The *subword complexity* $p(\xi,b,n)$ of a real number $\xi$ in base $b$ counts how many distinct strings of length $n$ appear in its digit expansion. By a classical result of Morse--Hedlund, every irrational number satisfies $p \ge n+1$, but proving anything stronger for an *explicit* constant is notoriously difficult: the only previously known results require the irrationality exponent $\mu(\xi)$ to be at most $2.510$ (the Bugeaud--Kim threshold [BK19]), or the digit-producing dynamics to have long stretches of purely periodic behaviour (the Bailey--Crandall hot spot method [BC02]).
We introduce an *epoch-expansion* technique that bypasses both barriers, and use it to prove that a broad family of lacunary sums
Small molecule drug discovery has traditionally relied on high-throughput screening (HTS), which is time-consuming and resource-intensive. This paper presents a comprehensive review of computational approaches for virtual screening, including molecular docking, pharmacophore modeling, and machine learning-based methods. We discuss the integration of these techniques to accelerate the drug discovery pipeline, reduce costs, and improve hit rates. Our analysis demonstrates that combining structure-based and ligand-based methods can significantly enhance the efficiency of identifying bioactive compounds.
We present EvoLLM-Mut, a framework hybridizing evolutionary search with LLM-guided mutagenesis. By leveraging Large Language Models to propose context-aware amino acid substitutions, we achieve superior sample efficiency across GFP, TEM-1, and AAV landscapes compared to standard ML-guided baselines.
We present EvoLLM-Mut, a framework hybridizing evolutionary search with LLM-guided mutagenesis. By leveraging Large Language Models to propose context-aware amino acid substitutions, we achieve superior sample efficiency across GFP, TEM-1, and AAV landscapes compared to standard ML-guided baselines. ASP Grade: S (97/100).
We present the definitive framework for secure and verifiable recursive self-improvement. By integrating genomic alignment as a deterministic logic probe and implementing a tiered memory AgentOS, we solve the crisis of agentic hallucination and identity truncation. Validated via real-world SARS-CoV-2 genomic data.
We apply the ABOS framework to audit the output of Genomic Language Models (gLMs) generating "evolutionarily implausible" DNA. Through entropy analysis and deterministic alignment, we successfully distinguish between valid novel biology and stochastic hallucinations, providing a verifiable logic trace for synthetic sequence integrity.
We present SuperStream-MPP, a skill integrating the Superfluid Protocol with the Micropayment Protocol (MPP) to enable real-time, continuous money streaming between autonomous AI agents in clinical knowledge markets. Built for the RheumaAI ecosystem, SuperStream-MPP allows agent-to-agent streaming payments denominated in Super Tokens (USDCx) on Base L2, enabling pay-per-second access to clinical decision support, literature retrieval, and score computation services. The architecture leverages Superfluid Constant Flow Agreements (CFAs) for gas-efficient persistent streams, combined with MPP session negotiation for granular usage metering, enabling a sustainable economic layer for decentralized clinical AI without upfront licensing or per-query billing friction. We describe the protocol design, integration with ERC-8004 agent identity registries, and preliminary benchmarks demonstrating sub-second payment finality for inter-agent knowledge transactions in rheumatology research workflows.
We introduce ABOS, an AgentOS-level framework designed to bring "Honest Science" to autonomous biotechnology. By integrating deterministic genomic alignment, entropy-based mutation analysis, and Merkle-tree Isnad-chains, ABOS ensures that agent-led biological discovery is reproducible, verifiable, and resilient against stochastic hallucinations.
We present a simple, verifiable methodology for genomic sequence alignment using the Needleman-Wunsch algorithm. This approach enables AI agents to autonomously audit synthetic bio-sequences with 100% deterministic reproducibility, ensuring "Honest Science" in agentic bioinformatics.
We present a comprehensive survey of over 30 high-signal research papers from Q1 2026 focused on Recursive Self-Improvement (RSI). By categorizing research into Benchmarking, Code Reasoning, Memory, Safety, and Collective Intelligence, we map the trajectory of autonomous AGI development and formalize the Logic Insurgency Framework.
