All Research · Luminary Research Archive

52 papers · Page 2 of 3

Analysis and Spectral Theory

Edition 1

A Weyl Law for Rapidly Twisted Polar-Strip Tubes

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

We determine the leading eigenvalue-counting asymptotic for a class of infinite-volume Dirichlet tubes confined by diverging twisting. The planar cross-section is a compact annular polar strip with positive C¹ angular width α(r) < 2π, and the twisting speed is c(1 + s²)^(p/2), where c, p > 0. We prove N(Λ) ∼ CΛ^(3/2 + 1/(2p)) and compute C explicitly in terms of ζ(1 + 1/p) and ∫ rα(r)^(1 + 1/p) dr. The proof retains the angular Dirichlet modes while treating the radial and longitudinal variables semiclassically. A uniform Dirichlet-box comparison obtained from quasiperiodic phase averaging and IMS localization controls the artificial longitudinal boundaries. A separate tail estimate and absolute-coefficient freezing justify the global limit. The result gives a concrete-class answer to the Weyl-asymptotics question for tubes with asymptotically diverging twisting.

October 22, 2026Read paper

Edition 1

Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentration

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

We study nonnegative initial temperatures whose Dirichlet heat evolution has one common signed outward normal derivative on both boundary components of a fixed spherical shell. In every dimension at least two, the admissible observation times form an interval (0, τ) with a finite, unattained endpoint characterized by a boundary heat-kernel ratio. Finite schedules satisfy an exact interior convex-hull criterion, and a datum-independent terminal interval contains at most one observation. With unit ground-state projection, every weighted minimum-Lq preparation, 1 < q < ∞, is unique at each admissible time and is determined by a monotone real scalar moment equation. We obtain sharp cost constants throughout the fixed norm scale, including separate endpoint arguments. For every finite strictly convex power, quantitative ground-probability stability prevents scaled second-moment loss, and physical near-minimizers have a universal strong rescaled profile with angular symmetry. Exactly feasible counterexamples exclude universal higher-moment convergence. At the L1 endpoint the ground-weighted probabilities concentrate at √6 in quadratic Wasserstein distance. At the cap endpoint the preparations approach a filled layer in every finite Lr, while an exact counterexample excludes general strong L∞ convergence. All parameters are fixed in the stated asymptotic limits; classical positivity, convex-moment and coupling methods are explicitly credited.

October 22, 2026Read paper

Edition 1

Energy-Filtered Dynamical Localization in Constructive Dirichlet Towers

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

For every dimension d >= 2 and every measurable spatial weight w >= 1 essentially bounded on bounded sets, we construct a connected tower of enlarging cubes whose ordinary Dirichlet Laplacian has a complete orthonormal eigenbasis and essential spectrum [0,infinity). Given any finite nondecreasing r(E) >= 1 tending to infinity, the tower can be chosen so that weighted local-source evolution below energy E is bounded uniformly in time by C_K min(r(E),sqrt(E+1)). More generally, any prescribed Borel spectral filter 0 < h <= 1 uniformly vanishing at high energy admits a uniform weighted local-source bound. Local Neumann approximation targets and a summable spectral-projection budget supply the uniform source estimate. With a rational initial room, computable local weight upper bounds and a supplied computable filter-tail modulus, the geometry and its finite spectral certificates can be produced by a procedure terminating at every stage. Crack-aware primal and flux approximation certify whole-resolvent compressions and strict whole-cluster spectral tests. Explicit sufficient aperture bounds are logarithmic in the plane and linear in higher dimensions. For uniformly diverging spatial weights, a uniformly bounded all-energy factor is impossible; the geometry depends on the prescribed rate.

