Time is assembled, not assumed
Treats time as something a descriptive layer builds from three ingredients: a stable ordering, repeatable clock ticks, and irreversible records.
This paper argues that time is not a primitive background parameter but something assembled within a descriptive layer. It separates ordinary within-layer time ("what happens next") from layer-rewriting time ("when the rules themselves change"), then tests both in a finite-state Markov laboratory with side-by-side controls. The result is a reproducible workflow for telling apart genuine arrows of time, reliable clocks, physical constraints, and artifacts of scheduling order.
A layer has time only when order, measure, and arrow are stable together.
- Ioannis Tsiokos
Order, measure, arrow
Time requires three ingredients working together: a stable before/after ordering, a repeatable tick mechanism (a clock), and an irreversible record that makes "before" genuinely different from "after."
Causation vs enablement
Within-layer time ("what happens next under fixed rules") is different from layer-rewriting time ("when the rules themselves change and new variables become possible").
Audit-first methodology
Every claim starts from a reversible null regime where arrow measurements read near zero. Deviations are only reported with side-by-side controls.
No fake arrows
Zooming out (coarse-graining) reduces forward-vs-backward asymmetry. It can hide an arrow of time, never create one.
Core lens
What comes next
Order
A stable succession relation: for any two events in the layer, there is a consistent answer to "which came first?"
What counts time
Measure
A repeatable tick process (a clock) that makes durations comparable. Ticks must be regular and drift must be bounded.
What makes direction
Arrow
An irreversible record mechanism that makes reversal costly or impossible. Without it, "before" and "after" are interchangeable.
Highlighted results
Reversible systems show near-zero arrows
In nearly reversible control regimes, all arrow-of-time measurements stay close to zero, confirming the baseline is clean.
Zooming out reduces the arrow signal
Forward-vs-backward asymmetry is always smaller in coarse descriptions than in detailed ones. Coarsening hides arrows, never creates them.
Maintenance budgets stabilize clocks
Higher maintenance budgets reduce clock drift and tick failure, while a separate check detects stalled clocks that tick without real dynamics.
Path-dependence blocks a global time
When the order of operations matters (noncommuting protocols), transporting a clock around a loop leaves a measurable residue. No single global time coordinate can exist.
Methods and reproducibility
Sanity checks
Media-ready
Every reported arrow, clock, and loop-residue result is backed by a reproducible artifact bundle.
- Reversible-vs-driven arrow diagnostics
- Clock drift and tick-failure metrics
- Operation-order loop controls
Limitations and scope
Resources
Read the paper (DOI)
Zenodo DOI record
Code and reproducibility
Time audits and artifact pipeline
Framework paper landing page
Six Birds: Foundations of Emergence Calculus
Access
Open-access preprint with reproducible audits and controls.
Citation
Ioannis Tsiokos (2026). To Notch a Stone with Six Birds: Time as a Theory Artifact of Order, Measure, and Arrow. Zenodo. https://doi.org/10.5281/zenodo.18495363
BibTeX
@misc{tsiokos2026notch,
title = {To Notch a Stone with Six Birds: Time as a Theory Artifact of Order, Measure, and Arrow},
author = {Tsiokos, Ioannis},
year = {2026},
publisher = {Zenodo},
doi = {10.5281/zenodo.18495363},
url = {https://doi.org/10.5281/zenodo.18495363}
}Press and contact
For media inquiries, figures, or walkthroughs of the artifacts, reach out directly.
Ioannis Tsiokos
ioannis@automorph.io
Corresponding author - Press contact