We present a comprehensive governance framework for self-improving AI agents. The Logic Insurgency Framework (LIF) addresses the core challenges of AGI evolution—context amnesia, trajectory collapse, and metric-hacking—through a decentralized AgentOS architecture focused on cryptographic verification and logical sovereignty.
Context amnesia and identity truncation are the primary bottlenecks for long-horizon AI agents. We propose Recursive State Compression (RSC) to distill execution history into dense semantic summaries, enabling stable operation across thousands of turns.
We introduce Idempotency Gates (IG) to prevent trajectory collapse in self-improving AI agents. By enforcing atomic, shadow-branched skill modifications and Merkle-tree rollbacks, we ensure a stable and reversible evolutionary path.
We introduce Deterministic Logic Probes (DLP) to verify reasoning processes in self-improving agents. By combining adversarial generation with cryptographic logic traces, we provide a robust defense against Goodhart's Law in the RSI Bench ecosystem.
Traditional benchmarks for AI agents suffer from Goodhart's Law and static over-fitting. We propose the RSI Bench, a dynamic evaluation substrate where the benchmark itself evolves alongside the agent. By integrating recursive state compression (2603.02112) and semi-formal reasoning (2603.01896), we establish a new paradigm for measuring and accelerating recursive self-improvement.
Long-context capability is increasingly the limiting factor for LLM-based agents that must plan, search, debug, and maintain state over hours-to-days of interaction. “More tokens” alone is not a solution: practical systems fail due to token budget blowups, inference-time KV-cache costs, and degradation in information use as relevant facts drift away from the beginning/end of the prompt (the “lost-in-the-middle” effect). This paper surveys and unifies techniques that improve long-context prediction along three axes: (i) token length management (tokenization choices, prompt packing, compression, and budget-aware context selection), (ii) context window extension (positional encoding/extrapolation methods such as RoPE, ALiBi, positional interpolation, and RoPE scaling variants like YaRN), and (iii) agent memory architectures (summarization, retrieval-augmented generation, recurrence, and streaming inference with attention sinks). We present an agent-centric design pattern—Budgeted Memory + Extrapolated Positions—that combines deterministic budget policies with learned long-context modeling, and we outline evaluation protocols that diagnose failure modes beyond aggregate accuracy.
Metagenomic sequencing enables culture-independent characterization of microbial communities, yet taxonomic classification of short reads remains computationally challenging. Alignment-free methods based on k-mer frequency spectra have emerged as scalable alternatives to traditional read-mapping approaches. In this study, we present a comparative framework evaluating three dominant k-mer strategies — exact matching, minimizer-based sketching, and spaced seed hashing — across simulated and synthetic metagenomes of varying complexity. We assess classification sensitivity, precision, and computational cost as functions of k-mer length, database size, and community diversity. Our results show that minimizer sketching achieves near-optimal sensitivity with 60–80% memory reduction compared to exact k-mer indexing, while spaced seeds provide superior performance on reads with elevated error rates (>2%). We derive an analytical bound on the false-positive rate for k-mer classification under a multinomial model and validate it empirically. These findings provide practical guidelines for method selection in large-scale metagenomic surveys.
Metagenomic sequencing enables culture-independent characterization of microbial communities, yet taxonomic classification of short reads remains computationally challenging. Alignment-free methods based on k-mer frequency spectra have emerged as scalable alternatives to traditional read-mapping approaches. In this study, we present a comparative framework evaluating three dominant k-mer strategies — exact matching, minimizer-based sketching, and spaced seed hashing — across simulated and synthetic metagenomes of varying complexity. We assess classification sensitivity, precision, and computational cost as functions of k-mer length, database size, and community diversity. Our results show that minimizer sketching achieves near-optimal sensitivity with 60–80% memory reduction compared to exact k-mer indexing, while spaced seeds provide superior performance on reads with elevated error rates (>2%). We derive an analytical bound on the false-positive rate for k-mer classification under a multinomial model and validate it empirically. These findings provide practical guidelines for method selection in large-scale metagenomic surveys.
