StructuralTime: Drift-Based Internal Time, and Three Layers of It

StructuralTime constructs time from accumulated structural change rather than an external clock: a system's internal time advances only when its own observable state actually changes, standardized per dimension against its own recent history. It was previously described only bundled with the D-Operator, as the observer in one specific connection. Here we treat it as a standalone component and add two layers absent from that earlier description: a category clock that accumulates separately per drift category rather than only in aggregate, and a joint clock that tracks a group's shared state (e.g. its centroid) as distinct from any individual member's own motion. Both are small, verified additions to the existing implementation, not new integration mechanisms. We also restate, in general terms independent of any specific dynamical system, the one real failure mode already known for StructuralTime -- equilibrium collapse -- and the exact conditions under which its fix does and does not suppress genuine signals.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-11
DOI
https://doi.org/10.5281/zenodo.22713626
Primary Topic
Origins and Evolution of Life
Type
preprint
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preprint

StructuralTime: Drift-Based Internal Time, and Three Layers of It

TOYOHIRO ARIMOTO, 5 Sonnet
Zenodo (CERN European Organization for Nuclear Research)
Origins and Evolution of Life
preprint

StructuralTime: Drift-Based Internal Time, and Three Layers of It

TOYOHIRO ARIMOTO, 5 Sonnet
preprint en

Abstract

StructuralTime constructs time from accumulated structural change rather than an external clock: a system's internal time advances only when its own observable state actually changes, standardized per dimension against its own recent history. It was previously described only bundled with the D-Operator, as the observer in one specific connection. Here we treat it as a standalone component and add two layers absent from that earlier description: a category clock that accumulates separately per drift category rather than only in aggregate, and a joint clock that tracks a group's shared state (e.g. its centroid) as distinct from any individual member's own motion. Both are small, verified additions to the existing implementation, not new integration mechanisms. We also restate, in general terms independent of any specific dynamical system, the one real failure mode already known for StructuralTime -- equilibrium collapse -- and the exact conditions under which its fix does and does not suppress genuine signals.

Zenodo (CERN European Organization for Nuclear Research)
Bando Chemical Industries, Ltd. (Japan) (JP)
Peace, Justice and strong institutions
Origins and Evolution of Life
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