arXiv subjects

Ruiliang Li

Publications and source records attributed to Ruiliang Li.

9 recordsLinked to original sources

arXiv2026

Resolved Maxwell-Boundary Normal Forms and Exact Reentrant Scaling in Accelerating AdS Black Holes

Reentrant phase transitions of accelerating anti-de Sitter black holes are known numerically, but their apparent loss at small string tension has lacked an analytic explanation. In the single-string ensemble at fixed pressure, charge, and tension, we solve the unrestricted two-phase Maxwell-turning problem for the charged slowly accelerating C-metric. Elimination forces the two horizon coordinates to coincide and yields a closed one-parameter locus. An exhaustive enumeration of the remaining equilibria establishes global phase selection throughout the physical black-hole sector. The locus exists for $0<\mu<0.202602$, with no positive lower threshold. As $\mu\to0$, the pressure and temperature widths of the reentrant window contract as the fourth and third powers of the tension, while the entropy gap and latent heat diverge. A two-chart blow-up gives a parameter-free limiting profile and identifies thermodynamic-volume inversion as the turning mechanism between two distinct noncritical phases. At a Maxwell boundary with fixed sheet incidence, projective Newton data of the thermodynamic jumps determine the leading coexistence profile. Their positive simple roots fix the turn count, order, and curvature signs; the C-metric realizes the primitive binomial class.

hep-th↗

arXiv2026

Finite-energy hard celestial current algebra from the Banerjee--Mandal--Sahoo dipole Ward identity in QED

We use the Banerjee--Mandal--Sahoo dipole-current Ward identity for the one-loop logarithmic soft-photon theorem as input and determine its finite-energy action on Mellin-difference hard currents. The commutator with such hard currents has a scheme-independent hard-hard residue that survives every one-particle redefinition. With the meromorphic continuation stated explicitly below, a two-particle Plancherel transform identifies this residue with an analytic two-particle primary module, and the coefficient map is a hard-current one-cocycle. The cocycle defines a minimal filtered abelian extension. It has a canonical two-particle primitive and integrates to an affine action. For scalar hard legs, the fixed-leg operator agrees coefficient by coefficient with the symmetry-governed long-range logarithmic tower of Choi, Kadhe, and Puhm. Applied to a tree-level scalar-QED photon-exchange block, the finite-energy analysis determines the logarithmic two-particle coefficient functional from the ordinary hard amplitude and the Banerjee--Mandal--Sahoo ordered-pair soft kernel. This gives a finite-energy relation between the Banerjee--Mandal--Sahoo dipole-current Ward identity and the exponentiated long-range celestial OPE.

hep-th↗

arXiv2026

When does a state-dependent proto-area define a bulk geometry?

An area-like function for each boundary region need not come from a single bulk geometry. Cross-region locality requires the data for all regions to factor through a single boundary-length map. We formulate this common-source condition as a nonlinear sewing problem. For a fixed network chamber, we derive exact primal and dual certificates together with an operator-valued criterion for central area operators. On the hyperbolic disk, the first variation lies in the range of the rank-two geodesic X-ray transform. At second order, extremality no longer removes geodesic displacement, and the forced Jacobi equation determines the normal Hessian of renormalized boundary length. We prove a gauge-invariant necessary and sufficient criterion for a regular proto-area coefficient two-jet to arise from a metric two-jet. At a product reference, we prove an exact orthogonal decomposition for the Bogoliubov--Kubo--Mori (BKM) metric associated with the Petz recovery map. If the traced-out factor is nontrivial, no unrestricted reverse stability bound exists; on an observable tangent space the sharp constant is $(1-\alpha_E)/\alpha_E$, with $\alpha_E$ the minimum retained BKM fraction. Combining the geometric and information-theoretic structures yields BKM--Jacobi matching: the negative BKM information-loss form must equal the Jacobi normal acceleration across the full interval family. We construct two isometric code families with complementary obstructions. Exact regional central area operators on the recoverable algebra can fail to sew into one local graph geometry, while a fixed-central-fiber affine logical path has zero first response and a nonzero quadratic witness. Under source density, sampled-data convergence, and first- and second-derivative consistency, corrected discrete witnesses converge to the continuum obstruction.

