A. Esterov

L. Vladimirov

A. Yuran

A Whitney-type cusp and fold theorem is proved for general algebraic surface projections and for sparse univariate polynomial discriminants. 

Whitney fold and cusp for algebraic surfaces, and singularities of discriminants

Whitney revisited

L. B. Anderson

 A. Constantin

J. Gray

Y. He

S. Lee

A. Lukas

We introduce CIPro, a new toolkit that automates calculations on Calabi–Yau geometries and helps explore string compactifications and vacua.

CIPro package: complete intersections in products of projective spaces and line bundles

A Calabi–Yau toolkit

K. Lee

T. Oliver

Y. Qi

Computer vision distinguishes elliptic curves from random data and predicts analytic rank by reading arithmetic patterns in digital images.

Computer vision and converse theorems

Arithmetic as images

O. Gamayun

M. Gritskov

A. Losev

A new algebraic method shows beta functions arise when conformal symmetry breaks, reproducing Cardy’s formula without computing correlators.

Cohomological beta function

Cohomological beta

O. I. Pat

C. Pascu Moca

Strong interactions reshape transport in one-dimensional quantum gases, with unusual temperature effects and anomalous current fluctuations.

Nonequilibrium full counting statistics of multicomponent strongly-interacting quantum gases with defects

Multicomponent flow

N. Kurnosov

C. Spicer

The Global Spherical Shell conjecture is proved for a class of complex surfaces with two singular holomorphic foliations, a key open case.

Class VII surfaces with b₂ = 3 and two foliations are Kato

From Foliations to Kato

D. Lu

M. Li

Z. Zeng

W. Hou

J. Wang

F. Yang

 Y. You

How doping a featureless Mott insulator yields high-temperature superconductivity and explains pressure effects in bilayer nickelates.

Superconductivity from doping symmetric mass generation insulators: application to La₃Ni₂O₇ under pressure

Mott to superconductor

C. Mishra

J. Tan

Canonical connections in string compactifications are computed for a broad class of bundles over Calabi-Yau manifolds by a new method.

Hermitian Yang-Mills connections on general vector bundles: geometry and physical Yukawa couplings

Physics of bundles

E. Sobko

The principle of maximal transcendentality is proved to all orders for the vacuum energy of a strongly interacting quantum field theory.

Maximal transcendentality of the double-scaled PCM

Transcendentality proof

R. Mahore

G. Noetinger

R. Fleury

C. Coulais

B. Apffel

A new metamaterial composed of oscillators driven by external pumping is used to study the unidirectional drift of stable phase dislocations.

Dynamical frustration in space-time metamaterials

Dynamical frustration

T. Fink

The output distribution of a deep-layered machine with random logics exhibits a critical network depth, at which it is maximally biased.


Exact distribution of the output of a deep-layered machine

Deep-layer distribution

Z. Wan

S. T. Yau

A colour symmetry extension of baryon plus lepton symmetric gapped quantum topological order replaces families of massive sterile neutrinos.

Fermion families and Pontryagin class: Topological field theory via colour symmetry extension

Three fermion families

V. Lysov

Supersymmetric systems are classified via BV formalism, extending localisation and identifying when integrals reduce to critical points.

BV-refinement of the on-shell supersymmetry and localization

Localisation in BV

A new proof of the Chern–Gauss–Bonnet theorem is derived using supersymmetry and BV localisation, reducing geometry to critical points.

Chern-Gauss-Bonnet theorem via BV localization

Gauss–Bonnet via BV

A. Stepanenko

K. Chernova

M. Gorlach

Simultaneous propagation along multiple paths speeds excitation transfer in long-range lattices, proving an evident quantum advantage.

Quantum advantage in transfer of quantum states

Multi-path transfer

S. Yau

Extending family symmetry by colour cancels a Standard Model global anomaly, linking three colours to favour three fermion generations.

Three families and Pontryagin class mod 3: topological order via symmetry extension

Three-family puzzle

D. Pesce

G. Caldarelli

Weight pruning uncovers critical behaviour in deep neural networks with a sharp transition from functional cooperation to disordered failure.

Phase transitions in neural networks pruning

An AI phase change

We give a theory for the output of deep-layered machines and show that, as the network depth increases, it is biased towards simple outputs.

Deep-layered machines have a built-in Occam’s razor

Deep learning simplicity

A. Kasprzyk

Q. Le

D. Riabchenko

Machine learning finds “champion” codes by predicting and optimising their minimum Hamming distance, a measure of a code’s robustness.

Machine learning discovers new champion codes

AI for error correction

M. Panfil

A canonical quantum fluid model is solved exactly, revealing universal correlation patterns governed by Gaussian random-matrix ensembles.

