[
  {
    "id": "blomer-naewe11v2-cvp-lp-exact",
    "categoryId": "cvp-lp-exact-arithmetic",
    "paperId": "blomer-naewe-2011",
    "year": 2011,
    "date": "2011-05-16",
    "time": {
      "coefficient": 2.5,
      "expression": "poly(p, log r) · n^{(5/2 + o(1))n} arithmetic operations"
    },
    "space": {
      "coefficient": null,
      "expression": "No polynomial-space guarantee asserted for this version"
    },
    "tags": [
      "ℓp norms",
      "exact",
      "arithmetic model"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Version 2 states the 5/2 leading coefficient for the family of ℓp norms. Its arithmetic bound is retained with the version’s weaker space and intermediate-bit-size documentation.",
    "extra": {
      "norm": "Every fixed ℓp, 1 < p < ∞",
      "target": "Target in span(L); restrict to full-rank L ⊂ R^n",
      "preprocessing": "Included",
      "model": "Deterministic arithmetic operation count",
      "success": "Exact output",
      "input": "r bounds encoded basis/target coefficients; polynomial p-dependence suppressed"
    },
    "evidence": {
      "url": "https://arxiv.org/pdf/1104.3720v2",
      "locator": "Abstract; Theorems 3.2 and 3.3",
      "sourceVersion": "arXiv:1104.3720v2, 16 May 2011"
    }
  },
  {
    "id": "blomer-naewe11v3-cvp-lp-exact",
    "categoryId": "cvp-lp-exact-arithmetic",
    "paperId": "blomer-naewe-2011",
    "year": 2011,
    "date": "2011-07-12",
    "time": {
      "coefficient": 2,
      "expression": "poly(p, log r) · n^{(2 + o(1))n} arithmetic operations"
    },
    "space": {
      "coefficient": null,
      "expression": "Polynomial in the encoded input size"
    },
    "tags": [
      "ℓp norms",
      "exact",
      "polynomial space"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Version 3 improves the ℓp-family leading coefficient from 5/2 to 2 and explicitly bounds the working space and intermediate number sizes polynomially. The arXiv landing-page abstract remains stale; the original versioned PDF contains this stronger statement.",
    "extra": {
      "norm": "Every fixed ℓp, 1 < p < ∞",
      "target": "Target in span(L); restrict to full-rank L ⊂ R^n",
      "preprocessing": "Included",
      "model": "Deterministic arithmetic count with polynomial intermediate bit size",
      "success": "Exact output",
      "input": "r bounds encoded basis/target coefficients; polynomial p-dependence suppressed"
    },
    "evidence": {
      "url": "https://arxiv.org/pdf/1104.3720v3",
      "locator": "Abstract; Theorems 3.2 and 3.3; Corollary 6.5",
      "sourceVersion": "arXiv:1104.3720v3, 12 July 2011"
    }
  }
]