All limits.

Conditional-entropy bound induced by any estimator's error probability.

Information cannot increase under stochastic post-processing.

A subgaussian measurement matrix satisfies k-order restricted isometry with high probability at logarithmic oversampling.

The exact Euclidean kissing number in dimension 1 is 2.

The exact Euclidean kissing number in dimension 2 is 6.

The exact Euclidean kissing number in dimension 3 is 12.

The exact Euclidean kissing number in dimension 8 is 240.

The exact Euclidean kissing number in dimension 24 is 196560.

UCB1 has logarithmic instance-dependent expected regret for bounded iid arm rewards.

Classic zero-metallicity stellar models predict complete disruption over a model-dependent helium-core mass interval.

Every k-sparse solution of Ax=y is unique exactly when the measurement matrix spark exceeds 2k.

Model-dependent lower main-sequence mass for sustained hydrogen burning near solar composition.

Upper brown-dwarf mass boundary is the same composition-dependent transition to sustained hydrogen burning.

Squared concurrence shared by one qubit with two others obeys the CKW monogamy inequality.

Linearity forbids universally deleting one copy of an unknown state while retaining the other.

IPv6 jumbo-payload length maximum is 4294967295 bytes under the RFC 2675 32-bit Jumbo Payload option. Jumbograms begin at 65,536 bytes.

Posterior expected risk is controlled by empirical risk and divergence from a data-independent prior.

Any reliably dated star supplies a one-sided lower bound on cosmic age, with stellar-model uncertainty retained.

Averaged uniformly over all objective functions, optimization algorithms have identical performance.

Ideal entangled N-probe estimation can scale no better than inverse total coherent resource number.

Independent-probe phase estimation exhibits inverse-square-root resource scaling.

Asymptotic existence lower bound for families of binary stabilizer quantum codes.

A set of mixed quantum states can be broadcast exactly if and only if the states commute.

Weighted majority competes with the best of N experts under bounded losses.

Covariance of an unbiased estimator is bounded below by inverse Fisher information.

Van Trees lower bound combines expected data Fisher information and prior information.

Estimation MSE is bounded through binary hypothesis-testing error probabilities.

Deterministic exact teleportation of one arbitrary qubit consumes one ebit and two classical bits.

A noiseless qubit channel assisted by one shared ebit transmits two classical bits per use.

Tabular Q-learning converges under finite MDP, sufficient exploration, bounded rewards, and Robbins-Monro step sizes.

Finding weights consistent with labeled examples is NP-complete even for the specified three-node network.

Online halving makes at most logarithmically many mistakes when a finite class contains a perfect hypothesis.

Winnow learns a monotone disjunction with k relevant variables among n attributes with logarithmic dimension dependence.

Optimal deterministic realizable online mistake complexity equals the class Littlestone dimension.

DNS-over-UDP historical message-size limit is 512 bytes under original RFC 1035 DNS over UDP. The historical limit excludes IP and UDP headers and predates EDNS.

Sufficient realizable-case sample size for a consistent learner over a finite hypothesis class.

Sample order sufficient for uniform convergence over a finite binary hypothesis class.

N Euclidean points admit a low-dimensional embedding preserving all pairwise distances within 1±epsilon.

IPv4 total-length field maximum is 65535 bytes under the RFC 791 16-bit Total Length field. The value includes the IPv4 header and payload.

UDP length-field width is 16 bits under the RFC 768 UDP header. The encoded length includes the eight-byte UDP header.

Maximum CHSH correlator allowed by quantum mechanics.

A bank of generalized sampling channels must collectively provide Nyquist density to reconstruct an arbitrary B-bandlimited signal.

Universal Lempel–Ziv coding converges to entropy rate for stationary ergodic finite-alphabet sources.

Rate-distortion function with correlated side information only at the decoder.

Perfect-secrecy capacity of a degraded discrete memoryless wiretap channel.

Semiclassical temperature of an uncharged nonrotating black hole.

M unit vectors in an N-dimensional complex space cannot all have smaller pairwise coherence.

Idealized mass-cubed lifetime from blackbody Hawking power for a neutral nonrotating black hole.

Lossless separate-encoder rate region for two correlated memoryless sources.

Two-user capacity region for a physically degraded discrete memoryless broadcast channel.