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When amplified noise kills the signal, the method reduces to rescaling one noisy measurement, overshooting the ideal by up to 21%.
· “Benchmarking Error Mitigation: Artefactual Improvements in Zero-Noise Extrapolation”
New Jacobian lens reads, swaps, and ablates the representations that drive silent reasoning and strategic deliberation.
· “Verbalizable Representations Form a Global Workspace in Language Models”
A sharp projection estimate proves the 2-copy threshold matches the 1-copy threshold in every dimension.
At least d^{2−o(1)} copies are needed for constant-precision spectrum, entropy, and rank estimates.
Every eligible pair count now obeys the 2^{k−1} bound, settling a cryptographic conjecture from 2011.
A 2/3-1/3 mix of known mechanisms beats the old factor-4 on every Euclidean space.
· “Breaking the 4-Approximation Barrier in Strategyproof Two-Facility Location”
Field-line-dependent bounce actions are fine as long as the drift loop closes inside the plasma
· “Symmetry-agnostic stellarators for collisionless confinement”
Proof of the pyramid-over-Ramsey-base theorem by induction on colours, using only classical product and simplex arguments.
Proof resolves the maximizer conjecture for n≥123: every graph with 2(n−2) edges has algebraic connectivity at most 2.
· “Maximizing Algebraic Connectivity with 2(n-2) Edges: The Large Vertex Number Case”
Certified interval arithmetic proves a noncircular real-analytic domain with a boundary-constant Neumann eigenfunction.
· “A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures”
Pre-trained on auto-captioned real-world trajectories, it tops four benchmarks and learns new tasks in under 10 hours.
It settles a decades-old open problem and resolves Feige's conjecture as well.
A fractional obstacle decomposition plus a Lewy-Stampacchia estimate settles a 1986 problem from the International Congress of…
· “A dimension-free weak-type (1,1) bound for the vector Riesz transform on mathbb{R}^n”
Heat-flow inequality yields the optimal M* bound and extends Pisier's MM* estimate to nonsymmetric bodies.
The Gaussian guess is only the leading term; higher-order corrections are explicit Bernoulli polynomials of the fractional displacement of t
Staged writes and gated tool calls beat eight baselines across five LLM backbones.
· “MemTX: Transactional Belief Commit for Stateful Agent Memory”
The proof replaces numerical invariants by a well-founded history of certified blowup steps.
A wavefunction-only probe reads off the parity anomaly in gapless 2D matter, converging to 1/2 with power-law corrections.
· “Parity Anomaly as Modular Commutator with Massless Dirac Fermion”
Non-abelian lifted-product codes reach distance 18 at 20% encoding rate, promising practical fault-tolerant processors.
Inverse level matrices flow to mirror SCFTs; the duality wall reproduces the E8_1 character.
· “3d mathcal N=4 rank-zero mirror symmetry, TQFT interfaces, and Zagier duality of Nahm sums”
Exact rank and a new lower bound show every convex calibrated surrogate pays quadratic dimension.
· “Exact Rank and Convex Calibration Dimension Lower Bounds for the Multi-Label F1 Loss”
Full answer to a 1989 conjecture: any measurable set concentrates no more L²-mass than the interval of the same length.
On complete graphs, every edge pair is strictly negatively correlated at every size.
Cube orientation plus suffix averaging settles agnostic PAC sample complexity up to universal constants.
A unified framework covers general separable kernels and mirror flows, closing a decades-old iterate convergence gap.
· “A Unified Framework for Iterate Convergence of Bregman Proximal Methods”
A bifurcation branch on a real-symmetry relaxation reaches integer symmetries, refuting Schiffer and Pompeiu together.
SOP1, SOP2, and SOP3 are one property, collapsing the bottom of the finite-cycle hierarchy.
Dimension-free lower bound and matching worst-case construction settle the tight rate for projectively separated data.
· “Tight Worst-Case Bounds for the Smallest Eigenvalue of ReLU NTK Gram Matrices”
Both feasibility and refutation now have explicit witnesses up to a 1/poly(log log d) factor.
Answers the area-integral problem: bounded solutions vanish for every α; smooth unbounded ones persist for α<1.
· “Variable-Radius Disk Transforms and an Area-Integral Problem of Zalcman”
At criticality avalanches stay finite; just above it they go infinite—so the stationary law has a sharp cutoff.
· “Sharpness of the avalanche phase transition in the Bak--Sneppen model”
A matching lower bound closes the factor-r gap and sets the polynomial sample-complexity order.
One tensor merges the metric with SU(2) curvature and bounds 4D volume by the second Chern number.
· “Quaternion-Kahler geometry of time reversal symmetric crystals”
Algebra inclusions decide which side can steer which—not tomography.
· “Quantum steering is equivalent to state-preserving conditional expectations”
The least C in the polynomial bound is max of 1 and 2|q|/(1+sqrt(1-|q|^2)).
It proves Shannon-entropy Bregman iterates converge to critical points on nonconvex problems.
· “On the Iterate Convergence of Bregman Projected Gradient Method”
New charges from Einstein equations realize the deformed celestial algebra on the radiative (A)dS4 phase space.
· “Higher-spin charges and the L_(Λ) w_(1 + infty) algebra in (A)dS₄”
New rule predicts how laser polarization and phase switch odd-, even-, and mixed-parity spin splitting in one material.
One Schwinger integral gives all tree-level bispectra; squeezed limit shows an exponentially enhanced collider clock.
A partonic re-analysis cuts hard production rates, changing forecasts for dark matter, leptogenesis, and gravitational waves.
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