hep-th↗

arXiv2026

Spherical-DAHA predictions for boundary monopole bubbling of non-minuscule 't Hooft lines in $\mathcal N=4$ SYM

We study non-minuscule boundary 't Hooft lines in four-dimensional $\mathcal N=4$ $U(N)$ super Yang--Mills theory with the regular Nahm-pole boundary condition. For one-row charges we construct the exact spherical-DAHA operator $\mathbf e_+h_r(Y)\mathbf e_+$, determine its finite shift expansion and discrete Macdonald spectrum, and evaluate the S-dual Neumann Wilson two-line index as a finite-$N$ Macdonald pairing. For the first non-minuscule $U(2)$ coefficient, a local two-minuscule convolution model with Higgs branch $T^*\mathbb P^1$ has two Jeffrey--Kirwan residues, while subtracting the determinant intersection-cohomology summand supplies the additional $-\mathfrak t$ term. The same transverse $A_1$ calculation, dressed by the spectator-root factor, reproduces the first lower $U(3)$ coefficient. The local convolution calculation and its spectator lift provide low-rank checks of the complete DAHA coefficients independent of the inverse recursion, while their boundary-localization interpretation remains conjectural. Assuming an isometric oriented boundary Fourier intertwiner, the DAHA construction is compatible with the expected boundary S-duality relation.

math-ph↗

arXiv2026

Deterministic Trust Regions for Finite-Window Black-Hole Spectroscopy in GW250114

We study finite-window black-hole spectroscopy in the loud-event regime and ask when a multimode ringdown fit supports a stable common-remnant Kerr interpretation. Starting from whitened, tapered detector-frame data, we prove a deterministic frequency-extraction theorem for a projected sampled Prony--matrix-pencil pipeline with explicit statistical, algorithmic, omitted-tail, and mismatch terms. We then construct a local inverse atlas for the Kerr $(\ell,m,n)=(2,2,0)$ map on an event-local detector-frame remnant box for GW250114 and propagate the resulting primary uncertainty into $(2,2,1)$ and $(4,4,0)$ consistency tests. These ingredients yield a detector-frame trust criterion for individual windows. We calibrate mismatch and colored-noise radii on a GW250114-like synthetic waveform bank built from public surrogate, CCE, and numerical-relativity information, and we apply the resulting bounds to the public H1/L1 strain and public parameter-estimation products for GW250114. The accepted windows form an intermediate post-peak band: earlier windows remain sensitive to start-time drift and structured nuisance fits, whereas later windows become variance dominated. Within that band, the recovered remnant remains consistent with the public inspiral--merger--ringdown estimates and supports a common-remnant Kerr interpretation that survives the full preprocessing and robustness checks. For loud events, the relevant question is therefore which finite detector-frame windows sustain spectroscopy, not whether some multimode fit can be made in isolation.

gr-qc↗

arXiv2026

Two-mode dominance and deterministic parameter bias bounds for equatorial Kerr-de Sitter ringdown

We study scalar waves on subextremal Kerr-de Sitter spacetimes in a compact slow-rotation regime and at a fixed overtone index. Working initially at a fixed cosmological constant $\Lambda>0$ and uniformly for $(M,a)$ in a compact slow-rotation set, using the meromorphic/Fredholm framework for quasinormal modes and a semiclassical equatorial labeling proved in a companion paper, we establish a quantitative two-mode dominance theorem in an equatorial high-frequency package: after exact azimuthal reduction, microlocal equatorial localization, and analytic pole selection by entire localization weights constructed from equatorial pseudopoles, the $k=\pm\ell$ sector signals are each governed by a single quasinormal exponential, up to an explicitly controlled tail and an $\mathcal O(\ell^{-\infty})$ contribution from all other poles. We then develop a fully deterministic frequency-extraction stability estimate based on time-shift invariance, and combine it with the two-mode dominance result and the companion paper's inverse stability theorem to obtain an explicit parameter bias bound for ringdown-based recovery of $(M,a)$. Finally, using the companion paper's three-parameter inverse theorem and a damping observable based on the scaled imaginary part of one equatorial mode, we propagate the same deterministic error chain to a local bias bound for recovery of $(M,a,\Lambda)$ on compact parameter sets with $|a|$ bounded away from $0$. As a further consequence, we obtain a localized pseudospectral stability statement for the equatorial resolvent package, quantifying how large microlocalized resolvent norms enforce proximity to the labeled equatorial poles. The resulting estimates clarify the conditioning mechanisms (start time, window length, shift step, and detector nondegeneracy) and provide a rigorous PDE-to-data interface for high-frequency black-hole spectroscopy.

