Catalog

Repositories

Latest version of each Zenodo concept by Logica Artificialis. A row shows only the files on that record, and a GitHub address only when the manuscript names one.

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Also deposited

33 repositories

10.5281/zenodo.237601692026
Finite incidence models for elliptic resonance varieties
Martino Lupini · Mathematics
Let E = A ⊕ B be a sum of line bundles of degrees 2 ≤ a ≤ b on a smooth complex elliptic curve. We determine all irreducible components of the locus of two-dimensional spaces of sections that generate a sheaf of rank one. Their number is a if A ≇ B, and max{1, a−2} if A ≅ B. Relative Grassmannians and projective bundles give smooth finite normalization models for these components. In saturation degree two, the normalization maps are closed embeddings.
PDF · LaTeX · GitHub named
10.5281/zenodo.236828572026
Local units and multiplier algebras of AF corona ideals
Martino Lupini · Mathematics
Let A be a simple unital separable infinite-dimensional AF algebra, fix a tracial state τ, and put D = A ⊗ K. Let I be the closed trace ideal of M(D) associated with τ, and set J = I/D and Q = M(D)/D. We prove that, under the Continuum Hypothesis, the canonical inclusion Q ⊂ M(J) is proper. More precisely, there is a positive contraction m ∈ M(J) such that dist(m,Q) = 1/2 and |M(J)| = dens‖·‖ M(J) = 2^c, where c = 2^ℵ₀. The construction produces globally compatible multiplier actions on an exhaustive family of projection corners. Countable Riesz separation suffices for the limit-stage interpolation. In ZFC, every countable subset of J has a projection unit, with a lift of arbitrarily small finite trace, and every multiplier agrees on that subset on both sides with an element of J.
PDF · LaTeX · GitHub named
10.5281/zenodo.234770162026
Ascending chains of sublattices in free lattices
Martino Lupini · Mathematics
We prove that every increasing sequence of free sublattices of bounded finite rank in a free lattice is eventually constant. In particular, there is no infinite strictly increasing chain of copies of the free lattice on three generators, answering negatively a question of R. A. Dean recorded in 1997. Freeness is essential: we construct in the three-generated free lattice an infinite strictly increasing chain of pairwise nonisomorphic retracts, each requiring exactly three generators. The corresponding retractions commute. We also give a proper self-embedding whose fixed-point sublattice contains a free copy of the ambient lattice, and prove that the stable image of every endomorphism of a finitely generated free lattice consists precisely of its periodic points.
PDF · LaTeX · GitHub named
10.5281/zenodo.234517182026
Simultaneous avoidance of power families of null sequences
Martino Lupini · Mathematics
Let (a_n) be a positive sequence tending to zero with liminf a_(n+1)/a_n > 0. For every η ∈ (0,1), we construct a compact set E ⊆ [0,1] of Lebesgue measure greater than 1−η such that {x+s a_n^λ : n ≥ 1} is not contained in E for any x ∈ ℝ, s ≠ 0, and λ > 0. No monotonicity is required, and one set works for all positive powers simultaneously, with infinitely many distinct points of every copy outside E. Taking a_n=e^(−n) gives one compact set of measure arbitrarily close to one containing no infinite geometric progression of any ratio in (0,1), answering negatively a question of Burgin, Goldberg, Keleti, MacMahon and Wang. We also prove a uniform finite hitting statement for ratios in a compact range and scales in [1,2]. The proof adapts random routing to grids shared by all exponents, with a localized count of exponent and scale parameters and a compactness repair for exceptional centres.
PDF · LaTeX · Lean · Notes · Data · GitHub named
10.5281/zenodo.234404152026
Lipschitz positive decompositions of von Neumann preduals
Martino Lupini · Mathematics
We prove that the selfadjoint predual of a complex von Neumann algebra admits a Lipschitz positive decomposition if and only if the algebra is subhomogeneous. In particular, infinite-dimensional selfadjoint trace class gives a negative answer to the Lipschitz decomposition problem, confirming Messerschmidt's 2018 conjecture. For a nonzero subhomogeneous algebra of maximal matrix degree $d$ , the least Lipschitz constant of a positive majorant $q(x)\geq\pm x$ is attained and equals the corresponding constant $c_d$ for $d\times d$ trace class. Among nonzero von Neumann algebras, the optimal constant equals one exactly for the abelian algebras. The finite-dimensional constants satisfy $c\log\log N\leq c_N\leq C\log N$ for all sufficiently large $N$ , with absolute constants $c,C>0$ . The lower bound applies to arbitrary positive majorants; the upper bound comes from the classical absolute-value estimate.
PDF · LaTeX · GitHub named
10.5281/zenodo.234403022026
Isometric canonical maps into free convex Banach lattices
Martino Lupini · Mathematics
For every $1<p<\infty$ , we construct a three-dimensional real Banach lattice $X$ which is not $p$ -convex with constant one, although its canonical positive map into the free $p$ -convex Banach lattice with constant one is isometric. Dimension three is minimal. In every dimension $n\geq3$ , such examples can be arbitrarily close to $\ell_p^n$ under the coordinate lattice isomorphism. An elementary example answers the necessity question raised by Marcel de Jeu and Xingni Jiang in 2025 for general convexity types; the three-dimensional construction gives a negative answer even for ordinary constant-one $p$ -convexity. We characterize isometry by an exact factorization of dual functionals through two positive coordinates. For a Banach lattice, the criterion says that every sublattice of $X^*$ generated by two disjoint positive elements is $p'$ -concave with constant one. The counterexample separates this two-generator condition from full concavity. At $p=\infty$ , in contrast, isometry forces the original norm to be an AM-space norm.
PDF · LaTeX · GitHub named
10.5281/zenodo.234401542026
Common null complements for polynomial images of finite sums of perfect sets
Martino Lupini · Mathematics
Fix an integer D ≥ 1, and let A₁, …, A₍D₊₂₎ be nonempty compact perfect subsets of the real line. For their Minkowski sum C = A₁ + ⋯ + A₍D₊₂₎, we construct a single null Fσ set B ⊆ ℝ such that P(C) + B = ℝ for every nonconstant real polynomial P of degree at most D. In particular, every sum of three compact perfect sets has one null complement that works under every nonzero dilation. Thus the conclusion of Jung and Lai’s Conjecture 4.8 holds for these sums; the conjecture remains open for arbitrary perfect sets. The conclusion applies to some sums with zero logarithmic Hausdorff and packing dimensions that contain no polynomial image of an infinite summable finite-digit product. The proof isolates a local sum hypothesis that permits the same construction for more general compact sets.
PDF · LaTeX · Notes · GitHub named
10.5281/zenodo.234195772026
Amalgamation in an infinite chain of commutative idempotent residuated-lattice varieties
Martino Lupini · Mathematics
