Abstract We propose a mechanism for the particle mass spectrum within the Algorithmic Theory of Reality (ATR) framework, identifying particle rest masses with the discrete decay-rate quanta of the Lindblad steady state on the complete graph Kn. In ATR, matter is not fundamental; rather, it represents the informational processing cost projected into the observer's data-state by wavefunction collapse at the Zeno Threshold. Core Mechanism: Mass as Processing Cost This paper redefines inertial mass, abandoning the need for free parameters: Informational Load Quanta: The Lindblad dynamics on Kn produce a unique steady state with a discrete spectrum of perturbation decay rates. These decay rates define the minimum computational costs the pre-geometric substrate must continuously pay to sustain persistent excitations against entropic decay. The Bootstrap Resolution: The framework resolves the bootstrap paradox by identifying the Lindblad steady state as the observer's self-consistent data-state. It defines the physical substrate size n* as a finite local interaction cluster, effectively saving the theory from the O(1/n) cosmological paradox. Finite-Size Effect: In the strict thermodynamic mean-field limit, the mass ratios degenerate to unity. The Standard Model mass hierarchy is proven to be strictly a finite-size quantum informational effect. Computational Verification & Emergent Structures The theoretical derivations are validated by an extensive GPU-native Implicitly Restarted Arnoldi Method (IRAM) extraction, scaling up to a 1-million-dimensional Lindblad superoperator at n=10. The computational results reveal profound structural parallels to the known particle spectrum: Two-Sector Spectral Structure: At n ≥ 8, the eigenspectrum spontaneously bifurcates into "slow modes" (analogous to force mediators) and a dense "physical mass cluster" (matter particles). Generation-Like Clustering: Within the extracted physical modes, the spectrum exhibits natural triplet clustering, mirroring the topological generations of the Standard Model. Computational Optimality: The framework mathematically demonstrates why the universe is predominantly made of the "cheapest" stable particles (like electrons and up/down quarks), as they maximize the number of constituents available to build complex observers under a strict total processing budget.
Serdar Hanzala Yaman (Fri,) studied this question.