{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"82bc02119f75e5e70e87b881fbacd60c71fd5585e72bf569baf35784cb9c6d61","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["1232c36fa3b984b9f7e8b0fcea61df77159a03e98ae63ab6c1ea1036aaf3955c","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"08d46b950144ee86f6f79f3be5019a3539150330965b19e894b879428d8a4df7","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"mathph.quantum-chaos.hilbert-polya","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"If the Riemann zeros were the energy levels of a quantum system, they would all be real numbers, which is the Riemann hypothesis. The task is to find such a system.","posed_since":"","precise":"Find a self-adjoint operator $H$ on a Hilbert space, defined independently of the zeros, with spectrum $\\{\\gamma_n\\}$ where $\\zeta(1/2 + i \\gamma_n) = 0$, and prove the spectral identity. The Berry-Keating proposal $H = xp$ with suitable boundary conditions reproduces the smooth counting function $N(E) \\sim (E/(2 \\pi)) \\log(E/(2 \\pi e)) + 7/8$ but not the individual zeros. Answer: an explicit operator with proof.","problem_ref":"1232c36fa3b984b9f7e8b0fcea61df77159a03e98ae63ab6c1ea1036aaf3955c","references":"","settled_by":"A proof that the spectrum of an explicitly constructed self-adjoint operator equals the set of nontrivial zeros.","status_note":"Connes and collaborators proposed trace-formula and prolate-operator constructions (1998 to 2026) whose low spectra approach the zeros numerically; no proof of the identity.","title":"A self-adjoint operator whose eigenvalues are the Riemann zeros","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"be9044b7353def82e0aa54d9e68ee2996ffe2803dd73d9261279d16c24a7493a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"9ff02bd0ccf7b4b3db6980b2ca2c8758e47842bb0fc8ace650c63a1346a56aef","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"AryuhqaS0u2bKzLbCC3_LuADMqqiGaDXrRtvqJaEs1u7332wMbkb-DUsLzYurbcdmLJ_u-InJ9J-Vkmx-MwWAw"},"schema":"pubphys.envelope/1"},"record_hash":"be9044b7353def82e0aa54d9e68ee2996ffe2803dd73d9261279d16c24a7493a","leaf_index":3444}