Tubular tilings of binary mixtures obey global Euler balance laws that infer hidden-phase topology from the observable phase plus interface geometry, and for d>2 they form a subclass of soft (corner-free) tilings.
Cambridge University Press
7 Pith papers cite this work. Polarity classification is still indexing.
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2026 7representative citing papers
Asymptotic Shannon entropy on G/H equals the spectral radius c(G,H;μ) for finite-entropy measures, with Rényi rates converging and explicit classifications for subgroups having pair rapid decay or subexponential Lorentz control, including equivalence to finite index in SL_n(Z) for n≥3.
Cross-index of free G-posets satisfies a sharp union bound xind(P) ≤ xind(A) + xind(B) + 1 for Z2 but only xind(P) ≤ xind(A) + 2(xind(B)+1) for other G, with arbitrarily large gap to the topological index.
Computations for A1, Ak, D4, E8 and other singularities show finite discriminant torsion is a codimension-two phenomenon, not generic for nodes, with threefold ordinary double points being torsion-free.
Contradictory preference cycles in Condorcet's paradox are non-orientable surfaces: the Klein bottle (unrealised) or the real projective plane (realised), yielding an orientability reformulation of Arrow's theorem.
For bounded surfaces the mapping class group is isomorphic to the boundary-fixing automorphisms of the fundamental groupoid.
Proposes a hierarchy of structured flow models bridging continuous fields and data-driven graphs, with cross-domain validation on physical systems to guide model simplification.
citing papers explorer
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Soft cells, Tubular Tilings and the Hidden Phases in Binary Mixtures
Tubular tilings of binary mixtures obey global Euler balance laws that infer hidden-phase topology from the observable phase plus interface geometry, and for d>2 they form a subclass of soft (corner-free) tilings.
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Entropy on Homogeneous Spaces and Classification Results for Subgroups with the Pair Rapid Decay Property
Asymptotic Shannon entropy on G/H equals the spectral radius c(G,H;μ) for finite-entropy measures, with Rényi rates converging and explicit classifications for subgroups having pair rapid decay or subexponential Lorentz control, including equivalence to finite index in SL_n(Z) for n≥3.
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The mapping index through the lens of the cross-index
Cross-index of free G-posets satisfies a sharp union bound xind(P) ≤ xind(A) + xind(B) + 1 for Z2 but only xind(P) ≤ xind(A) + 2(xind(B)+1) for other G, with arbitrarily large gap to the topological index.
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Torsion Trajectories from Local Discriminants to Global Obstructions
Computations for A1, Ak, D4, E8 and other singularities show finite discriminant torsion is a codimension-two phenomenon, not generic for nodes, with threefold ordinary double points being torsion-free.
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The Non-Orientable Topology of Condorcet's Paradox
Contradictory preference cycles in Condorcet's paradox are non-orientable surfaces: the Klein bottle (unrealised) or the real projective plane (realised), yielding an orientability reformulation of Arrow's theorem.
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The Dehn-Nielsen-Baer Theorem for Bounded Surfaces
For bounded surfaces the mapping class group is isomorphic to the boundary-fixing automorphisms of the fundamental groupoid.
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A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations
Proposes a hierarchy of structured flow models bridging continuous fields and data-driven graphs, with cross-domain validation on physical systems to guide model simplification.