![The minimum resolvable deficit in a conditional-variance statistic-a measure reflecting the precision with which primordial fluctuations can be discerned-scales inversely with the effective number of usable Fourier modes, though foreground contamination and systematic effects can reduce this precision, and crossing a classical bound defined by [latex]\mathcal{E}^{(\mathrm{cl})}=10^{-2}[/latex] would falsify any classical stochastic description, a threshold potentially within reach of next-generation multi-tracer galaxy surveys and 21 cm intensity mapping experiments where decoherence is parametrically suppressed ([latex]\Gamma\_{\rm dec}\sim g^{2}H\ll H[/latex]).](https://arxiv.org/html/2601.13053v1/x1.png)
New research proposes a way to distinguish between quantum and classical origins of primordial fluctuations by searching for violations of specific inequality constraints in cosmological observations.
A new benchmark reveals the challenges of evaluating long-term memory in large language models and highlights limitations in current reward systems.
![Refractive index measurements, when analyzed with piecewise linear fits, validate the relationship described in Eq.(13) regarding the ratios [latex]\frac{\langle I^{q}\rangle}{\langle I\rangle^{q}}\big|\_{\boldsymbol{x}\_{0}}[/latex] for [latex]q=4,5,6[/latex] as a function of [latex]\frac{\langle I^{2}\rangle}{\langle I\rangle^{2}}\big|\_{\boldsymbol{x}\_{0}}[/latex], demonstrating how even seemingly precise data can be framed by the limitations of constructed models.](https://arxiv.org/html/2601.11213v1/Q_SUM_4_5_6.jpg)
A new stochastic model captures how light propagates through complex, ever-changing environments, offering insights into phenomena like atmospheric scintillation.
This review clarifies the conditions under which solutions exist for complex hybrid systems driven by continuous-time signals.
Researchers have uncovered a surprising link between charge ordering, liquid crystal behavior, and superconductivity within a unique silicon-based material.
![The effective mass squared of the D5 embedding field, examined across varying angular coordinates at a fixed value of [latex]u_0 = 1[/latex], indicates a violation of the BF bound-and consequent chiral symmetry breaking-prior to the emergence of a geometric singularity, except in the specific case of [latex]\theta = 0[/latex] and its immediate vicinity.](https://arxiv.org/html/2601.11136v1/x16.png)
New research explores how the transition between confined and deconfined states of matter relates to the breaking of chiral symmetry using a unique holographic model.
A new analysis reveals how overlapping harmonic signals create ‘spectral interference’ in time-frequency representations, impacting the accuracy of signal processing techniques.
![Autocorrelation functions reveal how stored patterns - assessed with [latex]K=1[/latex] and [latex]K=100[/latex] - evolve across sub-critical, critical, and super-critical dynamical phases, demonstrating a relationship between temporal lag [latex]\Delta n[/latex] and the system’s responsiveness to initial conditions.](https://arxiv.org/html/2601.11478v1/Autocorrelation_Coincidences_IETs_PDF_N_patterns_100.png)
New research explores the dynamic interplay between complexity and order in a model of associative memory, revealing how networks achieve optimal information storage and recall.
A new theoretical framework explores the unusual singularities that emerge in the parameter spaces of complex systems undergoing phase transitions, revealing hidden connections between symmetry and topology.
New research provides a generalized algebraic framework for understanding the Page transition, the moment when information escapes a black hole during Hawking radiation.