Measure-Relational Algebra

A specification for data systems that carry measurement uncertainty. A stored quantity is a probability measure on a metrized domain, not a point; dependence is carried as data; computation is pushforward; and collapsing a measure to a single number is an explicit, audited operation rather than a silent default. The classical model of exact values is recovered inside it as a special case. The core is, in the manner of Codd’s 1970 paper, implementation-independent: it states what any conforming system must preserve, and provides the instruments to gauge what an implementation loses.

Collapse commutes with a numerical derivation, for every joint input law, if and only if the derivation is affine — and with every measurable derivation if and only if the values were exact to begin with.

The central theorem. Everywhere else, the collapsed computation is a different computation, with a signed, quantifiable discrepancy.

Documents

Measure-Relational Algebra: The CorePDF

The specification: objects, operations, the non-commutation theorem and its instruments, the geophysical case, and seven open problems. arXiv, August 2026.

The Cost of Writing Down a NumberPDF

The companion essay for non-specialists: a forty-year ceiling that wasn’t there, the mechanism behind it, and why the repair is structural. Four pages.