The Topology of Influence: Latent Structure, Wave Propagation, and Organizational Resilience in Online Populations

Executive Summary

We demonstrate that a population's behavioral data, when embedded in a latent space via dimensionality reduction, reveals persistent structure that predicts influence propagation and organizational resilience. Using 1.4 billion Reddit comments across six months (January-June 2022) and 44,837 subreddits, we establish seven empirical findings that build on each other in a logical chain where each finding depends on and validates the ones before it.

Key Findings

• Cross-domain latent space: A shared latent space of 12 independent dimensions exists across behaviorally distinct domains
• Temporal stability: Individual positions in this space are temporally stable across two-week windows (Mantel r = 0.41)
• Event detection: The space detects real-world events and distinguishes unifying from polarizing signatures via displacement coherence
• Persistent subpopulations: Three stable subpopulations persist across independent time windows (ARI = 0.47)
• Influence wave propagation: Influence propagates as a wave through proximity in the space, with a measurable boundary where proximity-driven influence gives way to broadcast media (Spearman ρ = 0.27, p < 10^-6)
• Simpson's paradox in leadership: Leadership is topic-specific, not a global trait — per-dimension enrichment averages 18.5x while global enrichment is 1.0x, a Simpson's paradox caused by different people leading in each dimension
• Topology predicts resilience: Influence propagates along the topology of the latent space defined by shared leadership identity between dimensions (ρ = 0.56, p < 10^-6). Dimensions with no cross-dimensional leadership are structurally fragile; connected dimensions exhibit distributed resilience

Methodology

The analysis pipeline processes 1.4 billion comments through TF-IDF vectorization and dimensionality reduction to construct position tensors for each subreddit across two-week windows. Leader scores are computed per-dimension, and the topology is constructed from cross-dimensional leadership overlap. Each finding was designed to fail fast if the prior findings were wrong. None failed.

Central Contribution

The topology of the latent space — defined by who leads where and how those leader populations overlap — connects influence propagation to organizational structure in a way that is computable from behavioral data, requires no content analysis, makes no assumptions about what the dimensions represent, and produces falsifiable predictions about future events. The space is not random. The influence, when it comes, will travel a direction the topology already defines.

Key References