math-ph↗

arXiv2026

Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes

We study an inverse resonance problem for the scalar wave equation on the Kerr-de Sitter family. In a compact subextremal slow-rotation regime and at a fixed overtone index, high-frequency quasinormal modes admit semiclassical quantization and a real-analytic labeling by angular momentum indices. Using this structure, we first prove that a finite equatorial high-frequency package of quasinormal-mode frequencies determines the mass and rotation parameter $(M,a)$ (for fixed cosmological constant $\Lambda>0$), with a quantitative stability estimate. As a key geometric input we compute explicit second-order (in $a$) corrections to the equatorial photon-orbit invariants which control the leading real and imaginary parts of the quasinormal modes. Finally, allowing $\Lambda$ to vary in a compact interval, we show that adding one damping observable (the scaled imaginary part of a single equatorial mode) yields a three-parameter inverse theorem: a finite package of three independent real observables determines $(M,a,\Lambda)$ locally in the slow-rotation regime away from $a=0$.

math-ph↗

arXiv2026

Canonical torsion linking pairings and explicit TMF state spaces of closed 3-manifolds

We study the TMF-valued $(3+1)$-dimensional TQFT of Gukov--Krushkal--Meier--Pei and give an explicit description of the TMF-module state space assigned to a closed $3$-manifold. Our starting point is the torsion linking pairing on $H_1$, viewed as a discriminant form. We construct a canonical, computable package of invariants for torsion linking pairings (uniformly for odd and $2$-primary parts), and from it a canonical tokenization together with an explicit symmetric integral matrix representative realizing the same stable class. This yields an explicit model for the GKMP state space in terms of a rank-one TMF-module $L_b$ with a canonical degree shift determined by signature data. As applications we identify the values on $CP^2$ and, conditional on a natural functoriality/duality statement in GKMP, on $S^2\times S^2$ with the Hopf elements $\pm\nu$ and $\eta$, respectively. Finally, we establish a rank-one time-reversal duality $L_{(-n)}\simeq L_{(n)}^\vee[1]$ for all integers $n$.

math.AT↗

arXiv2025

On an Erd\H{o}s--Lov'asz problem: 3-critical 3-graphs of minimum degree 7

Erd\H{o}s and Lov'asz asked whether there exists a "3-critical" 3-uniform hypergraph in which every vertex has degree at least 7. The original formulation does not specify what 3-critical means, and two non-equivalent notions have appeared in the literature and in later discussions of the problem. In this paper we resolve the question under both interpretations. For the transversal interpretation (criticality with respect to the transversal number), we prove that a 3-uniform hypergraph $H$ with $\tau(H)=3$ and $\tau(H-e)=2$ for every edge $e$ has at most 10 edges; in particular, $\delta(H)\le 6$, and this bound is sharp, witnessed by the complete 3-graph $K^{(3)}_5$. For the chromatic interpretation (criticality with respect to weak vertex-colourings), we give an explicit 3-uniform hypergraph on 9 vertices with $\chi(H)=3$ and minimum degree $\delta(H)=7$ such that deleting any single edge or any single vertex makes it 2-colourable. The criticality of the example is certified by explicit witness 2-colourings listed in the appendices, together with a short verification script.

cs.DM↗