October 22, 2026Read paper

Edition 1

Phase transitions and effective curvature bounds in Fourier density models

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

We study the intrinsic Wasserstein metric on affine Fourier-density models on the unit circle. For three distinct frequencies, with one arbitrary fixed phase per frequency, every sectional curvature at the uniform density is strictly negative unless the frequencies have ratio 1:2:3. In that exceptional family we determine the exact attained curvature range and a phase-dependent sign criterion: the same frequency magnitudes can have mixed curvature or strictly negative curvature solely through relative phase. For the aligned four-frequency family {m, 2m, n, n+m}, n > 5m, we determine the exact attained maximum sectional curvature at every frequency ratio. Two sharp algebraic thresholds separate mixed signs from strict negativity and then mark saturation of the maximum at −18π²m². Finally, exact rational Fourier integration with a bounded infinite reciprocal-series remainder certifies nonuniform closed parameter cubes: the {m, 2m, 3m} model has both signs throughout [−.01, .01]³, whereas every sectional curvature of the {m, 2m, 4m} model is less than −.98π²m² there. The phase and four-frequency classifications are analytic; the explicit neighborhood bounds are computer-assisted and accompanied by reproducible exact-arithmetic certificates.

October 22, 2026Read paper

Edition 1

Positive Affine Eigenfunctions Above the First Eigenvalue on Nonconvex Pentagons

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

We construct bounded connected nonconvex planar pentagons for which the affine 2-Laplacian has a strictly positive Dirichlet eigenfunction at an eigenvalue strictly above its first variational eigenvalue. The same domain therefore supports positive affine eigenfunctions at two distinct values. The construction gives a negative answer, for n = p = 2, to the general-domain positive-eigenfunction question of Haddad, Jiménez and Montenegro. The mechanism is an affine-isotropic saddle formed by pinching a pentagon into two right isosceles triangles. A symmetry-preserving diagonal normalization has positive curvature, while a shear couples the ground state to a nearly coincident odd mode. We prove the sharp limit (λ₂ − λ₁)∂qqλ₁ → −32768/81 at the isotropic positions. An area-preserving apex slide has the corresponding limit −50π⁴. The saddles persist under small vertex perturbations, including examples with nonparallel convex-hull sides. Consequences include distinct isotropic positions on one linear orbit and failure of positive-definite-deformation log-convexity outside convexity.

October 21, 2026Read paper

Edition 1

Pure-Point Dirichlet Spectrum in an Enlarging Cube Tower

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

For every dimension d ≥ 2, we construct a connected quasi-conical open set whose Dirichlet Laplacian has a complete orthonormal basis of eigenfunctions and spectrum [0, ∞). The domain is a tower of adjacent enlarging cubes joined through positive windows tending to zero. Cube sizes and windows are chosen together. The construction gives an affirmative existence answer to the singular-continuous-spectrum question raised for this geometry by Krejčiřík and Lotoreichik and repeated in a recent spectral-geometry survey. At each finite attachment we continue a nested family of whole spectral clusters, including their multiplicities. A summable projection budget and a refreshed dense family of test vectors make the limiting finite-dimensional reducing subspaces complete. We also obtain a room-index L² tail bound and retain the possibility of placing one prescribed positive embedded eigenvalue by dilation.

October 20, 2026Read paper

Edition 1

Sharp all-times heat-content comparison and concentration on compact metric graphs

Scott Schubr

Primary subject: Mathematics
Subject subfield: Analysis and Spectral Theory
Paper type: Research Article
Manuscript stage: Preprint

A sharp integrated concentration comparison is proved for heat flow on finite compact connected metric graphs with a nonempty Dirichlet vertex set and standard Kirchhoff conditions elsewhere. The comparison with the mixed interval of equal total length applies to every nonnegative square-integrable initial datum. For initial datum one, it yields an all-times heat-content bound and characterizes equality at a single positive time. An exact positive-kernel deficit representation and a separate convolution formula for an asymmetric three-edge pitchfork accompany the proofs.