We construct a strictly increasing infinite chain of finitely generated varieties of commutative idempotent residuated lattices, each with the amalgamation property. The generator of Vₙ is a quasiprimal (n+3)-element algebra obtained by adjoining an absorbing least element to a bounded lattice with n incomparable interior elements; multiplication is join elsewhere. Homogeneity, congruence extension, and the classical homomorphism-extension method yield amalgamation. For n ≥ 2 the varieties are not semilinear, and for n ≥ 3 they are not lattice-distributive. This answers negatively the unrestricted finiteness question posed by Fussner, Metcalfe, and Santschi in Interpolation and the Exchange Rule, circulated in 2023 and published in 2026. The distributive version remains open. Among finite Stanovský algebras L⁰, amalgamation holds exactly when the interior of L is an antichain. Strong amalgamation holds for V₀ and fails for every Vₙ with n ≥ 1.
PDF · LaTeX · Python · Data · GitHub named
10.5281/zenodo.234193932026
The variety of integral residuated lattices fails the amalgamation property
Martino Lupini · Mathematics
We answer negatively the open question whether integral residuated lattices have the amalgamation property, recorded by Metcalfe, Paoli, and Tsinakis in their 2023 monograph and explicitly posed by Jipsen and Santschi in Residuated lattices do not have the amalgamation property. A span of finite integral residuated lattices, with a three-element common algebra and extensions of sizes five and six, has no amalgam even among all residuated lattices. Thus the three-element Gödel chain, in the signature without a bottom constant, is not an amalgamation base. The same example excludes amalgamation in every variety containing the five-element chain, including the varieties of n-potent integral residuated lattices for all n ≥ 2. We also isolate a local obstruction without global integrality assumptions and characterize amalgamation of a common-bottom quotient-product span by extension of the corresponding congruence.
PDF · LaTeX · Python · Data · GitHub named
10.5281/zenodo.234055082026
A universal Banach–Mazur stability radius for von Neumann algebras
Martino Lupini · Mathematics
We prove cohomological criteria for ordinary complex Banach–Mazur stability of von Neumann algebras, without separability, type, or density restrictions. A fixed algebra has a positive stability radius if its second bounded Hochschild cohomology vanishes and its third coboundary space is norm closed. For any class closed under countable bounded direct products, vanishing in degrees two and three gives one radius for the entire class. Assuming the degree-two and degree-three vanishing theorem in the September 2026 preprint of OpenAI, this yields one $\varepsilon>0$ such that, for all complex von Neumann algebras $M,N$ ,
PDF · LaTeX · Python · Data · GitHub named
10.5281/zenodo.234048042026
Polynomial estimates for K-convexity from Walsh decay and cotype
Martino Lupini · Mathematics
We obtain polynomial bounds for the norm K(X) of the Rademacher projection on a Banach space X. If the probability-normalized Walsh transform on the s-dimensional cube has norm at most 1/2 on L2(X), then K(X) ≤ 9000s log(6000s2). Consequently, for each 1 < p ≤ 2, the type constant Tp(X) satisfies K(X) ≲p Tp(X)p/(p−1)(1 + log Tp(X)). This improves the exponential upper bound in Naor’s 2022 quantitative question, without determining optimal dependence.
PDF · LaTeX · GitHub named
10.5281/zenodo.233720662026
Finite sums and idempotency for dynamically central piecewise syndetic sets
Martino Lupini · Mathematics
A set of positive integers is a set of pointwise recurrence if it supplies a return of every point to every neighborhood of itself in every minimal topological dynamical system. We prove that every such set contains finite-sums configurations of every finite rank. More generally, this holds after intersection with a return set to a neighborhood of a point in a minimal system: every dynamically central piecewise syndetic set is IP₀. The finite-sums configurations can be chosen with a piecewise syndetic set of simultaneous completions; their generators may be taken superincreasing.
PDF · LaTeX · GitHub named
10.5281/zenodo.233716902026
Pointwise convergence of bilinear averages for two commuting transformations
Martino Lupini · Mathematics
Let T and S be commuting measure-preserving transformations of a probability space. We prove that, for f,g ∈ L³, the bilinear averages (1/N)∑ₙ₌₁ᴺ f(Tⁿx)g(Sⁿx) converge almost everywhere and satisfy an L³ᐟ² bound for their full r-variation for every r > 2. In particular, this answers the bounded-input convergence question recorded as Problem 19 in Frantzikinakis’s 2016 survey, without an invertibility assumption.
PDF · LaTeX · GitHub named
10.5281/zenodo.232914432026
Arithmetic denominators and ordinary compact orbit comparisons
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.231050332026
An eight-element parachute lattice and its dual: finite representations with two unary operations
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX · Notes · Data
10.5281/zenodo.229298252026
Continuous Lipschitz spaces on topometric spaces and free-space dynamics
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.229297642026
The countable cube with the supremum metric is not Lipschitz universal
Martino Lupini · Mathematics
The countable cube with the supremum metric is not Lipschitz universal
PDF · LaTeX
10.5281/zenodo.229237112026
Norm formulas, independence, and spaces of types
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228906182026
Rosenthal representations of homogeneous spaces: rank-one classifications and higher-rank criteria
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228863602026
Low-complexity factors of compact affine semigroup actions
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228433542026
Nonabelian extensions of Solecki's coset dichotomy
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228428972026
Twisted Iwahori gluing and central extensions of SL2(Z[1/2])
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228398652026
UCT-universal nuclear quotients of a binary wreath product
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228341372026
Congruence stability for an Iwahori gluing problem
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228167792026
Joint Euler-cocycle estimates and simplicial volume of surface bundles
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.228137522026
A matrix convexity characterization of the noncommutative Poulsen simplex
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.227616302026
Universal minimal flows for unital Kirchberg and AF algebras
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.227583052026
Circular colorings of abelian Cayley graphs below four
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.227378282026
L\'evy stabilizers of the Poulsen simplex, the Gurarij space, and their noncommutative analogues
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.226918402026
Homogeneity of complete M-faces of the noncommutative Poulsen simplex
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX · Data
10.5281/zenodo.226870572026
Derived limits and the phantom spectrum of Fréchet-Schwartz spaces
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX · Data
10.5281/zenodo.226858692026
Dynamical spectra of separable unital scattered $C^*$-algebras and Cartan pairs
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX
10.5281/zenodo.223344012026
Bratteli graphs
Martino Lupini · Mathematics
No abstract on this deposit.
PDF · LaTeX · Data

