Numberyear

Numberyear is a compact numeric encoding designed to merge a non-temporal identifier with a calendar year into a single key for time-aware indexing. It is used in data systems that require rapid lookups and simple storage of both identity and year without maintaining separate fields.

The most common construction is numberyear(n, y) = n × 10000 + y, where y is a four-digit year. Variants may use string concatenation or more sophisticated reversible encodings such as the Cantor pairing function. The standard form yields an integer that can be decoded by n = floor(numberyear / 10000) and y = numberyear mod 10000. The approach relies on fixed-width years (four digits) to avoid ambiguity and ensure a unique mapping.

Properties include injectivity under the fixed-width assumption: distinct pairs (n, y) map to distinct numbers. Decoding is straightforward, which makes the representation suitable for compact databases, indexing schemes, or archival identifiers. Limitations arise when years fall outside the fixed width, or when different systems use different year conventions, potentially leading to collisions or ambiguous decoding unless explicitly documented.

Applications span bibliographic catalogs, archival systems, inventory and versioning schemes, and time-series datasets where a single key must convey both identity and year. The method is often favored for its simplicity and compatibility with numeric databases, though it is sometimes supplanted by separate fields or more explicit timestamp formats in modern systems. See also: timestamp, composite key, and Cantor pairing function.