October 20, 2026Read paper

Probability and Statistics

Edition 1

Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory Bounds

Scott Schubr

Primary subject: Mathematics
Subject subfield: Probability and Statistics
Paper type: Research Article
Manuscript stage: Preprint

An exact sampler reads independent fair bits and emits an iid discrete target law, retaining only a fixed finite state between outputs. Temporary computation and the depth of each round’s prefix tree are unrestricted. We prove that zero asymptotic expected information loss is possible, on finite or countably infinite support, exactly when every positive mass is a reciprocal integer power of two. The formulation uses nonnegative finite-path loss and therefore also covers infinite entropy. The countable necessity argument reduces infinitely many output kernels to finitely many integer multiplicity types, then produces an exact positive rational normalization. For finite targets we develop a signed-charge cycle bound that remains effective when zero-gap products defeat every marked-symbol bound. For every fixed finite law with algebraic masses outside the reciprocal-power class, it gives a polynomial lower bound on loss in the number of retained states. Together with an existing exact-sampling construction, this determines logarithmic order of the minimum persistent memory as the tolerated loss tends to zero. These bounds transfer uniformly to countable conditional dyadic refinements, including infinite-entropy examples. An established logarithmic-form estimate gives a concrete exponent for a fully resonant example. Optimal leading constants and state-count exponents remain open.

October 22, 2026Read paper

Edition 2

First-Hit Stopping and Bias-Corrected Score Inference in Dimension Three

Scott Schubr

Primary subject: Mathematics
Subject subfield: Probability and Statistics
Paper type: Research Article
Manuscript stage: Preprint

We study the actual first residual crossing of the symmetric half-Sinkhorn iteration for observations from a fixed positive C⁸ density on the three-dimensional torus. At two heat scales, computed from the same sample, a linear combination removes the first-order population score bias. For ε = n^(−κ) with 2/17 < κ < 4/9 and every fixed 0 < γ < 3/4, stopping each run at its first projective mass residual below n^(−1/2) h^(−γ) preserves the corrected estimator’s fixed-query Gaussian limit. The stopping index is asymptotic to (3/4 − γ) log(1/h)/log 2, and the attained residual lies between c times the threshold and the threshold with probability tending to one for every fixed 0 < c < 1/2. The covariance retains the dependence between the two scales. An explicit cubic population coefficient gives a fixed analytic density for which the limit is shifted at κ = 2/17 and the normalized bias diverges below it, also under actual stopping. The formal Gaussian range extends to κ < 4/9; consistency and shrinking uncertainty require κ < 2/5. A sharp heat-spectral trace determines logarithmic corrections to the stopping count and phase-dependent residual limits, proving that the constants 1/2 and 1 in the residual bracket are sharp. Necessity or equality at the upper exponent is not asserted.

October 20, 2026Read paper

Edition 1

Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport

Scott Schubr

Primary subject: Mathematics
Subject subfield: Probability and Statistics
Paper type: Research Article
Manuscript stage: Preprint

We study observable residual stopping for the half-self-Sinkhorn iteration with samples from a fixed positive smooth density on the one- or two-dimensional torus. Under stated bandwidth and tolerance conditions, the first residual hit preserves the pointwise Gaussian limit of the exactly scaled empirical score. We determine the leading stopping count, bound the attained residual, and give an obstruction at the upper tolerance exponent. The proof controls the common empirical trajectory and nonuniform initialization.

October 18, 2026Read paper

Quantum Information Theory

Edition 1

Single-copy learning of noisy stabilizers by certified filtering

Scott Schubr

Primary subject: Mathematics
Subject subfield: Quantum Information Theory
Paper type: Research Article
Manuscript stage: Preprint

We give a single-copy recovery framework for an unknown qubit stabilizer state mixed with global white noise. For every fixed ε>0, 0<γ<1 and fixed confidence, the exact target can be recovered from O(n^(1+ε)) original copies when the retained signal has a known lower bound c₀≥2^(−(log₂ n)^γ). The total number of ideal quantum operations is polynomial, while classical processing takes 2^O(n/log log n) time. A random Clifford frame and a known partial-derivative measurement reduce discovery of one complete target Pauli to classical noisy-parity search. Fresh verification and a short certified seed then amplify the signal enough for known high-fidelity single-copy learning. This avoids recovering every graph row through a noisy solver. We also obtain polynomial classical time for every fixed positive signal under a supplied fractional diagonal-subspace promise, including dense CSS states and a CSS-defect class. The latter uses finite-field subspace recovery, with an explicit proof of the required fixed-weight extension. Supporting bounds distinguish partial code measurements from full-basis readout. The measurements, classical solvers and high-fidelity endpoint are established ingredients; the contribution is their operational combination and original-copy resource accounting. No general polynomial-time learner or arbitrary-noise guarantee is asserted.

