[
  {
    "id": "adrs15-constant-approximation",
    "categoryId": "svp-constant-approximation",
    "paperId": "paper-86925aff6e6c",
    "year": 2015,
    "date": "2014-12-26",
    "time": {
      "coefficient": 1,
      "expression": "2^{n + o(n)}"
    },
    "space": {
      "coefficient": 1,
      "expression": "2^{1 n + o(n)}"
    },
    "tags": [
      "arbitrary lattices",
      "Euclidean",
      "exact implies constant approximation"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The exact-SVP theorem immediately supplies this approximation guarantee without changing time or space. This is a transferred guarantee, not another algorithm or a separate new result. STOC 2015. Randomized exact Euclidean SVP via DGS; time and space 2^{n+o(n)}. The chronology uses the first arXiv submission date.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "success": "High probability",
      "model": "Classical randomized; polynomial factors suppressed",
      "reference": "ADRS15",
      "approximation": "Exact output (μ = 1), hence meets every relaxed constant-factor guarantee"
    }
  },
  {
    "id": "hhan-midpoint26-constant-approximation",
    "categoryId": "svp-constant-approximation",
    "paperId": "paper-2fcc11c09e6a",
    "year": 2026,
    "date": "2026-08-03",
    "time": {
      "coefficient": 0.6039,
      "expression": "2^{0.6039 n + o(n)}"
    },
    "space": {
      "coefficient": 0.5,
      "expression": "2^{0.5 n + o(n)}"
    },
    "tags": [
      "arbitrary lattices",
      "Euclidean",
      "exact implies constant approximation"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The exact-SVP theorem immediately supplies this approximation guarantee without changing time or space. This is a transferred guarantee, not another algorithm or a separate new result. Preprint claim, also arXiv:2608.02478. Uses the Hessian of the periodic Gaussian at a half shortest vector. First arXiv date shown. Source checked; proof not independently audited.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "success": "High probability",
      "model": "Classical randomized; polynomial factors suppressed",
      "reference": "Hhan26a",
      "approximation": "Exact output (μ = 1), hence meets every relaxed constant-factor guarantee"
    }
  },
  {
    "id": "hhan-coset26-constant-approximation",
    "categoryId": "svp-constant-approximation",
    "paperId": "paper-0f3a0f011219",
    "year": 2026,
    "date": "2026-09-02",
    "time": {
      "coefficient": 0.5,
      "expression": "2^{n/2 + o(n)}"
    },
    "space": {
      "coefficient": 0.5,
      "expression": "2^{0.5 n + o(n)}"
    },
    "tags": [
      "arbitrary lattices",
      "Euclidean",
      "exact implies constant approximation"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The exact-SVP theorem immediately supplies this approximation guarantee without changing time or space. This is a transferred guarantee, not another algorithm or a separate new result. Preprint claim: exact worst-case SVP in time and space 2^{n/2+o(n)}. Its separate distance-guarantee CVP result is not treated as unrestricted exact CVP here. Source checked; proof not independently audited.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "success": "High probability",
      "model": "Classical randomized; polynomial factors suppressed",
      "reference": "Hhan26b",
      "approximation": "Exact output (μ = 1), hence meets every relaxed constant-factor guarantee"
    }
  },
  {
    "id": "hkkl26-constant-approximation",
    "categoryId": "svp-constant-approximation",
    "paperId": "paper-c70730f20075",
    "year": 2026,
    "date": "2026-11-04",
    "time": {
      "coefficient": 0.409,
      "expression": "2^{0.409 n + o(n)}"
    },
    "space": {
      "coefficient": 0.259,
      "expression": "2^{0.259 n + o(n)}"
    },
    "tags": [
      "arbitrary lattices",
      "Euclidean",
      "exact implies constant approximation"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The exact-SVP theorem immediately supplies this approximation guarantee without changing time or space. This is a transferred guarantee, not another algorithm or a separate new result. Claim in the 4 November 2026 preprint abstract: optimized worst-case SVP time 0.409 and space 0.259. Dense superlattices, random shifts, and midpoint-shell tests. Source checked; proof not independently audited.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "success": "High probability",
      "model": "Classical randomized; polynomial factors suppressed",
      "reference": "HKKL26",
      "approximation": "Exact output (μ = 1), hence meets every relaxed constant-factor guarantee"
    }
  },
  {
    "id": "ams26-spherical-code-unconditional",
    "categoryId": "svp-constant-approximation",
    "paperId": "aggarwal-morolia-stephens-davidowitz-2026-spherical",
    "date": "2026-10-07",
    "datePrecision": "day",
    "year": 2026,
    "time": {
      "coefficient": 0.6078,
      "expression": "2^{(0.6078 + ε_μ)n + o(n)}, ε_μ → 0 as μ → ∞"
    },
    "space": {
      "coefficient": 0.6078,
      "expression": "2^{(0.6078 + ε_μ)n + o(n)}, ε_μ → 0 as μ → ∞"
    },
    "tags": [
      "constant approximation",
      "provable",
      "spherical codes",
      "nearest-neighbor sieving",
      "large-factor limit"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Corollary 3.8 gives unconditional time and space with coefficient 0.6078 + ε_μ, where ε_μ tends to zero as the constant approximation factor μ grows. The stored 0.6078 is the limiting family coefficient; it is not an exact-SVP exponent or a guarantee at every fixed μ. Nearest-neighbor filtering and a perturbation proof give a new provable sieving method. Hhan’s earlier exact-SVP exponent 0.5 already implies a faster constant-approximation bound.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "approximation": "For every ε > 0 choose a sufficiently large constant μ(ε); μ is not uniform in ε",
      "success": "High probability",
      "model": "Classical randomized; unconditional spherical-code upper bound"
    },
    "evidence": {
      "url": "https://eprint.iacr.org/2026/2388.pdf",
      "locator": "Theorem 1.1; Theorem 3.7; Corollary 3.8, printed p. 27 (PDF p. 28)",
      "sourceVersion": "7 October 2026 preprint; full text checked through eprint.iacr.asia mirror"
    }
  }
]