The exact dynamical structure factor of one-dimensional hard rods and its universal random matrix behavior

Exact hard-rod dynamics

Gravitational anomalies causing baryon and lepton number violation in the Standard Model are resolved using new fermionic topological orders.

Anomalous (3+1)d fermionic topological quantum field theories via symmetry extension

Fermionic dark matter

Time-optimal control of large quantum systems is computed efficiently by applying boundary conditions to a brachistochrone–Lax framework.

Efficient computation of quantum time-optimal control

Towards optimal control

I. Rodkin

D. Orel

K. Smirnov

A. Bolatov

B. Elbouardi

B. Hassan

Y. Kuratov

A. Bulatov

P. Nakov

T. Baldwin

A. Shelmanov

M. Burtsev

By increasing the effective depth of neural networks, we improve their sequential reasoning abilities in tasks involving cellular automata.

Beyond memorization: extending reasoning depth with recurrence, memory and test-time compute scaling

Boosting AI reasoning

T. Mudarisov

T. Petrova

R. State

We demonstrate that transformer attention can only discriminate well at shorter context lengths, losing clarity as input length increases.

Limitations of normalization in attention mechanism

Limits of attention

A. V. Kosyak

We demonstrate that the Lawrence–Krammer representation arises as a q-deformation of the symmetric square of the Burau representation.

The Lawrence-Krammer representation is a quantization of the symmetric square of the Burau representation

Braid representations

Y. You

Fractional conductivity between the nuclear and electromagnetic higher symmetries reveals four global Lie gauge groups of the Standard Model.

Topological responses of the standard model gauge group

Topological responses

V. Jejjala

B. D. Nelson

 H. Schenck

M. Stillman

The rich and intricate vacuum geometry of the Minimal Supersymmetric Standard Model—a complex manifold—is characterised for the first time.

Vacuum geometry of the standard model

Standard Model vacuum

Birational methods in algebraic geometry are used to explicitly describe the vacuum structure of the Minimal Supersymmetric Standard Model.

The vacuum moduli space of the minimal supersymmetric standard model

Analysing the vacuum

Z. K. Minev

K. Najafi

S. Majumder

 A. Stern

E. Kim

C. Jian

G. Zhu

With IBM Quantum, we braid non-abelian Fibonacci anyons in string-net condensates to realise fault-tolerant universal quantum computation.

Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

Fibonacci anyons

A general approach to proving the irreducibility of representations of infinite-dimensional groups within the frame of Ismagilov's conjecture.

The generalized characteristic polynomial, corresponding resolvent and their application

Group representations

M. A. Mir

O. Lychkovskiy

Z. Ristivojevic

Quantum many-body systems share patterns of dynamics that are exactly described by tridiagonal matrices based on continuous Hahn polynomials.

Exactly solvable models for universal operator growth

On universal dynamics

F. Carta

A. Gauntlett

F. Griffin

We show reinforcement learning can be used to check whether a certain class of quantum field theory has a finite spectrum of stable particles.

BPS spectroscopy with reinforcement learning

Reinforcing spectra

S. Lal

We introduce an AI-based framework for finding solutions to the Yang-Baxter equation and discover hundreds of new integrable Hamiltonians.

Deep learning based discovery of integrable systems

Learning integrability

Sterile neutrinos are replaced by topological order as dark matter candidates to counterbalance the Standard Model’s gravitational anomalies.

Topological quantum dark matter via global anomaly cancellation

Topological dark matter

The abilities and power of a type of transformer model with memory are greatly improved by learning several key tasks at once during training.

Mastering long-context multi-task reasoning with transformers and recurrent memory

Multitasking memory

K. Anokhin

P. Bateson

Based on computer simulations, we argue developmental plasticity accelerates evolution and drives organisms towards ever-greater complexity.

Facilitation of evolution by plasticity scales with phenotypic complexity

Adaptability speeds evo

Y. Li

Charge conjugation C, space reflection R, and time-reversal T operators are regularised in a quantum many-body Hilbert space on a discrete lattice.

Quantum many-body lattice C-R-T symmetry: fractionalisation, anomaly, and symmetric mass generation

Regularising CRT

Varying the spacetime dimensions fermions occupy shows charge-conjugation C, space-reflection R and time-reversal T symmetries are 8-fold periodic.

C-R-T fractionalisation in the first quantised Hamiltonian theory

An 8-fold way for CRT

Charge-conjugation, space-parity and time-reversal symmetries are shown to form noncommutative groups, including the order-16 Pauli group.

C-R-T Fractionalisation, Fermions, and Mod 8 Periodicity

C, P and T in fractions

Disentangling links in networks

Clusters of neurons