| { |
| "models": [ |
| { |
| "key": "sft", |
| "label": "v6 SFT (midtrain final, iter 2981)", |
| "short": "Midtrain (SFT)" |
| }, |
| { |
| "key": "s150", |
| "label": "RL step 150 (outcome-only run, iter_0000149)", |
| "short": "RL step 150" |
| }, |
| { |
| "key": "s250", |
| "label": "RL step 250 (final, iter_0000249)", |
| "short": "RL step 250 (final)" |
| } |
| ], |
| "problems": [ |
| { |
| "id": "p00", |
| "problem_id": "tcsbench_2026_eval:FOCS_2026:0040", |
| "bench": "TCSBench-2026", |
| "problem": "Let \\(n\\ge 1\\), let \\(N=2^n\\), and let \\(\\varnothing\\ne\\mathcal K\\subseteq\\{0,1\\}^n\\) have cardinality \\(K\\). For \\(k\\in\\{0,1\\}^n\\), define\n\\[\nH|k\\rangle=\\frac1{\\sqrt N}\\sum_{x\\in\\{0,1\\}^n}(-1)^{k\\cdot x}|x\\rangle,\n\\]\nwhere \\(k\\cdot x\\) is computed modulo \\(2\\). For a Boolean function \\(f:\\{0,1\\}^n\\to\\{0,1\\}\\), let\n\\[\nF_f=\\sum_{x\\in\\{0,1\\}^n}(-1)^{f(x)}|x\\rangle\\langle x|.\n\\]\n\nConsider an arbitrary decoder with the following resources. A function \\(f\\) is chosen uniformly from all Boolean functions on \\(\\{0,1\\}^n\\), and independently \\(k\\) is chosen uniformly from \\(\\mathcal K\\). The decoder receives one copy of the state \\(F_fH|k\\rangle\\) and an advice state \\(\\rho_f\\) on at most \\(S\\) qubits. The advice may depend arbitrarily on \\(f\\), but the decoder has no other access to \\(f\\): its quantum operation and its classical output rule are fixed independently of \\(f\\). Its output lies in \\(\\mathcal K\\), and \\(\\varepsilon\\) denotes the probability, averaged over \\(f\\), \\(k\\), and the decoder's internal randomness, that its output equals \\(k\\).\n\nProve that for every integer \\(t\\ge1\\),\n\\[\n\\varepsilon^t\\le 2^S\\left(\\frac{8t}{K}\\right)^t.\n\\]\nDeduce that for every integer \\(S\\ge1\\),\n\\[\n\\varepsilon\\le \\frac{16S}{K}.\n\\]\n\nStandard results from finite-dimensional quantum mechanics and elementary linear algebra may be used, but any problem-specific decoding or amplification estimate must be proved.", |
| "reference": null, |
| "models": { |
| "sft": { |
| "file": "p00__sft.json", |
| "score": 0.14285714285714285, |
| "verdict": "1/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 6.0 |
| }, |
| "s150": { |
| "file": "p00__s150.json", |
| "score": 1.0, |
| "verdict": "7/7", |
| "n_layers": 4, |
| "termination": "terminated", |
| "n_compactions": 2, |
| "mean_width": 5.75 |
| }, |
| "s250": { |
| "file": "p00__s250.json", |
| "score": 0.0, |
| "verdict": "0/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p01", |
| "problem_id": "tcsbench_2026_eval:FOCS_2026:0149", |
| "bench": "TCSBench-2026", |
| "problem": "Let $\\mathbb{F}$ be a field. Let $\\overline{x}$, $\\overline{y}$, and $\\overline{z}$ be pairwise disjoint tuples of variables, where $\\overline{x}$ and $\\overline{y}$ are private variables and $\\overline{z}$ is the tuple of shared Boolean variables. Let $P_0(\\overline{x},\\overline{z})$ and $P_1(\\overline{y},\\overline{z})$ be finite sets of polynomial equations over $\\mathbb{F}$. Assume that the appropriate Boolean axioms are included. A specialized system is called satisfiable when its equations have a common Boolean solution in its remaining private variables.\n\nA read-once oblivious algebraic branching program ($\\mathrm{roABP}$) is a layered source-to-sink algebraic branching program in a fixed variable ordering, with each variable assigned one layer and each edge in that layer labeled by a univariate polynomial in that variable. Its polynomial is the sum of the weights of all source-to-sink paths, and its width is the maximum number of vertices in a layer. A width-$w$ $\\mathrm{roABP\\text{-}IPS}_{\\mathrm{LIN}}$ refutation of $P_0\\cup P_1$ is an identity\n$$\n\\sum_{p\\in P_0}a_p(\\overline{x},\\overline{y},\\overline{z})p(\\overline{x},\\overline{z})\n+\n\\sum_{q\\in P_1}b_q(\\overline{x},\\overline{y},\\overline{z})q(\\overline{y},\\overline{z})=1,\n$$\nwhere all certificate polynomials $a_p,b_q$ are computed by width at most $w$ roABPs in one common variable ordering.