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

Q: What does this research mean for the field?

In a minimal stochastic causal growth model, the number of causal parents P is geometrically constrained by the Simplex Condition, such that the emergent dimension d₀ is approximately equal to P−1. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Goran Amidzic

doi:10.5281/zenodo.19228429

March 26, 2026Open Access

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

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Key Points

To examine the relationship between the number of causal parents and the emergent dimension in a stochastic causal growth model.
Defined a minimal stochastic causal growth model based on four axioms.
Explored the geometric constraint of the Simplex Condition.
Performed numerical simulations for various values of causal parents.
Confirmed d₀ ≈ P−1 for the number of causal parents P = 2, 3, 4, and 5.
Demonstrated a consistent relationship between the number of causal parents and the emergent dimension.

Implication

Numerical evidence supports geometric constraints in causal growth models, indicating strong relationships among model parameters.

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

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Cite This Study

Goran Amidzic (2026) studied this question.

synapsesocial.com/papers/69c772d98bbfbc51511e339d https://doi.org/10.5281/zenodo.19228429

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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