files / problems / simon-lieb-thirring / compute / q3 / certs / leftover.json

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{
  "schema": "slt-q3-leftover-v1",
  "date": "2026-09-02",
  "published_record": {
    "paper": "arXiv:2403.04347v2",
    "L_over_Lcl": 1.44655,
    "M3": 0.371185695
  },
  "q2_clausen_envelope": {
    "L_over_Lcl_upper": 1.4465531,
    "beats_CCR": false
  },
  "attempts": [
    {
      "name": "Weidl interpolation with HLT L_{1/2,1}=1/2",
      "ratio": 3.838539,
      "beats_CCR": false
    },
    {
      "name": "Seiringer-Solovej Airy R_1 after HO absorption",
      "R1_upper": 0.13202325,
      "ratio": 2.752167,
      "beats_CCR": false
    },
    {
      "name": "Neumann covering at gamma=1, alpha=3",
      "constant_well_ratio": 2.720699,
      "beats_CCR": false
    },
    {
      "name": "1D trial potentials (square, two-sech, gauss-sum, histogram)",
      "best_ratio_over_classical": 1.154701,
      "above_sobolev": false,
      "note": "Keller one-bound-state exact; no trial exceeded 2/sqrt(3)"
    },
    {
      "name": "Eden-Foias empirical kappa",
      "min_empirical_kappa": 2.7173,
      "kappa_needed_for_CCR": 1.35,
      "proved_kappa": 1.0,
      "beats_CCR": false
    }
  ],
  "beats_CCR_1.44655": false,
  "note": "Incomplete as an upper-bound hunt: every closed alternative conversion sits above 1.44655, and the test-potential search did not raise the one-bound-state lower bound. Not a lower bound on L. Conjecture open."
}