\n\nThe system $P_0$ is in $\\overline{z}$-normal form if each of its members is either $p'(\\overline{x})$ or $p'(\\overline{x})+z_jp''(\\overline{x})$, with $p',p''\\in\\mathbb{F}[\\overline{x}]$. It is in monotone $\\overline{z}$-normal form if each member is either $p'(\\overline{x})$ or $z_jp''(\\overline{x})$.\n\nA span program over $\\mathbb{F}$ consists of a finite-dimensional vector space $V$, a target $t\\in V$, and a finite set of labeled vectors $(\\ell,v)$, where $\\ell$ is $1$, $z_j$, or $1-z_j$. On $\\overline{\\alpha}\\in\\{0,1\\}^{|\\overline{z}|}$, the available vectors are those whose labels evaluate to $1$, and the program outputs $1$ exactly when they span $t$. Its size is the number of labeled vectors, and it is monotone if no label $1-z_j$ occurs. Such a program computes an interpolant for $P_0$ and $P_1$ if, for every $\\overline{\\alpha}$, output $1$ implies that $P_0(\\overline{x},\\overline{\\alpha})$ is unsatisfiable, while output $0$ implies that $P_1(\\overline{y},\\overline{\\alpha})$ is unsatisfiable.\n\nAssume that every polynomial in $P_0$ has degree and sparse encoding length bounded by $\\operatorname{poly}(|\\overline{x}|+|\\overline{z}|)$, and let $|P_0|$ denote the total sparse encoding length of $P_0$. Suppose that $P_0$ is in $\\overline{z}$-normal form and that $P_0\\cup P_1$ has a width-$w$ refutation whose common variable ordering places every variable of $\\overline{x}$ before every variable of $\\overline{y}\\cup\\overline{z}$.\n\nDevelop a proof blueprint—not a complete formal proof—for the claim that this refutation yields a span program of size $\\operatorname{poly}(w\\cdot|P_0|)$ computing an interpolant for $P_0$ and $P_1$, and that the span program may be chosen monotone when $P_0$ is in monotone $\\overline{z}$-normal form.\n\nThe blueprint should be concrete enough to recover the span-program construction and verify its correctness and size, but no intermediate decomposition or choice of vector space is prescribed. In particular, derive rather than assume the structural consequence of bounded roABP width that makes the construction possible, and explain where the prefix ordering and the two forms of the normal-form hypothesis enter. A satisfactory strategy must justify both interpolation implications for an arbitrary shared assignment and the monotonicity conclusion without citing feasible interpolation for $\\mathrm{roABP\\text{-}IPS}_{\\mathrm{LIN}}$ as a black box. You may use the elementary path-sum semantics of layered branching programs and the soundness of polynomial identities equal to $1$.", |
| "reference": null, |
| "models": { |
| "sft": { |
| "file": "p01__sft.json", |
| "score": 0.0, |
| "verdict": "0/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.25 |
| }, |
| "s150": { |
| "file": "p01__s150.json", |
| "score": 0.7142857142857143, |
| "verdict": "5/7", |
| "n_layers": 3, |
| "termination": "terminated", |
| "n_compactions": 1, |
| "mean_width": 6.0 |
| }, |
| "s250": { |
| "file": "p01__s250.json", |
| "score": 1.0, |
| "verdict": "7/7", |
| "n_layers": 7, |
| "termination": "terminated", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p02", |
| "problem_id": "tcsbench_2026_eval:FOCS_2026:0097", |
| "bench": "TCSBench-2026", |
| "problem": "Let $\\mathbb{F}$ be a field, let $n\\ge 2^{12}$, let $d\\ge 2$ be even, and let $X=\\{x_1,\\dots,x_n\\}$. Write $\\mathbb{F}\\langle X\\rangle$ for the free noncommutative polynomial algebra, whose monomials are words over $X$ and whose multiplication is concatenation.\n\nA noncommutative arithmetic circuit $C$ is a directed acyclic graph with variable or field-element leaves, sum gates of arbitrary fan-in, and product gates with two ordered children. For a gate $v$, let $f_v$ be the polynomial it computes, and let $f$ be the output polynomial. A product gate is called non-scalar if both children compute polynomials of positive degree, and scalar otherwise.