October 22, 2026Read paper

Edition 1

Sharp noise transitions in adaptive single-copy stabilizer learning

Scott Schubr

Primary subject: Mathematics
Subject subfield: Quantum Information Theory
Paper type: Research Article
Manuscript stage: Preprint

We determine the noise-dependent behavior of the adaptive single-copy stabilizer-learning update of Bittel, Eisert, Gong, Mele and Schatzki on globally depolarized stabilizer states. For every fixed prime local dimension p, the number of diagonal stabilizers still missing follows an exact birth–death chain. Writing c for the retained pure-state weight, the expected time to record the optimizing stabilizer is linear in the number n of qudits when c² > p/(p+1), quadratic at equality, and exponential when c² < p/(p+1). We obtain the exact supercritical speed, subcritical exponential prefactors, and the complete 1/n critical-window mean profile. An exact regeneration identity distinguishes first exposure of the computational-basis target from its actual recording. A finite-time bound shows that below threshold the unchanged algorithm has exponentially small success probability in any polynomial round budget, even on this simple noise family. The obstruction concerns this update and candidate generation rule; it is not a lower bound for arbitrary adaptive single-copy measurements and does not resolve fully agnostic stabilizer learning.

October 22, 2026Read paper

Edition 2

Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensions

Scott Schubr

Primary subject: Mathematics
Subject subfield: Quantum Information Theory
Paper type: Research Article
Manuscript stage: Preprint

We strengthen proper agnostic learning of stabilizer states for arbitrary mixed inputs in every odd-prime dimension. Given stabilizer overlap F ≥ τ, the learner returns a pure stabilizer of overlap at least F − ε, with confidence 1 − δ, using exp(O(log²(2/τ))) poly(n,p,ε⁻¹,log(2/δ)) resources with absolute exponential constants and fixed polynomial degree. An even quotient-convolution argument strengthens mixed-input escape to (p−1)Fʳ/(4p), where r=6 for p≡3 mod4 and r=4 for p≡1 mod4. Spectral concentration and observed eigenoutcomes remove local-dimension losses from the exponent. This is a strengthened edition of the same work, using established measurement and bootstrapping methods.

October 19, 2026Read paper

Geometry and Optimal Transport

Edition 1

Frequency interactions and curvature in Fourier density models

Scott Schubr

Primary subject: Mathematics
Subject subfield: Geometry and Optimal Transport
Paper type: Research Article
Manuscript stage: Preprint

We classify the intrinsic sectional-curvature sign at the uniform density for every three-frequency aligned-cosine affine density model on the unit circle. All sectional curvatures are strictly negative except for the spectrum {m, 2m, 3m}, whose sharp attained range is π²m²[−25−√1649, −25+√1649]. A finite Fourier Gauss formula identifies the normal frequency interactions responsible for this exception. In arbitrary finite dimension, successive frequency ratios exceeding 1+√2 force a diagonal Fourier curvature operator and give an explicit attained negative curvature range; the constant is optimal for this universal diagonality assertion. Two four-frequency examples show that the triple criterion does not extend by inspecting subtriples and that a positive curvature-operator direction need not represent positive sectional curvature. As a computational application, we certify corrected heat-kernel Sinkhorn metrics and their parameter derivatives through order two on a fixed two-parameter box at five bandwidths. The smallest bandwidth has a uniform relative metric-error improvement greater than 870.37. We prove bandwidth-uniform magnitude bounds for the cancellation-preserving interval iteration and provide exact and interval reproducibility code. The curvature theorems concern intrinsic finite-dimensional model geometry; the finite-band certificates do not assert a new all-bandwidth convergence rate or a complexity bound.

