZVOGVDTCCMYU/events.json","paper":"https://pith.science/paper/MVF6CUE3"},"agent_actions":{"view_html":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU","download_json":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU.json","view_paper":"https://pith.science/paper/MVF6CUE3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.03136&json=true","fetch_graph":"https://pith.science/api/pith-number/MVF6CUE3UFMLZKZVOGVDTCCMYU/graph.json","fetch_events":"https://pith.science/api/pith-number/MVF6CUE3UFMLZKZVOGVDTCCMYU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU/action/storage_attestation","attest_author":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU/action/author_attestation","sign_citation":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU/action/citation_signature","submit_replication":"https://pith.science/pith/MVF6CUE3UFMLZKZVOGVDTCCMYU/action/replication_record"}},"created_at":"2026-07-05T02:39:14.088221+00:00","updated_at":"2026-07-05T02:39:14.088221+00:00"}