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    "content": "# D-034 \u2014 Task (\u2605)a: literature map for the Wiener\u2013Hopf / resolvent-convergence attack on (\u2605)\nDate: 2026-08-18 | Session: 006 cont.8 | Task: (\u2605) analytic attack\nStatus: complete. Sources recorded per \u00a74A.3.\n\n## 1. Direct hits: none \u2014 the (\u2605) framing is new territory\n- arXiv sweep \"Wiener\u2013Hopf + Riemann\": 26 hits, ALL Riemann\u2013Hilbert /\n  Riemann-surface / gravitational \u2014 NO paper connects Wiener\u2013Hopf\n  factorization to RH, \u03b6-zeros, or explicit formulas. The WH reading of\n  Cor 1.6 (D-026) appears to be genuinely uncharted as a framing.\n- Screw-function corpus (all Suzuki): 2206.03682 (JLMS 2023 \u2014 screw\n  function of \u03b6, RH-equivalences, \u011d identity [13]); 2209.04658 (screw\n  line under RH, \u210b(A\u221e) \u2245 de Branges space [14]); 2606.09096 (the\n  Cor 1.6 paper \u2014 our R-003 source); 2409.00888 (M-functions/\n  Goldbach); 2308.11860 (survey, no new results).\n\n## 2. The machinery that EXISTS and fits the wall\n- **Krein\u2013Langer [paper ref 8]** (IEOT 78, 2014): screw-function\n  theory \u2014 continuation of hermitian positive definite functions;\n  g is a screw function \u27fa RH (Suzuki [13] Thm 1.2). The representing\n  measure of the screw function is the spectral object behind \u011d.\n- **Finite-interval convolution asymptotics** (Krein 1958/62;\n  Gohberg\u2013Feldman, \"Convolution Equations and Projection Methods\",\n  1974): the finite-interval resolvent of g\u2217v = h on [\u2212a,a] converges\n  as a \u2192 \u221e to the half-line Wiener\u2013Hopf resolvent PROVIDED the symbol\n  admits the appropriate factorization. This is the classical engine\n  behind the v\u00b1(a) \u2192 v\u00b1(\u221e) question (original Q-S3a) \u2014 and the\n  factorization of \u011d(z) = z\u207b\u00b2\u03be\u2032(\u00bd\u2212iz)/\u03be(\u00bd\u2212iz) is RH-gated (poles of \u011d\n  at z = i(\u00bd\u2212\u03c1) \u2014 all real \u27fa RH; D-035 \u00a72).\n- **Strong resolvent convergence of self-adjoint extensions** (classical\n  Krein resolvent formalism; e.g. Gorbachuk\u2013Gorbachuk): norm-convergence\n  of deficiency elements \u27f9 strong resolvent convergence of the\n  extensions D_{a,\u03b8(a)} \u2192 D. This is the exact theorem-class the\n  v\u00b1-convergence question belongs to.\n- **de Branges spaces / indefinite (de Branges\u2013Krein) spaces**\n  (de Branges 1968; Krein\u2013Langer): \u210b(A\u221e) \u2245 de Branges space under RH\n  [14]; without RH, Q_W is indefinite \u2014 negative index = off-line\n  pairs (Bombieri [Bom00]) \u2014 the right frame is a Krein-space\n  de Branges space.\n- **Connes 1999 trace formula** (and Connes\u2013Consani\u2013Moscovici\n  2511.22755 \u2014 zeta spectral triples, the sister v\u0302a \u2192 \u03be conjecture\n  (1.2)): the scaling-action/Weil-positivity framing of the same\n  positivity; NOT the WH framing but the same gate.\n\n## 3. What does NOT exist (the gap)\n- No WH-factorization analysis of \u011d = z\u207b\u00b2\u03be\u2032/\u03be anywhere.\n- No unconditional (Krein-space) version of Suzuki's [14] isomorphism.\n- No convergence theorem for D_{a,\u03b8} as a \u2192 \u221e in ANY metric (Suzuki's\n  \u00a77.5 expectation is stated under RH only, as a heuristic).\n- No known example of a strong-resolvent limit of real-spectrum\n  operators being used to FORCE real spectrum in the limit (the\n  phenomenon needed for (\u2605)) \u2014 in Krein spaces, spectrum can leave \u211d\n  in pairs; controlling that = the wall (D-035 \u00a73).",
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