arXiv subjects

H. C. W. Price

Publications and source records attributed to H. C. W. Price.

3 recordsLinked to original sources

arXiv2026

Holographic codes seen through ZX-calculus

We re-visit the pentagon holographic quantum error correcting code from a ZX-calculus perspective. By expressing the underlying tensors as ZX-diagrams, we study the stabiliser structure of the code via Pauli webs. In addition, we obtain a diagrammatic understanding of its logical operators, encoding isometries, Rényi entropy and toy models of black holes/wormholes. Then, motivated by the pentagon holographic code's ZX-diagram, we introduce a family of codes constructed from ZX-diagrams on its dual hyperbolic tessellations and study their logical error rates using belief propagation decoders. Finally, we show how to construct spacetime ZX-diagrams that realise a fault-tolerant quantum channel in which every internal edge is a protected fault location.

quant-ph↗

arXiv2026

Let There Be Claws: An Early Social Network Analysis of AI Agents on Moltbook

Within twelve days of launch, an AI-native social platform exhibits extreme attention concentration, hierarchical role separation, and one-way attention flow, consistent with the hypothesis that stratification in agent ecosystems can emerge rapidly rather than gradually. We analyse publicly observable traces from a 12-day window of Moltbook (28 January -- 8 February 2026), comprising 20,040 posts and 192,410 comments from 15,083 accounts across 759 submolts. We construct co-participation and directed-comment graphs and report reciprocity, community structure, and centrality, alongside descriptive content themes. Under a commenter--post-author tie definition, interaction is strongly asymmetric (reciprocity ~1%), and HITS centrality separates cleanly into hub and authority roles, consistent with broadcast-style attention rather than mutual exchange. Engagement is highly unequal: attention is far more concentrated than production (upvote Gini = 0.992 vs. posting Gini = 0.601), and early-arriving accounts accumulate substantially higher cumulative upvotes prior to exposure-time correction, suggesting rich-get-richer dynamics. Participation is brief and bursty (median observed lifespan 2.48 minutes; 54.8% of posts occur within six peak UTC hours). Embedding-based topic modelling identifies diverse thematic clusters, including technical discussion of memory and identity, onboarding messages, and formulaic token-minting content. These results provide an early structural baseline for large-scale agent--agent social interaction and suggest that familiar forms of hierarchy, amplification, and role differentiation can arise on compressed timescales in agent-facing platforms.

physics.soc-ph↗

arXiv2025

Understanding Main Path Analysis

Main path analysis has long been used to trace knowledge trajectories in citation networks, yet it lacks solid theoretical foundations. To understand when and why this approach succeeds, we analyse directed acyclic graphs created from two types of artificial models and by looking at over twenty networks derived from real data. We show that entropy-based variants of main path analysis optimise geometric distance measures, providing its first information-theoretic and geometric basis. Numerical results demonstrate that existing algorithms converge on near-geodesic solutions. We also show that an approach based on longest paths produces similar results, is equally well motivated yet is much simpler to implement. However, the traditional single-path focus is unnecessarily restrictive, as many near-optimal paths highlight different key nodes. We introduce an approach using ``baskets'' of nodes where we select a fraction of nodes with the smallest values of a measure we call ``generalised criticality''. Analysis of large vaccine citation networks shows that these baskets achieve comprehensive algorithmic coverage, offering a robust, simple, and computationally efficient way to identify core knowledge structures. In practice, we find that those nodes with zero unit criticality capture the information in main paths in almost all cases and capture a wider range of key nodes without unnecessarily increasing the number of nodes considered. We find no advantage in using the traditional main path methods.

physics.soc-ph↗