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This note aims to introduce the irreversible bit as a foundational concept in information theory, emphasizing its role in time-related distinctions.

May 12, 2026Open Access

The irreversible bit

Key Points

This note aims to introduce the irreversible bit as a foundational concept in information theory, emphasizing its role in time-related distinctions.
Theoretical exploration of the irreversible bit within the context of global non-invertibility.
Discussion on the implications of the irreversible bit for records, adjacency, and spatial considerations.
Mathematical analogies proposed for further development in future work.
Proposes a framework for understanding time through the lens of the irreversible bit.
Highlights the relationship between mediation, adjacency, and temporally stabilized structures.

Abstract

This short foundational note proposes the Irreversible Bit (IB) as a time-first primitive: the minimal distinction preserved across a globally non-invertible commit-step. From this primitive, temporally preserved distinguishables, mediated adjacency, records, and space are presented as progressively stabilized structures. The note is intended as a compact conceptual foundation and priority record for later formal development.Formal-direction note: A possible mathematical analogue for the QB stage is a Bergman-type admissibility projection, where a projection operator extracts a coherent admissible sector from ambient content. This analogy is not developed in v0.9 and is deferred to later work. Related prior note: Kernel Geometry on the Unit Ball in C4, DOI: 10.5281/zenodo.18031409.

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