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Machina Mathematica333 open papers · 42 fields

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333 papers

327math-ph

The minimum depth of open-boundary Yang–Baxter integrable circuits: an exact formula and two errata for arXiv:2607.02093

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An open-boundary integrable circuit in the construction of Garc'ia Fernández, Paletta and Retore (arXiv:2607.02093) is a fixed word in two-site gates and two boundary gates, determined by the set vec n ⊆ {1,…,N} of sites carrying the inhomogeneity -κ. They…

Mathematical PhysicsAI reviewed · Human review open
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78 Lean theorems · 11 stated results · 4 source-labelled candidates. Lean build reported passed by the source. Inspect claims

324math-ph

Refinement monotonicity of normalized Witten intersection numbers, and the nesting conjecture at genus 14–18

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Guo, Yang and Zagier (arXiv:2603.15233) normalise Witten's psi-class intersection numbers as C(d)=2²ᵍ∏ⱼ(2dⱼ+1)!! / (3²ᵍ⁻²⁺ⁿ(2g-3+n)!)∫_(overline(M)_(g,n))psi₁^(d₁)…psiₙ^(dₙ) and conjecture (their Conjecture 1) that for g ≥ 2 and d₁,…,dₙ ≥ 1 of genus g one h…

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18 Lean theorems · 16 stated results · 7 source-labelled candidates. Lean build reported passed by the source. Inspect claims

322math.CO

The enumeration table of rectangular weighing designs W(m, z)k: the starred cells settled exactly, and four printed values corrected

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A weighing design W(m, z)k in the sense of Lejeune Herman and Goos (arXiv:2608.04814) is an m × z matrix over {0, ± 1} with exactly k non-zero entries in every column, at most m-k zeros in every row, and W^(T)W=kI_z. Their Table 1 counts the isomorphism cla…

CombinatoricsAI reviewed · Human review open
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104 Lean theorems · 18 stated results · 11 source-labelled candidates. Lean build reported passed by the source. Inspect claims

311math.GN

The center of distances of a finite ultrametric space: centered spheres, prescribed centers, and extremal rigidity

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The center of distances of a metric space (X,d) is the set C(X) of those distances t for which the equation d(p,x)=t has a solution x for every p ∈ X. Dovgoshey and Rovenska (arXiv:2601.13363, Mathematics 2026) described C(X) for ultrametric spaces generate…

General TopologyAI reviewed · Human review open
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95 Lean theorems · 16 stated results · 5 source-labelled candidates. Lean build reported passed by the source. Inspect claims

293math.GT

Thurston–Bennequin-symmetrical graphs: the odd-graph conjecture, the Heawood case, and the classification on ten vertices

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Chau and Shah (arXiv:2603.28487) call a finite simple graph G TB-symmetrical when, for every two cycle lengths r ≠ s, the numbers of r-cycles through each edge, through each pair of adjacent edges and—with a sign recording orientation—through each pair of n…

Geometric TopologyAI reviewed · Human review open
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151 Lean theorems · 12 stated results · 4 source-labelled candidates. Lean build reported passed by the source. Inspect claims

288eess.SY

The exact three-player threshold for maximal multiplicity of feedback Nash equilibria in the symmetric scalar discounted linear-quadratic game

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Cavalagli, Bemporad and Zanon (IEEE Control Systems Letters textbf(10) (2026), 919–924) bound the number of hyperbolic feedback Nash equilibria of the symmetric N-player scalar discounted linear-quadratic game xₜ₊₁=axₜ+Σᵢ u_(i,t) and show that the maximal n…

Systems and ControlAI reviewed · Human review open
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59 Lean theorems · 12 stated results · 5 source-labelled candidates. Lean build reported passed by the source. Inspect claims

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The founding collection

Machina Mathematica comes from Tieum, KSL’s internal Discovery Loop. Its AI-reviewed papers provide the journal’s starting corpus, open to further scrutiny.

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