\n\nFor nonnegative integers $a,b$, let $X^a$ be the set of words of length $a$. For $g\\in\\mathbb{F}\\langle X\\rangle$, define the prefix-suffix coefficient matrix $M_g^{a,b}$ by\n\n$$\nM_g^{a,b}[u,w]=[uw]g \\qquad (u\\in X^a,\\;w\\in X^b),\n$$\n\nwhere $[uw]g$ denotes the coefficient of the word $uw$ in $g$.\n\nDevelop a structured proof strategy for the implication\n\n$$\n\\operatorname{rank}\\!\\left(M_f^{d/2,d/2}\\right)=n^{d/2}\n\\quad\\Longrightarrow\\quad\nC\\text{ contains }\\Omega(d\\sqrt n)\\text{ non-scalar product gates}.\n$$\n\nYou are not asked for a complete formal proof. Instead, formulate a small collection of precise intermediate statements that would suffice to establish the result, and explain how they fit together quantitatively. The strategy must apply directly to circuits as DAGs: it should handle constants and nonhomogeneous computations, arbitrary fan-in at sum gates, and reuse of subcomputations without silently replacing the circuit by a formula. In particular, make clear why the argument counts distinct non-scalar product gates and where both the factor $d$ and the factor $\\sqrt n$ enter.\n\nYou may use standard linear-algebraic facts such as linearity of coefficient extraction,\n\n$$\n\\operatorname{rank}(A+B)\\le \\operatorname{rank}(A)+\\operatorname{rank}(B),\n\\qquad\n\\operatorname{rank}(A\\otimes B)=\\operatorname{rank}(A)\\operatorname{rank}(B),\n$$\n\nas well as identities derived directly from the definitions for coefficients of sums and ordered products. Any circuit preprocessing or global bookkeeping principle used in the strategy must be stated and justified as part of the plan, including why it does not increase the resource being lower-bounded. A proposal that only invokes a formula lower bound, follows one input-directed path, or appeals qualitatively to rank without controlling fan-in and sharing is not sufficient.", |
| "reference": null, |
| "models": { |
| "sft": { |
| "file": "p02__sft.json", |
| "score": 0.0, |
| "verdict": "0/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.5 |
| }, |
| "s150": { |
| "file": "p02__s150.json", |
| "score": 0.35714285714285715, |
| "verdict": "2.5/7.0", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.75 |
| }, |
| "s250": { |
| "file": "p02__s250.json", |
| "score": 0.14285714285714285, |
| "verdict": "1/7", |
| "n_layers": 2, |
| "termination": "no_summary", |
| "n_compactions": 1, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p03", |
| "problem_id": "tcsbench_2026_eval:STOC_2026:0116", |
| "bench": "TCSBench-2026", |
| "problem": "Let $\\Sigma^*$ be a countable universe of strings, and let $\\mathcal{X}=(L_1,L_2,\\ldots)$ be a countable listed family in which every $L_i\\subseteq\\Sigma^*$ is infinite. An adversary chooses an index $z$, sets $K=L_z$, chooses an arbitrary infinite subset $C\\subseteq K$, and reveals an enumeration $(w_1,w_2,\\ldots)$ of $C$. At round $t$, the learner knows only $S_t=\\{w_1,\\ldots,w_t\\}$ and must output a string $a_t$. The learner may depend on $\\mathcal{X}$ but not on $z$, $K$, or $C$.\n\nWork in an idealized information-theoretic model: the candidate sets are available, and any set-theoretic tests or choices appearing in the proposed learner may be performed. Prove at the level of a structured strategy—not a complete formal proof—that for every such family $\\mathcal{X}$ there is a learner for which, for every adversarial choice, some finite $t^*$ satisfies\n\n$$a_t\\in K\\setminus S_t\\qquad\\text{for all }t\\ge t^*.$$\n\nYour strategy must give a concrete, total round-by-round rule rather than merely asserting that a suitable output exists. Identify the decisive invariant or stabilization mechanism that simultaneously keeps outputs available and eventually prevents outputs outside the unknown target, despite the fact that the observations may remain compatible with several candidates forever. Explain where the countable listing and the infinitude assumptions enter the argument, and indicate how the main claims compose into the limiting guarantee. The reasoning must tolerate arbitrary overlap patterns among the $L_i$; do not assume eventual identification of $K$, eventual uniqueness of a compatible candidate, or any unstated compactness or minimality property of the family.", |
