Weiqi Jiang

Nodal-Length Bounds for Surface Metrics with Isolated Non-Analytic Points

We prove a C_g sqrt(lambda) upper bound for nodal lengths on closed surfaces whose metrics are analytic away from finitely many isolated points and satisfy a summable quantitative analytic-scale condition near those points. The result includes an explicit smooth non-analytic toru...

Nodal-Length Bounds for Surface Metrics with Isolated Non-Analytic Points

We prove a C_g sqrt(lambda) upper bound for nodal lengths on closed surfaces whose metrics are analytic away from finitely many isolated points and satisfy a summable quantitative analytic-scale condition near those points. The result includes an explicit smooth non-analytic toru...

Nodal-Length Bounds for Surface Metrics with Isolated Non-Analytic Points

We prove a C_g sqrt(lambda) upper bound for nodal lengths on closed surfaces whose metrics are analytic away from finitely many isolated points and satisfy a summable quantitative analytic-scale condition near those points. The result includes an explicit smooth non-analytic toru...

An exact constant-term reduction and partial p-adic results for Sun's Conjecture 2.2(i)

We prove several rigorous partial results for Zhi-Wei Sun's Conjecture 2.2(i). The numerator is positive, and the exact 2-adic valuation gives the complete 2-adic unit criterion; whenever the quotient is integral, this yields the conjectured parity criterion. An exact all-index f...

Forward-KL Learning Curves of Maximum Likelihood Estimators Need Not Be Monotone

Let L_n be the expected forward Kullback–Leibler risk of the maximum-likelihood estimator based on n independent observations from a correctly specified model. We show that L_n need not be nonincreasing, even for a one-dimensional full, regular, minimal natural exponential family...

Forward-KL Learning Curves of Maximum Likelihood Estimators Need Not Be Monotone

Let L_n be the expected forward Kullback–Leibler risk of the maximum-likelihood estimator based on n independent observations from a correctly specified model. We show that L_n need not be nonincreasing, even for a one-dimensional full, regular, minimal natural exponential family...

Dual General Position in Lexicographic Products with a Complete First Factor

Let G be a nonempty finite simple graph. For every m ≥ 2, we prove gp_d(K_m ∘ G) = m q_2(G), where q_2(G) is the maximum size of a set A ⊆ V(G) for which both G[A] and G[V(G) ∖ A] are complete, and set q_2(G) = 0 if no such set exists. This resolves a previously posed problem con...

Dual General Position in Lexicographic Products with a Complete First Factor

Let G be a nonempty finite simple graph. For every m ≥ 2, we prove gp_d(K_m ∘ G) = m q_2(G), where q_2(G) is the maximum size of a set A ⊆ V(G) for which both G[A] and G[V(G) ∖ A] are complete, with value zero if no such set exists. This answers the published complete-first-facto...

An algebraic 21-vertex intertwiner for a non-elliptic XYZ Lax operator

Fukai and Yamada introduced a Lax operator with a three-dimensional auxiliary space for the spin-1/2 XYZ chain whose entries are algebraic rather than elliptic. We give an explicit algebraic 9 × 9 intertwiner for this operator. The matrix has the 21-vertex pattern and is written...

An algebraic 21-vertex intertwiner for a non-elliptic XYZ Lax operator

Fukai and Yamada introduced a Lax operator with a three-dimensional auxiliary space for the spin-1/2 XYZ chain whose entries are algebraic rather than elliptic. We give an explicit algebraic 9 × 9 intertwiner for this operator. The matrix has the 21-vertex pattern and is written...

Type-Voltage Covers and Finite Locally Kneser Graphs

For every integer d ≥ 3, we construct a connected graph on twice the binomial coefficient ‘3d + 1 choose d’ vertices that is locally the Kneser graph K(2d + 1, d). The construction on the line n = 2d + 1 uses a binary voltage cover of K(3d + 1, d), with voltage determined only by...

Exact Signs and Sharp Boundaries for Product-Binomial Dold Coefficients

Let X be a rational exterior space and let f: X → X. Let A = Q(f*) be the graded action on the indecomposable quotient of the positive-degree rational cohomology of X. Suppose that χ_A(t) = t^s ∏_j (t^{n_j} − a_j)^{k_j}, with a nonempty product and every a_j ≥ 3. Powering the bin...

Prism-Slice h-star Polynomials: Interlacing Through Reduced Level Five and a Level-Six Counterexample

Let c be a positive integer capacity vector with total capacity C, let 1 ≤ k ≤ C − 1, and put m = min{k, C − k}. We prove both clauses of the prism-slice conjecture when m ≤ 5: the h-star polynomial is real-rooted, and for every legal unit split the unsplit polynomial weakly inte...

Prism-Slice h-star Polynomials: Interlacing Through Reduced Level Five and a Level-Six Counterexample

Let c be a positive integer capacity vector with total capacity C, let 1 ≤ k ≤ C − 1, and put m = min{k, C − k}. We prove both clauses of the prism-slice conjecture when m ≤ 5: the h-star polynomial is real-rooted, and for every legal unit split the unsplit polynomial weakly inte...

Bezoutian Decoupling for Conformal Yang–Mills Multiplets in (A)dS

Metsaev's formulation of conformal Yang–Mills theory in six, eight, and ten dimensions admits a change of variables from a generic auxiliary-field presentation to a direct sum of massless and massive Stueckelberg systems. The proposed matrices in arbitrary even dimension were lef...

Exact Signs and Sharp Boundaries for Product-Binomial Dold Coefficients

Let X be a rational exterior space and let f: X → X. Let A = Q(f*) be the graded action on the indecomposable quotient of the positive-degree rational cohomology of X. Suppose that χ_A(t) = t^s ∏_j (t^{n_j} − a_j)^{k_j}, with a nonempty product and every a_j ≥ 3. Powering the bin...