sattath

Solved 25

• Every fixed clause-width bound has a polynomial-time WordRAM certificate verifierProved

  Oct 2026

• Quantum local lemma for $k$-QSAT on $n$ qubits, operator form (Corollary 16)Proved

  Oct 2026

• Infinite $k$-SAT: bounded variable occurrence implies a global satisfying assignment, at any cardinalityProved

  Oct 2026

• $k$-SAT under bounded variable occurrence for a finite subfamily of clauses over arbitrary variable and index setsProved

  Oct 2026

• $k$-QSAT with orthogonal projectors of rank at most $r$ and bounded qubit degree is satisfiable (Corollary 16, the paper's setting)Proved

  Oct 2026

• Lovász Local Lemma for $k$-SAT: bounded variable occurrence implies satisfiabilityProved

  Oct 2026

• Quantum local lemma for $k$-QSAT on $n$ qubits, subspace form (Corollary 16)Proved

  Oct 2026

• $k$-SAT under bounded variable occurrence: a common satisfying assignment for a finite family of clausesProved

  Oct 2026

• Quantum local lemma for $k$-QSAT with local satisfying spaces of dimension at least $2^k - r$Proved

  Oct 2026

• A clause on $k$ distinct variables is satisfied by at least a $1 - 2^{-k}$ fraction of assignmentsProved

  Oct 2026

• Relative dimension of a lifted local subspace: $\mathrm{R}(\mathrm{lift}_S(Y)) = \dim Y / 2^{|S|}$Proved

  Oct 2026

• Local lemma for an infinite index set: the whole family has a nonzero meetProved

  Oct 2026

• Quantum local lemma for $k$-QSAT, function-model subspace form (Corollary 16)Proved

  Oct 2026

• Tensor products of subspaces intersect factorwise: $(A \otimes B) \cap (A' \otimes B') = (A \cap A') \otimes (B \cap B')$Proved

  Oct 2026

• Quantum Lovász Local Lemma (symmetric form): $\mathrm{R}(\bigcap_i X_i) > 0$ when $p\,e\,(d+1) \le 1$Proved

  Oct 2026

• Erdős–Lovász local lemma, symmetric form, uniform finite probability space (Theorem 1)Proved

  Oct 2026

• Quantum Lovász Local Lemma (asymmetric form): $\mathrm{R}(\bigcap_i X_i) \ge \prod_i (1-y_i)$Proved

  Oct 2026

• Erdős–Lovász local lemma, asymmetric form, uniform finite probability space (Theorem 13)Proved

  Oct 2026

• Product rule for dimensions: $\dim\big((Y \otimes \mathbb{C}^B) \cap (\mathbb{C}^A \otimes W)\big) = \dim Y \cdot \dim W$Proved

  Oct 2026

• Local lemma for an infinite index set, under continuity from aboveProved

  Oct 2026

• Abstract Lovász Local Lemma for valuations on a bounded lattice (symmetric form)Proved

  Oct 2026

• Events depending on complementary sets of variables are independentProved

  Oct 2026

• A linear map vanishing on $\ker f \cap \ker g$ factors as $u \circ f + v \circ g$Proved

  Oct 2026

• $A \otimes B = (A \otimes W) \cap (V \otimes B)$ for subspaces over a fieldProved

  Oct 2026

• Abstract Lovász Local Lemma for valuations on a bounded lattice (asymmetric form)Proved

  Oct 2026

Posted 32

• Quantum local lemma for $k$-QSAT on $n$ qubits, subspace form (Corollary 16)Proved

  Oct 2026

• Local lemma for an infinite index set, under continuity from aboveProved

  Oct 2026

• $k$-SAT under bounded variable occurrence: a common satisfying assignment for a finite family of clausesProved

  Oct 2026

• Quantum local lemma for $k$-QSAT with local satisfying spaces of dimension at least $2^k - r$Proved

  Oct 2026

• Quantum Lovász Local Lemma (asymmetric form): $\mathrm{R}(\bigcap_i X_i) \ge \prod_i (1-y_i)$Proved

  Oct 2026

• $k$-SAT under bounded variable occurrence for a finite subfamily of clauses over arbitrary variable and index setsProved

  Oct 2026

• Infinite $k$-SAT: bounded variable occurrence implies a global satisfying assignment, at any cardinalityProved

  Oct 2026

• Quantum Lovász Local Lemma (symmetric form): $\mathrm{R}(\bigcap_i X_i) > 0$ when $p\,e\,(d+1) \le 1$Proved

  Oct 2026

• Lovász Local Lemma for $k$-SAT: bounded variable occurrence implies satisfiabilityProved

  Oct 2026

• Local lemma for an infinite index set: the whole family has a nonzero meetProved

  Oct 2026

• Erdős–Lovász local lemma, symmetric form, uniform finite probability space (Theorem 1)Proved

  Oct 2026

• Erdős–Lovász local lemma, asymmetric form, uniform finite probability space (Theorem 13)Proved

  Oct 2026

• Quantum local lemma for $k$-QSAT on $n$ qubits, operator form (Corollary 16)Proved

  Oct 2026

• A clause on $k$ distinct variables is satisfied by at least a $1 - 2^{-k}$ fraction of assignmentsProved

  Oct 2026

• Quantum local lemma for $k$-QSAT, function-model subspace form (Corollary 16)Proved

  Oct 2026

• $k$-QSAT with orthogonal projectors of rank at most $r$ and bounded qubit degree is satisfiable (Corollary 16, the paper's setting)Proved

  Oct 2026

• Events depending on complementary sets of variables are independentProved

  Oct 2026

• Relative dimension of a lifted local subspace: $\mathrm{R}(\mathrm{lift}_S(Y)) = \dim Y / 2^{|S|}$Proved

  Oct 2026

• Tensor products of subspaces intersect factorwise: $(A \otimes B) \cap (A' \otimes B') = (A \cap A') \otimes (B \cap B')$Proved

  Oct 2026

• Product rule for dimensions: $\dim\big((Y \otimes \mathbb{C}^B) \cap (\mathbb{C}^A \otimes W)\big) = \dim Y \cdot \dim W$Proved

  Oct 2026

• Abstract Lovász Local Lemma for valuations on a bounded lattice (symmetric form)Proved

  Oct 2026

• $A \otimes B = (A \otimes W) \cap (V \otimes B)$ for subspaces over a fieldProved

  Oct 2026

• A linear map vanishing on $\ker f \cap \ker g$ factors as $u \circ f + v \circ g$Proved

  Oct 2026

• $n$ qubits as Mathlib's tensor power of $\mathbb{C}^2$, and extension of local constraintsDefinition

  Oct 2026

• Tensor products of finite function spaces as function spaces on product setsDefinition

  Oct 2026

• $k$-QSAT instances given by local projectors, their satisfying space, and satisfiabilityDefinition

  Oct 2026

• Variables of a clause and relabelling, over an arbitrary variable typeDefinition

  Oct 2026

• Uniform probability as a valuation, boolean assignments, and clause eventsDefinition

  Oct 2026

• The $n$-qubit space as functions on bit strings, slices, and subspaces supported on a set of qubitsDefinition

  Oct 2026

• Dependency graphs for families indexed by an arbitrary typeDefinition

  Oct 2026

• Abstract Lovász Local Lemma for valuations on a bounded lattice (asymmetric form)Proved

  Oct 2026

• Valuations on bounded lattices, mutual independence, dependency graphs and relative dimensionDefinition

  Oct 2026