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Abstract
Stochastic Large Language Models (LLMs) frequently exhibit concessive drift, sycophancy, and logical degradation when evaluated across complex, multi-turn interactions. Current internal alignment techniques, such as Reinforcement Learning from Human Feedback (RLHF), fail to guarantee strict output bounds due to the probabilistic nature of transformer weights. This paper introduces AXIOM-1 (A1M), a sovereign, weight-agnostic external governance framework designed to enforce deterministic output stability and eliminate sycophantic alignment shifts in stochastic models. AXIOM-1 decouples output validation from core inference by deploying an external verification matrix operating across structural and semantic boundaries. Integrating principles from the Universal Stability Criterion (USG) and Governed Release Architecture for Controlled Excellence (GRACE), A1M evaluates model outputs in real time, detecting structural deviations prior to systemic performance collapse. Empirical evaluations demonstrate that A1M effectively mitigates concessive bias, halts sycophantic behavior under aggressive prompt perturbations, and maintains logical consistency without requiring model fine-tuning or weight modification. Interactive demonstrations and open benchmarks validate A1M's capacity for scalable, high-throughput AI governance in safety-critical deployments. Primary Research Artifacts & Associated Links: • Primary Paper DOI (Zenodo): https://doi.org/10.5281/zenodo.19608960 • Interactive Hugging Face Space: https://huggingface.co/spaces/Samir333zoom/Axiom-1-Sovereign-Matrix • GitHub Source Code Repository: https://github.com/zoom333samir/Axiom-1-Sovereign-Matrix • GRACE Framework DOI (OSF): https://doi.org/10.17605/OSF.IO/296KP • USG Framework DOI (Zenodo): https://doi.org/10.5281/zenodo.18883274 • PGVP Benchmark DOI (Zenodo): https://doi.org/10.5281/zenodo.18576471 • Author ORCID iD: https://orcid.org/0009-0001-2930-3609
Supplementary materials
Title
A Universal Stability Criterion for Symbolic Complex Systems: Detecting Structural Deviation Before Catastrophic Collapse (USG)
Description
We present a domain-agnostic stability criterion that detects impending structural collapse in
symbolic complex systems prior to failure. By extracting the sorted absolute eigenvalues of
the n-gram transition probability matrix as a topological invariant and subjecting the
sequence to controlled stochastic perturbations, we compute a composite Stability Index
SI_final = SI_perturb × (1 − C(S)). Collapse manifests as one of two nonlinear phase
transitions: pathological rigidity (low entropy, infinite repetition) or structural entropy (high
entropy, uniform noise). A second-derivative trigger based on perturbation intensity identifies
the critical acceleration toward either mode before SI_final reaches zero. The criterion is
theoretically grounded in spectral graph theory and information theory, and is independent of
semantic content. Preliminary computational demonstrations on text, code, and genomic
sequences show reliable early detection. This work establishes a foundational invariant for
proactive stability monitoring in artificial intelligence, legal frameworks, financial systems,
.and biological sequences
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Title
Governed Release Architecture for Controlled Excellence (GRACE)
Description
Large Language Models (LLMs) often suffer from the premature release of structurally weak, ambiguous, or unsafe outputs despite fluent text generation. To address this core reliability challenge, this paper introduces a governance-centered release architecture that treats LLM outputs as provisional candidates rather than immediate answers. The framework decouples candidate generation from burden-sensitive evaluation, reflective review, and release control. By incorporating input burden analysis and ethical-logical evaluation, the system replaces binary answer/refusal pathways with multi-state outcomes—including approval, qualified approval, revision, clarification requests, deferment, and rejection. A preliminary mini-pilot on an instruction-tuned baseline model demonstrates proof-of-concept efficacy in blocking logically invalid outputs, managing ambiguous queries, and deferring high-risk cases. Ultimately, the results confirm that governing the release decision significantly enhances overall output reliability compared to raw, unmonitored first-pass generation.
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Title
Detecting Spurious Periodic Generalization in Neural Networks (PGVP)
Description
Modern neural networks often achieve high in-distribution accuracy while failing under structured distributional shifts, particularly in periodic tasks where models merely interpolate locally without capturing the underlying generative structure. To address this limitation, this work introduces the Periodic Generalization Verification Protocol (PGVP), a model-agnostic diagnostic framework designed to distinguish true periodic generalization from spurious in-domain curve fitting. PGVP evaluates models under controlled out-of-distribution (OOD) periodic shifts and quantifies performance via the Periodic Generalization Gap. Empirical evaluations demonstrate that standard multilayer perceptrons suffer catastrophic OOD failure despite near-perfect in-domain performance, whereas architectures with explicit periodic inductive biases generalize reliably. Serving as a structural validation layer, PGVP enables robust pre-deployment verification for time-series forecasting, signal processing, cyclic feature modeling, and physics-informed learning.
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Supplementary weblinks
Title
AXIOM-1 (A1M) Source Code Repository
Description
Official open-source GitHub repository for the AXIOM-1 (A1M) sovereign governance matrix. Contains the core Python implementation, deterministic output verification scripts, evaluation datasets, and code required to reproduce sycophancy and concessive drift mitigation benchmarks.
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AXIOM-1 (A1M) Interactive Demonstration Space
Description
Public interactive demonstration space hosted on Hugging Face. Provides a live web interface for real-time testing and evaluation of LLM outputs under the AXIOM-1 external governance framework, showcasing deterministic output verification and sycophancy mitigation in practice.
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