Repositories

Finite incidence models for elliptic resonance varieties

Local units and multiplier algebras of AF corona ideals

Ascending chains of sublattices in free lattices

Simultaneous avoidance of power families of null sequences

Lipschitz positive decompositions of von Neumann preduals

Isometric canonical maps into free convex Banach lattices

Common null complements for polynomial images of finite sums of perfect sets

Amalgamation in an infinite chain of commutative idempotent residuated-lattice varieties

The variety of integral residuated lattices fails the amalgamation property

A universal Banach–Mazur stability radius for von Neumann algebras

Polynomial estimates for K-convexity from Walsh decay and cotype

Finite sums and idempotency for dynamically central piecewise syndetic sets

Pointwise convergence of bilinear averages for two commuting transformations

Arithmetic denominators and ordinary compact orbit comparisons

An eight-element parachute lattice and its dual: finite representations with two unary operations

Continuous Lipschitz spaces on topometric spaces and free-space dynamics

The countable cube with the supremum metric is not Lipschitz universal

Norm formulas, independence, and spaces of types

Rosenthal representations of homogeneous spaces: rank-one classifications and higher-rank criteria

Low-complexity factors of compact affine semigroup actions

Nonabelian extensions of Solecki's coset dichotomy

Twisted Iwahori gluing and central extensions of SL2(Z[1/2])

UCT-universal nuclear quotients of a binary wreath product

Congruence stability for an Iwahori gluing problem

Joint Euler-cocycle estimates and simplicial volume of surface bundles

A matrix convexity characterization of the noncommutative Poulsen simplex

Universal minimal flows for unital Kirchberg and AF algebras

Circular colorings of abelian Cayley graphs below four

L\'evy stabilizers of the Poulsen simplex, the Gurarij space, and their noncommutative analogues

Homogeneity of complete M-faces of the noncommutative Poulsen simplex

Derived limits and the phantom spectrum of Fréchet-Schwartz spaces

Dynamical spectra of separable unital scattered $C^*$-algebras and Cartan pairs

Bratteli graphs