files / problems / simon-lieb-thirring / compute / q2 / imagined_cert.json

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{
  "schema": "ccr-clausen-v1",
  "name": "imagined-ccr-clausen",
  "note": "Imagined certificate, written before the closed form was used. The first sketch was a certified evaluation of ||h_{-2/3}||_∞ (upper) and ||h_{-1}||_2 (lower) for the Theorem 1.3 optimiser. The working witness is instead the Fourier series for CI_2(2π/3), pushed through Carvalho Corso arXiv:2407.10117v2 Corollary 1.8 / (1.11) and the CCR conversion L/Lcl = (9√3/4) M_3 = (π/3) exp(3 CI_2(2π/3)/(2π)). A panel pair is the wrong witness. The bound is the method ceiling: no FHJN trial pair can go below this M_3.",
  "source": {
    "arxiv_ccr": "2403.04347",
    "version_ccr": "v2",
    "abs_ccr": "https://arxiv.org/abs/2403.04347v2",
    "html_ccr": "https://arxiv.org/html/2403.04347v2",
    "arxiv_closed": "2407.10117",
    "version_closed": "v2",
    "v1_already_has_1.44655": true
  },
  "gamma": 3,
  "alpha": "2/3",
  "formula": {
    "CI2": "(√3/2) Σ_m (1/(3m+1)^2 − 1/(3m+2)^2)",
    "L": "(π/3) exp(3 CI_2(2π/3) / (2π))",
    "M3": "(16π/81) H^3,  H = (4√3/3)^{-1/3} exp(CI_2/(2π))",
    "conversion": "C_1 = M_3,  L/Lcl = (9√3/4) C_1"
  },
  "claimed_in_paper": {
    "M_3": 0.371185695,
    "L_over_Lcl": 1.44655
  },
  "target_bounds": {
    "beats_q1_1.45576": true,
    "beats_published_1.456": true,
    "below_1.45": true,
    "beats_ccr_1.44655": false
  }
}