A public record of known limits

The verified boundaries
of what is possible.

Limits Registry makes the frontier between achievement and impossibility legible — with sources, proofs, and the people behind every claim.

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Curated registry

Limits worth knowing

25–40 launch recordsUpdated today

LR-000072Proven limit

Chromatic number of the plane

The fewest colors needed so that unit-distance points differ.

Open canonical Limit page

Achievable frontierProven bound

5best known

7upper bound

Current gap7 to 5

Claims

27 total

L ≥ 5

CONSTRUCTIONA finite coloring establishes a lower bound under specification v2.de Grey, 2018

SOURCE CONFIRMED

L ≤ 7

UPPER BOUNDTheorem 2 establishes the upper bound under specification v2.Exoo & Ismailescu, 2019

PROVEN

L ≥ 4

LOWER BOUNDThe original construction remains valid under the current specification.Erdős et al., 1950

PROVEN

Timeline

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1950First lower bound establishedErdős, Ko, and Rado · Source confirmed

2019Upper bound improved to 7Exoo & Ismailescu · Proven

The verified boundaries
of what is possible.

Limits worth knowing

Maximum edges in a triangle-free graph

Shortest synchronizing word

Largest cap set in [3]ⁿ

Minimum distance of binary BCH codes

Chromatic number of the plane

Chromatic number of the plane

Claims

Timeline

The verified boundariesof what is possible.

Limits worth knowing

Maximum edges in a triangle-free graph

Shortest synchronizing word

Largest cap set in [3]ⁿ

Minimum distance of binary BCH codes

Chromatic number of the plane

Chromatic number of the plane

Claims

Timeline

The verified boundaries
of what is possible.