{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ICBYYGDEWGCKJYP3KZVNYDLX5O","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":"28f573db3592524dbff47354a1816a1990d9604e3228fa0a048bfa95239a473f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-24T18:46:39Z","title_canon_sha256":"2f4fcd02858091acf709968eab40295c3b6cd2432b46c9e475ff19d4d3329f70"},"schema_version":"1.0","source":{"id":"1909.11118","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.11118","created_at":"2026-07-05T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1909.11118v2","created_at":"2026-07-05T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.11118","created_at":"2026-07-05T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"ICBYYGDEWGCK","created_at":"2026-07-05T01:04:02Z"},{"alias_kind":"pith_short_16","alias_value":"ICBYYGDEWGCKJYP3","created_at":"2026-07-05T01:04:02Z"},{"alias_kind":"pith_short_8","alias_value":"ICBYYGDE","created_at":"2026-07-05T01:04:02Z"}],"graph_snapshots":[{"event_id":"sha256:79b4fc29e0750f442bc1e1add4820978f1a3a847f42fdfea7c5f02af2ed936eb","target":"graph","created_at":"2026-07-05T01:04:02Z","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/1909.11118/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a formula for the torus partition sum of the symmetric product of $T\\bar T$ deformed CFT's, using previous work on long strings in (deformed) $AdS_3$, and universality. The result is given by an integral transform of the partition function for the block of the symmetric product, summed over its Hecke transforms, and is manifestly modular invariant. The spectrum is interpretable as a gas of multiply wound long strings with a particular orientation.","authors_text":"Akikazu Hashimoto, David Kutasov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-24T18:46:39Z","title":"Strings, Symmetric Products, $T \\bar{T}$ deformations and Hecke Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.11118","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":"sha256:3ddc36c6984f11d53652691687c2b7b22fa5402a6374d3f66c8dc1baff13ac8f","target":"record","created_at":"2026-07-05T01:04:02Z","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":"28f573db3592524dbff47354a1816a1990d9604e3228fa0a048bfa95239a473f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-24T18:46:39Z","title_canon_sha256":"2f4fcd02858091acf709968eab40295c3b6cd2432b46c9e475ff19d4d3329f70"},"schema_version":"1.0","source":{"id":"1909.11118","kind":"arxiv","version":2}},"canonical_sha256":"40838c1864b184a4e1fb566adc0d77eb868c6e3b78e11288039e220191cdcb32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40838c1864b184a4e1fb566adc0d77eb868c6e3b78e11288039e220191cdcb32","first_computed_at":"2026-07-05T01:04:02.404669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:04:02.404669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L6SCXdw2FgQIKVEwH8tdo4KEscZYlMqpADQqf1+dZu1i/6RWtjL1/7DOCA7Th+jpHbFszj/T4FzxFw2dBTzNAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:04:02.405109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.11118","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ddc36c6984f11d53652691687c2b7b22fa5402a6374d3f66c8dc1baff13ac8f","sha256:79b4fc29e0750f442bc1e1add4820978f1a3a847f42fdfea7c5f02af2ed936eb"],"state_sha256":"c6d855d34a9d19ab082fd028b26018414e95959a59849e2d1e2db06584b7e0bb"}