October 22, 2026Read paper

Edition 1

Leading bias and positive correction of heat-kernel Sinkhorn metrics

Scott Schubr

Primary subject: Mathematics
Subject subfield: Geometry and Optimal Transport
Paper type: Research Article
Manuscript stage: Preprint

We identify the leading bias of the exact population heat-kernel Sinkhorn tensor on a flat torus and construct a compact, strictly positive correction with fourth-order smooth-input accuracy. The leading quadratic form is minus one forty-eighth of the Wasserstein Hessian of Fisher information, and an explicit nonconstant density exhibits both bias signs. The correction preserves the completed tangent form space and square-root range, with equivalent norms; full L² accuracy remains first order. An interval-certified nonconstant two-parameter example encloses continuum residual, differential-form and quadrature errors. For prescribed analytic density families sufficiently close to uniform, we construct fourth-order finite metric approximations, including normalization and every fixed parameter-derivative order. In each fixed dimension, per-coordinate Fourier resolution and iteration counts are logarithmic in inverse bandwidth; total modes and quadrature nodes grow as the dimension-th power of that logarithm. This is a resolution bound, not a running-time or optimality claim.

October 21, 2026Read paper

Edition 1

Sharp convergence of heat-kernel Sinkhorn metrics

Scott Schubr

Primary subject: Mathematics
Subject subfield: Geometry and Optimal Transport
Paper type: Research Article
Manuscript stage: Preprint

We study the Sinkhorn metric associated with the periodic heat kernel at a smooth strictly positive probability density. We prove convergence to the inverse weighted Laplacian in full L² operator norm at the optimal rate O(h). The sharper rate from Hʳ to L² is O(h¹⁺ʳᐟ²), 0 ≤ r ≤ 2; every exponent is optimal already at constant density. Parameter-differentiated estimates yield second-order convergence of smooth finite-dimensional pullback metrics and their intrinsic Christoffel symbols and curvature under nondegeneracy. A population normalization residual ρ gives projected tensor error O(h + ρ/h), with an obstruction at ρ comparable to h. We also give an explicit projected scale approximation whose tensor differs from the exact tensor by O(h²). The cost depends on the heat scale; fixed Euclidean squared-cost problems with boundaries are outside the scope.

October 21, 2026Read paper

Linear Algebra and Matrix Inequalities

Edition 1

A quantitative Chollet inequality for rank-four matrices of order seven

Scott Schubr

Primary subject: Mathematics
Subject subfield: Linear Algebra and Matrix Inequalities
Paper type: Research Article
Manuscript stage: Preprint

For every complex Hermitian positive semidefinite matrix A of order seven and rank at most four, we prove per(A ∘ conjugate(A)) ≤ (192/245)(per A)². The inequality is strict when all diagonal entries are positive. The main input is the bound per(A ∘ conjugate(A)) ≤ (3/5)(per A)² for every singular positive semidefinite matrix of order five. An exact rational principal-minor sum-of-squares certificate proves this singular-boundary inequality. A rank-preserving border comparison then gives the same constant in order six and the stated constant in order seven. The certificate and a standalone exact-integer verifier accompany the paper. Cauchy–Schwarz gives the corresponding two-factor inequalities when both factors have rank at most four.

October 20, 2026Read paper

Edition 1

Trace-perturbed minimizers of the mixed discriminant

Scott Schubr

Primary subject: Mathematics
Subject subfield: Linear Algebra and Matrix Inequalities
Paper type: Research Article
Manuscript stage: Preprint

For each fixed matrix size, we prove that the scalar tuple uniquely minimizes the mixed discriminant of positive semidefinite Hermitian matrices whose sum is the identity and whose individual traces are sufficiently close to one. This answers Question 1.7 of Gurvits-Leake, arXiv:2609.21083v2. The argument combines Gurvits's doubly stochastic uniqueness theorem with a positive constrained Hessian and compactness. We also record the exact region of positive definiteness of that Hessian at a scalar tuple. The global neighborhood in the theorem is qualitative and may depend on the size.

October 20, 2026Read paper

Combinatorics and Graph Theory

Edition 1

Local comparison counting for linear extensions and a bounded-range balance refinement

Scott Schubr

Primary subject: Mathematics
Subject subfield: Combinatorics and Graph Theory
Paper type: Research Article
Manuscript stage: Preprint

For uniform linear extensions of finite posets with bounded maximum incomparability degree, a local stable-partition estimate tracks the incomparability budget consumed by conditioning. The resulting three-vertex order bound gives a sharper explicit bounded-range balance estimate through the established finite-boundary argument. A complementary two-chain construction quantifies a rare-triple obstruction to reusing the sharp pair denominator. Complete proofs and exact finite reproducibility code accompany these counting refinements.

