What question did this study set out to answer?

This research aims to explore the relationships between causal parents and constraints in a stochastic causal growth model.

synapse

⌘+K

synapse

⌘+K

March 28, 2026Open Access

Emergent Dimension in a Minimal Causal Growth Model: Numerical Evidence for the Simplex Condition d₀ ≈ P−1

Key Points

This research aims to explore the relationships between causal parents and constraints in a stochastic causal growth model.
Defined a stochastic causal growth model based on four axioms (P1–P4)
Evaluated the relationship between causal parents and dimensions using numerical simulations
Confirmed the Simplex Condition for various values of P (2, 3, 4, 5)
Confirmed that the number of causal parents P is geometrically constrained
Established that d₀ is approximately equal to P−1 for P values of 2, 3, 4, and 5

Abstract

We present a minimal stochastic causal growth model defined by four axioms (P1–P4). We provide numerical evidence that the number of causal parents P is geometrically constrained by the Simplex Condition, with d₀ ≈ P−1 confirmed for P = 2, 3, 4, 5. Code available at https://github.com/goranamidzic-sys/causal-growth-model

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper

Cite This Study

Goran Amidzic (Thu,) studied this question.

synapsesocial.com/papers/69c770f78bbfbc51511e0dd6 https://doi.org/https://doi.org/10.5281/zenodo.19228428