| "reference": null, |
| "models": { |
| "sft": { |
| "file": "p03__sft.json", |
| "score": 0.2857142857142857, |
| "verdict": "2/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.88 |
| }, |
| "s150": { |
| "file": "p03__s150.json", |
| "score": 0.42857142857142855, |
| "verdict": "3/7", |
| "n_layers": 5, |
| "termination": "terminated", |
| "n_compactions": 3, |
| "mean_width": 5.6 |
| }, |
| "s250": { |
| "file": "p03__s250.json", |
| "score": 1.0, |
| "verdict": "7/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p04", |
| "problem_id": "tcsbench_2026_eval:STOC_2026:0049", |
| "bench": "TCSBench-2026", |
| "problem": "Fix an integer k\\ge 1. A k-CSP instance consists of a finite variable set V, an alphabet \\Sigma, and a multiset of constraints. Each constraint e has an ordered scope (u_1,\\ldots,u_k) of distinct variables and a predicate \\Phi_e:\\Sigma^k\\to\\{0,1\\}. The value of the instance is the maximum, over all assignments A:V\\to\\Sigma, of the fraction of constraints satisfied by A. The instance is k-partite if V admits a partition V_1\\sqcup\\cdots\\sqcup V_k such that the j-th variable in the ordered scope of every constraint belongs to V_j. Throughout, NP-hardness is with respect to deterministic polynomial-time reductions.\n\nAssume that for every \\gamma,\\delta>0 and all sufficiently large alphabet sizes R, it is NP-hard to distinguish a k-CSP over an alphabet of size R having value at least 1-\\delta from one having value at most\n\\[\nR^{-(1-\\gamma)(k-1)}.\n\\]\n\nUsing only this hypothesis, prove that for every \\varepsilon,\\delta>0 and all sufficiently large R, it is NP-hard to distinguish, given a k-partite k-CSP \\Psi over an alphabet of size R, between\n\\[\n\\operatorname{val}(\\Psi)\\ge 1-\\delta\n\\qquad\\text{and}\\qquad\n\\operatorname{val}(\\Psi)\\le R^{-(1-\\varepsilon)(k-1)}.\n\\]", |
| "reference": null, |
| "models": { |
| "sft": { |
| "file": "p04__sft.json", |
| "score": 0.9285714285714286, |
| "verdict": "6.5/7.0", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.75 |
| }, |
| "s150": { |
| "file": "p04__s150.json", |
| "score": 0.8571428571428571, |
| "verdict": "6/7", |
| "n_layers": 2, |
| "termination": "terminated", |
| "n_compactions": 0, |
| "mean_width": 5.0 |
| }, |
| "s250": { |
| "file": "p04__s250.json", |
| "score": 0.5714285714285714, |
| "verdict": "4/7", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p05", |
| "problem_id": "arxivmath-0626:35", |
| "bench": "ArxivMath-0626", |
| "problem": "Let $F_n$ denote the $n$-th Fibonacci number (with $F_1=1$ and $F_2=1$). Define $\\Phi(m)$ to be the number of nonempty sets $A \\subseteq \\{1, 2, \\dots, m\\}$ for which the greatest common divisor of the elements in $A$ is relatively prime to $m$. Let $S$ be the set of all pairs of positive integers $(n,m)$ that satisfy the equation $F_n = \\Phi(m)$. What is $\\sum_{(n,m)\\in S} nm$?\n\nReturn your final answer in \\boxed{}.", |
| "reference": "9", |
| "models": { |
| "sft": { |
| "file": "p05__sft.json", |
| "score": 0.0, |
| "verdict": "incorrect", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.62 |
| }, |
| "s150": { |
| "file": "p05__s150.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 7, |
| "mean_width": 5.5 |
| }, |
| "s250": { |
| "file": "p05__s250.json", |
| "score": 0.0, |
| "verdict": "incorrect", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p06", |
| "problem_id": "arxivmath-0626:5", |
| "bench": "ArxivMath-0626", |
| "problem": "In the theory of knotted surfaces in $S^4$, the tri-plane crossing number is defined as the minimal number of crossings in a tri-plane diagram for a bridge trisection of the surface. What is the exact value of the tri-plane crossing number of the 2-twist spun trefoil?\n\nReturn your final answer in \\boxed{}.", |
| "reference": "6", |
| "models": { |
| "sft": { |
| "file": "p06__sft.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 4.25 |
| }, |
