Claims

Classical von Neumann digital computer architecture necessarily keeps integrated information low because successful engineering design requires managing complexity through subsystems with clear interfaces, and this modular design principle—which is essential for human cognitive tractability—precludes high integrated information, meaning ChatGPT and other current AI systems cannot be conscious by IIT measures.

Cellular automata on graphs with random topologies where each node has k neighbors with k proportional to log(n) achieve consensus convergence time of O(log n / log log n), which is faster than high-dimensional grid topologies and represents the information-theoretic lower bound because the diameter of such graphs scales as log(n) / log(k-1)

In NKN's consensus protocol using cellular automata with random topology, malicious nodes achieve maximum disruption through the flip-side attack: setting their initial state to the minority opinion and never changing it, and the protocol is secure against this attack if and only if the fraction of malicious nodes is less than the absolute difference in honest node counts between the two states

Rule 184, a simple one-dimensional cellular automaton where cells move left or stay put based on local configuration, exhibits second-order phase transitions in block probabilities as a function of initial density when extended to infinite systems, with the probability of '11' blocks discontinuous at density 0.5 in the derivative but continuous in value

Byzantine-resilient consensus protocols based on cellular automata are fundamentally superior to classical quorum-based protocols because they don't require knowing exact network membership, tolerate Byzantine adversaries larger than a majority in some cases, scale to millions of nodes rather than hundreds, and degrade gracefully rather than having sharp security thresholds

Entanglement codes for distributed storage use XOR operations to create interdependent chains of data blocks where repairing any failed block requires only two chunks regardless of chain length, achieving storage overhead of factor α (number of parity blocks per data block) while distributed repair only requires two chunks to be downloaded even for large failures

The fundamental challenge of distributed consensus is related to the principle of computational equivalence: as systems become more sophisticated to handle complex consensus requirements, they become computationally universal, which makes it impossible to formally prove they cannot do undesired things because such proofs would require solving the undecidable halting problem

In a Nakamoto-style proof-of-stake consensus protocol like Ouroboros Praos, the staking procedure's property of independent aggregation uniquely determines the staking threshold and simplifies security analysis by ensuring that malicious actors gain no advantage from splitting resources into multiple accounts, making the protocol's behavior analyzable as a Markov chain with computable transition probabilities

Asynchronous cellular automata with random majority updates do not achieve the same level of reliable consensus as synchronous versions, but can be improved by adding state to track the local time modulo 3 for each node so neighbors know whether they should wait for updates from each other, though this introduces new challenges with deadlocks in 2D and long waiting chains that degrade error correction

NKN uses verifiable delay functions and blockchain-based randomness to generate node identities that cannot be controlled by attackers: a new node must first commit a transaction with proof-of-work, wait for several blocks (during which the node has no control over block producers), and then its identity is computed from the block hash of the block confirming its transaction, making it impossible to predict or grind for favorable positions

The majority rule cellular automaton on arbitrary graphs is P-complete to predict, meaning that determining whether a specific node will change state by time t is as hard as solving any problem in the complexity class P, but on planar graphs the problem remains P-complete due to the existence of a crossover gadget allowing signal routing without signal intersection

The distributed consensus problem fundamentally involves determining what the majority or consensus state is among a collection of nodes, which can be efficiently solved using distributed algorithms running computations in parallel rather than sequentially visiting each node

The Gax-Kadumov-Levin (GKL) rule, a one-dimensional cellular automaton that operates on a cell and its three neighbors on each side, successfully suppresses finite minorities and achieves consensus regardless of initial configuration, making it a foundational result for understanding distributed consensus in the presence of noise

The Golden Age approach of 'divide and conquer'—splitting intelligence into separate faculties and building search algorithms for each—hit a fundamental ceiling: most real-world problems are NP-complete or harder, meaning no efficient algorithm exists, and exhaustive search becomes computationally impossible at realistic scales.