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In a certain scaling limit, the big $q$-Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of JT gravity with an EOW brane. We also compute the half-wormhole amplitude in DSSYK and show that the amplitude is decomposed into the trumpet and the factor coming from the EOW brane."},"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":"2305.12674","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-05-22T03:28:46Z","cross_cats_sorted":[],"title_canon_sha256":"b4282fc6929765bdc0bd73712da56a5570cc33a7d1b608ffd13b2ffc2cd4ebdb","abstract_canon_sha256":"660208e8af4e8bdd11ca90ab9dcc2a9e49af8411a443d8b92181f313992d6fc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:37:32.880592Z","signature_b64":"qB6nC9AxQEHSXW08jT0k+efjGj9WdEtvbdFrA1ZBra1qeGn+EqfXDZqUzwYvSvUAVGjA69QGV/zA+lYTdVDrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b299dfb5c50a3e1547c86bc40fa1babdb31982ea0490efd3b71adda5e9f2611a","last_reissued_at":"2026-07-05T06:37:32.880104Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:37:32.880104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"End of the world brane in double scaled SYK","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Kazumi Okuyama","submitted_at":"2023-05-22T03:28:46Z","abstract_excerpt":"We study the end of the world (EOW) brane in double scaled SYK (DSSYK) model. We find that the boundary state of EOW brane is a coherent state of the $q$-deformed oscillators and the associated orthogonal polynomial is the continuous big $q$-Hermite polynomial. In a certain scaling limit, the big $q$-Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of JT gravity with an EOW brane. 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