All limits.

How few genes does a living cell need to independently grow and divide? The JCVI-syn3.0 synthetic bacterium demonstrates the smallest genome shown to support autonomous life in a laboratory setting — not a claim about the theoretical minimum for life itself.

Graphene is the strongest material ever measured. This record cites the specific tensile strength observed for defect-free monolayer graphene under controlled nanoindentation testing — a scoped experimental result, not a claim about bulk graphene sheets or composites.

Normal human cells don't divide forever — the Hayflick limit is the historical observation that established cellular senescence as a real biological phenomenon, not the discovery of a single universal number.

No measurement strategy, however clever, can extract more classical (readable) information out of a quantum ensemble than its Holevo quantity χ — a hard ceiling on quantum communication capacity that sits below the naive per-qubit rate one might expect.

The kissing number problem asks how many equal, non-overlapping spheres can simultaneously touch a central sphere of the same size — a question that gets dramatically harder as dimension increases, and is only exactly solved in a handful of dimensions.

Erasing one bit of information in a logically irreversible way necessarily dissipates heat into the environment — a fundamental link between information and thermodynamics. The minimum dissipated energy is Q ≥ k_B T ln(2), where T is the system's temperature.

The Margolus–Levitin theorem sets a fundamental speed limit on how fast any physical process, including computation, can occur: an isolated quantum system needs at least τ ≥ πℏ/[2(E−E₀)] to evolve into a fully distinguishable (orthogonal) state.

Beyond a certain mass, a neutron star's own gravity overwhelms the quantum pressure holding it up, and it collapses into a black hole. The exact maximum mass depends on the poorly-constrained neutron-star equation of state; this record cites an early rigorous bound assuming causality.

The no-cloning theorem is one of quantum mechanics' foundational impossibility results: unlike classical information, an arbitrary unknown quantum state cannot be copied — a direct consequence of the linearity of quantum evolution, and the basis for quantum cryptography's security guarantees.

The Nyquist–Shannon sampling theorem sets the minimum rate at which a continuous signal must be sampled to be perfectly reconstructed — sample too slowly and distinct frequencies become indistinguishable (aliasing).

Matrix multiplication underlies everything from computer graphics to machine learning. The naive algorithm takes O(n³) operations for n×n matrices, but faster algorithms exist — the matrix multiplication exponent ω tracks the best asymptotic speed anyone has proven achievable.

Optical fiber capacity-distance demonstrations track the practical frontier of how much data can be transmitted how far through fiber — a moving target as multi-core fiber and better amplification push the record higher each year.

Ramsey's theorem guarantees that large enough structures always contain order: however you two-color the edges of a large enough complete graph, a monochromatic triangle becomes unavoidable. R(3,3) is the smallest such threshold.

Long-context language models don't retrieve information from anywhere in their context window with equal reliability — accuracy varies with where the relevant fact sits, how many distractors surround it, and which model and prompt are used, so no single model-independent floor can be asserted.

Shannon's noisy-channel coding theorem defines the hard ceiling on reliable communication: no coding scheme can transmit information faster than a channel's capacity without introducing errors, no matter how sophisticated the encoding.

The traveling salesman problem — finding the shortest route visiting every city once — is NP-hard to solve exactly, so research focuses on how close a fast algorithm can guarantee to get to the true optimum for realistic (metric) instances.

Maximum regular-file size using extents on ext4 with 4 KiB filesystem blocks.

Maximum regular-file size using extents on ext4 with 64 KiB filesystem blocks.

Filesystem-size ceiling from 2^32 addressable blocks of 4 KiB each.

Arithmetic block-address ceiling from 2^64 blocks of 4 KiB; practical implementation limits may be lower.

The exact two-color Ramsey number R(3,4) is 9.

The exact two-color Ramsey number R(3,5) is 14.

The exact two-color Ramsey number R(3,6) is 18.

The exact two-color Ramsey number R(3,7) is 23.

The exact two-color Ramsey number R(3,8) is 28.

The exact two-color Ramsey number R(3,9) is 36.

The exact two-color Ramsey number R(4,4) is 18.

The exact two-color Ramsey number R(4,5) is 25.

The current verified interval for the open Ramsey number R(4,6) is 36–40.

The current verified interval for the open Ramsey number R(5,5) is 43–46.

The exact three-color triangle Ramsey number is 17.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance 30n20b8, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance 50v-10, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance academictimetablesmall, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance air05, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance app1-1, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance app1-2, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance assign1-5-8, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance atlanta-ip, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance b1c1s1, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance bab2, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance bab6, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance beasleyC3, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance binkar10_1, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance blp-ar98, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance blp-ic98, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance bnatt400, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance bppc4-08, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance brazil3, according to version 36 of the official solution catalog.

The proven optimal objective value for the canonical MIPLIB 2017 benchmark instance buildingenergy, according to version 36 of the official solution catalog.