| "s150": { |
| "file": "p06__s150.json", |
| "score": 0.0, |
| "verdict": "incorrect", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.25 |
| }, |
| "s250": { |
| "file": "p06__s250.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p07", |
| "problem_id": "arxivmath-0626:7", |
| "bench": "ArxivMath-0626", |
| "problem": "Let $\\mathcal{T}$ be a deterministic infinite tree with vertex set $V = \\{(i,j) : i \\ge 0, 0 \\le j \\le i\\}$ and root $(0,0)$. The edges of $\\mathcal{T}$ connect $(i,0)$ to $(i+1,0)$ for all $i \\ge 0$, and $(i,j)$ to $(i,j+1)$ for all $i \\ge 1$ and $0 \\le j \\le i-1$. For a parameter $0 < \\lambda < 1$, consider the $\\lambda$-biased random walk $(X_n)_{n \\ge 0}$ on $\\mathcal{T}$ with $X_0=(0,0)$, which from any non-root vertex moves to its parent with probability proportional to $\\lambda$ and to each of its children with probability proportional to $1$ (from the root, it moves to its only child $(1,0)$ with probability 1). Let $M(N)$ denote the number of cut times up to time $N$ (a time $k \\ge 1$ is a cut time if $\\{X_0, \\dots, X_{k-1}\\} \\cap \\{X_k, X_{k+1}, \\dots\\} = \\emptyset$). What is the almost sure limit $\\lim_{N \\to \\infty} \\frac{M(N)}{\\log N}$?\n\nReturn your final answer in \\boxed{}.", |
| "reference": "\\frac{1-\\lambda}{\\log(1/\\lambda)}", |
| "models": { |
| "sft": { |
| "file": "p07__sft.json", |
| "score": 0.0, |
| "verdict": "incorrect", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 5.38 |
| }, |
| "s150": { |
| "file": "p07__s150.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 6, |
| "mean_width": 4.75 |
| }, |
| "s250": { |
| "file": "p07__s250.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p08", |
| "problem_id": "arxivmath-0626:30", |
| "bench": "ArxivMath-0626", |
| "problem": "Let $X$ be a multi-dimensional fractional Brownian motion with Hurst parameter $H \\in (0, 1/2]$. We consider local, square-integrable rough path lifts of $X$. If we require the lift to be invariant in law under time translation, scaling, and coordinate permutation, it is known that only the canonical lift satisfies these constraints for almost all values of $H > 1/4$. However, there is exactly one exceptional value of $H \\in (0, 1/2]$ for which there exists a one-parameter family of lifts satisfying these constraints. What is this exceptional value of $H$?\n\nReturn your final answer in \\boxed{}.", |
| "reference": "1/3", |
| "models": { |
| "sft": { |
| "file": "p08__sft.json", |
| "score": 0.0, |
| "verdict": "incorrect", |
| "n_layers": 3, |
| "termination": "terminated", |
| "n_compactions": 1, |
| "mean_width": 4.67 |
| }, |
| "s150": { |
| "file": "p08__s150.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 4, |
| "termination": "terminated", |
| "n_compactions": 2, |
| "mean_width": 5.25 |
| }, |
| "s250": { |
| "file": "p08__s250.json", |
| "score": 0.0, |
| "verdict": "incorrect", |
| "n_layers": 3, |
| "termination": "terminated", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| }, |
| { |
| "id": "p09", |
| "problem_id": "arxivmath-0626:3", |
| "bench": "ArxivMath-0626", |
| "problem": "Let $ex(n, K_{t,t}, K_{2,t+1})$ denote the maximum number of copies of the complete bipartite graph $K_{t,t}$ that an $n$-vertex $K_{2,t+1}$-free graph can contain. For a fixed prime power $t \\geq 3$, evaluate the limit $\\lim_{e \\to \\infty} \\frac{ex(n_e, K_{t, t}, K_{2, t+1})}{n_e^2}$, where $n_e = t^{2e - 1}$.\n\nReturn your final answer in \\boxed{}.", |
| "reference": "\\frac{1}{2t(t-1)}", |
| "models": { |
| "sft": { |
| "file": "p09__sft.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 7, |
| "mean_width": 5.62 |
| }, |
| "s150": { |
| "file": "p09__s150.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 4, |
| "termination": "terminated", |
| "n_compactions": 3, |
| "mean_width": 6.0 |
| }, |
| "s250": { |
| "file": "p09__s250.json", |
| "score": 1.0, |
| "verdict": "correct", |
| "n_layers": 8, |
| "termination": "max_layers", |
| "n_compactions": 0, |
| "mean_width": 1.0 |
| } |
| } |
| } |
| ] |
| } |