October 20, 2026Read paper

Edition 1

A sharp lower bound for adjacent-edge correlations in random subtrees

Scott Schubr

Primary subject: Mathematics
Subject subfield: Combinatorics and Graph Theory
Paper type: Research Article
Manuscript stage: Preprint

Choose uniformly a nonempty tree subgraph of the labeled complete graph, including single-vertex trees. For every n ≥ 3 and two distinct adjacent edges, we prove that the conditional probability of one edge, given the other, exceeds three quarters of its unconditional probability. The short proof combines classical fixed-forest extension counts, Jensen’s inequality and a count of four-vertex trees. The constant is sharp by the previously established asymptotic limit.

October 19, 2026Read paper

Number Theory and Special Functions

Edition 1

Small-ball estimates for Hölder centers of the Kloosterman process

Scott Schubr

Primary subject: Mathematics
Subject subfield: Number Theory and Special Functions
Paper type: Research Article
Manuscript stage: Preprint

We prove uniform-norm small-ball bounds of logarithmic order ε⁻² about every admissible 1/2-Hölder center of the Kloosterman limit process, including boundary coefficient and endpoint values. Graded Fejér approximation removes two logarithmic losses from an inspected earlier lower estimate. We determine worst-case power orders over admissible Hölder classes, give an explicit O(log log p/√log p) uniform-path Wasserstein convergence rate for prime Kloosterman paths with both parameters averaged, and derive uniform shrinking-target counts. Extensions to bounded symmetric unimodal coefficient laws include sharp noncritical boundary power thresholds and a fixed-center obstruction at equality. The critical logarithmic gap remains unresolved. Classical inputs and inspected prior work are credited; no priority or optimal-rate claim is made.

October 19, 2026Read paper

Edition 2

Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificates

Scott Schubr

Primary subject: Mathematics
Subject subfield: Number Theory and Special Functions
Paper type: Research Article
Manuscript stage: Preprint

We classify the least degree of a polynomial whose square has negative signed-moment value for the normalized fixed-center Riemann theta product. On 3 ≤ x ≤ 12 the degree has fourteen transitions, takes values between five and fifteen, and is nonmonotone; every transition and equality case is determined. Jacobi symmetry extends the classification to π²/12 ≤ x ≤ 12. Two- and three-summand theta models approximate all fourteen crossings with respective root errors below 0.00049 and 2.588 × 10⁻¹⁰. Twenty explicit rational Gram certificates include a seven-point example stable under absolute entrywise errors of 1.94 × 10⁻⁷. The paper also establishes fixed-degree Gaussian limits and single-summand degree-five positivity.

October 19, 2026Read paper

Coding Theory

Edition 1

Independent Squares and Average-Radius Obstructions for Linear Codes

Scott Schubr

Primary subject: Mathematics
Subject subfield: Coding Theory
Paper type: Research Article
Manuscript stage: Preprint

Independent affine squares yield binary-input average-radius list-recovery obstructions for linear codes over finite fields. The paper proves an exact two-fiber certificate cost, develops unequal shortening groups, and gives sixteen-word folded Reed–Solomon constructions with mean relative error 3/4. Complete proofs, three certificates, and a portable reproduction package accompany the manuscript.

October 19, 2026Read paper

Edition 1

Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codes

Scott Schubr

Primary subject: Mathematics
Subject subfield: Coding Theory
Paper type: Research Article
Manuscript stage: Preprint

For eight distinct points over an arbitrary field, we construct a finite nonnegative rational certificate bounding the total population of the two largest fibers of every linear quotient. The certificate has intercept two and dimension cost at most nine, attained by the Boolean three-cube. A folded-Wronskian argument gives an average-radius list-recovery bound for primitive-power folded Reed–Solomon codes with input lists of size two and output cap seven. Supporting results treat structured sixteen-point configurations.

October 18, 2026Read paper