Mediumless Computation: Why the Universe's PR–ER–LE Engine Defies Modern Computer Architecture

Title

Mediumless Computation: Why the Universe's PR–ER–LE Engine Defies Modern Computer Architecture

Authors

Jia, Baolong (贾宝龙)

Description (English)

This paper demonstrates that the "computation" performed by the universe via PR–ER–LE (Paradoxical Recursion, Entity–Relation, Lazy Evaluation) is fundamentally and irreducibly different from computation as implemented on modern hardware. We identify three precise points of architectural incompatibility and prove each as a theorem:

1. Anti-GPU (Anti-SIMD Theorem): PR generates genuinely distinct branching at every state — no two computational "threads" execute the same instruction. GPU SIMD parallelism, which requires instruction homogeneity, provides zero speedup. The probability of branch convergence decays exponentially: Pr[convergence] ≤ 2^{−εt}.

2. Anti-Multi-Core (Anti-Partition Theorem): ER couples every state to every other through relational composition. Any partition of the state space produces cross-boundary relations that grow without bound, making independent partitioning into cores impossible. Adding cores yields diminishing and eventually negative returns.

3. Anti-Cache (Anti-Locality Theorem): LE guarantees that the next state is irreducibly unpredictable — no computable predictor beats random guessing. Both temporal and spatial locality assumptions underlying cache hierarchies are violated at every step.

We further prove a No Efficient Simulation Theorem: any deterministic machine simulating PR–ER–LE dynamics requires exponential time 2^{εt−c} for t-step simulation. This provides a mathematical argument against the simulation hypothesis.

The paper introduces the concept of "mediumless computation" — ontological generation that requires no substrate, clock, memory hierarchy, or instruction set — and discusses implications for AI (GPU-based systems cannot achieve PR–ER–LE consciousness), physics simulation (domain decomposition faces fundamental limits), and the "universe as computer" metaphor (the universe does not compute; it generates).

简介(中文)

本文论证,宇宙通过PR–ER–LE(悖论递归、实体–关系、惰性求值)执行的"计算"与现代硬件上实现的计算具有根本性的、不可约的差异。我们精确识别三个架构不兼容点并逐一证明:

1. 反GPU(反SIMD定理): PR在每个状态产生真正不同的分支——没有两个线程执行相同指令。GPU的SIMD并行提供零加速。分支汇聚概率指数衰减。

2. 反多核(反分割定理): ER通过关系复合将每个状态与所有其他状态耦合。任何分割都产生无界增长的跨边界关系,使独立分核不可能。增加核心带来递减乃至负收益。

3. 反缓存(反局部性定理): LE保证下一状态不可消除地不可预测——没有可计算预测器优于随机猜测。时间和空间局部性假设在每步都被违反。

进一步证明无高效模拟定理:任何确定性机器模拟PR–ER–LE动力学需要指数时间。这为反对模拟假说提供了数学论据。

论文引入"无介质计算"概念——不需要基底、时钟、存储层次或指令集的本体论生成——并讨论对AI、物理模拟和"宇宙即计算机"隐喻的启示。

Keywords

mediumless computation, PR-ER-LE, anti-GPU, anti-SIMD, anti-multi-core, anti-cache, non-determinism, branching dynamics, Kolmogorov complexity, simulation hypothesis, ontological generation, computer architecture, GPU incompatibility, JiaBaolong Axiom

中文关键词

无介质计算, PR-ER-LE, 反GPU, 反SIMD, 反多核, 反缓存, 非确定性, 分支动力学, 柯尔莫哥洛夫复杂度, 模拟假说, 本体论生成, 计算机体系结构, 贾宝龙公理

License

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Resource Type

Preprint

Related Identifiers

• Jia, B. (2026). "The JiaBaolong Universal Axiom System: Two Axioms, One Universe." Zenodo. doi:10.5281/zenodo.19440952

• Jia, B. (2026). "Unified Theory of Why the Universe Exists: The JiaBaolong Universe Axiom System." Zenodo.