All limits.

Stored keys and values grow linearly in layers, context tokens, KV heads, and head width.

Largest allocation cluster permitted by exFAT revision 1.00 sector and cluster shift fields.

Upper Cluster Heap count encoded by the exFAT ClusterCount field.

Largest sector count representable by the exFAT VolumeLength field.

Recommended upper volume size using the largest cluster and recommended cluster-count ceiling.

Largest directory DataLength permitted by exFAT revision 1.00.

Maximum minimum-sized file directory-entry sets in a 256 MiB directory stream.

Standard permutation-invariant message-passing GNNs cannot distinguish graphs that one-dimensional Weisfeiler-Leman cannot distinguish.

With injective aggregation and sufficient capacity, GIN matches one-dimensional Weisfeiler-Leman distinguishing power.

Non-injective neighborhood aggregation loses distinctions available to the 1-WL test.

Upper capacity bound for piecewise-linear networks with W parameters and L layers.

Constructive lower capacity bound for piecewise-linear networks over the stated parameter range.

Tight parameter-unit capacity order for networks with W parameters and U nonlinear units.

Arbitrarily deep residual networks with one-neuron hidden layers are universal L1 approximators.

Observed extremely low-mass white dwarfs establish a dated one-sided low-mass frontier rather than a universal minimum.

Exact dense dot-product attention forms all n-by-n query-key interactions of width d.

Explicit storage of the dense attention score or probability matrix grows quadratically with sequence length.

Summing per-step attention over a growing cached context gives quadratic total interaction work.

Radiative luminosity at which outward opacity force balances gravity in spherical steady flow.

Critical mass for gravitational instability in the conventional uniform isothermal Jeans analysis.

Classical disruption distance for a synchronously rotating fluid satellite on a circular orbit.

Leading-order radius of the secondary's gravitational sphere of influence in the restricted three-body approximation.

A k-layer local message-passing network depends only on each node's k-hop computation neighborhood.

IPv6 minimum link MTU is 1280 bytes under RFC 8200 IPv6 links. Links unable to convey it in one piece must provide lower-layer fragmentation and reassembly.

Exact two-way-assisted secret-key capacity of a pure-loss bosonic channel without repeaters.

The Leech lattice packing is optimal among all congruent-sphere packings in R^24.

Demonstrated coded DNA storage density reported by the DNA Fountain experiment.

Maximum ordinary UDP payload over IPv4 is 65507 bytes under UDP over IPv4 with a 20-byte IPv4 header and 8-byte UDP header. IPv4 options are excluded.

Maximum ordinary UDP payload over IPv6 is 65527 bytes under ordinary UDP over IPv6 with an 8-byte UDP header. IPv6 jumbograms and extension-header overhead are excluded.

Minimum iid labeled examples for distribution-free realizable PAC learning of VC dimension d.

Optimal distribution-free sample order for agnostic binary classification with VC dimension d.

Engineering far-field half-power beamwidth approximation for a uniformly illuminated continuous linear aperture.

Maximum affine regions cut by n ReLU hyperplanes in d-dimensional general position.

Parameter bound for an [[n,k,d]] quantum error-correcting code.

Sphere-packing parameter bound for nondegenerate binary quantum codes.

Unassisted quantum capacity of a qubit erasure channel with erasure probability p.

The general unassisted quantum capacity is open; the hashing coherent-information lower bound and dimensional upper bound form a verified interval.

Model-inferred current mass of R136a1 in the cited analysis; revisions and multiplicity remain part of the open frontier.

Largest capacity in the BDXL R3 multi-layer recordable format.

Second-order approximation to maximal code size at blocklength n and error epsilon.

Time and angular-frequency standard deviations of a finite-energy signal obey the Fourier uncertainty principle.

Engineering high-resolution SQNR approximation for a full-scale sinusoid quantized by an ideal N-bit uniform quantizer.

Gaussian compressed sensing with basis pursuit has a sharp asymptotic sparsity–undersampling transition.

A finite-dimensional code detecting arbitrary single-subsystem errors cannot have a universal transversal encoded gate set.

Capacity of a binary symmetric channel with crossover probability p.

Capacity of a binary erasure channel with erasure probability epsilon.

Capacity per use of a real discrete-time additive white Gaussian noise channel.

Necessary and sufficient length inequality for a binary prefix code.

Exact best error probability for fixed-length almost-lossless coding of a discrete source block.

Squared-error rate-distortion function of an iid zero-mean Gaussian source.