1. The Minimal Architecture of Distinguishability ANAM(X)Petina, A. (2026). Zenodo.

DOI: https://doi.org/10.5281/zenodo.18115774

This work presents the minimal architecture of distinguishability ANAM(X) as the limiting structure required for the emergence, retention, and actualization of differences in any system. The foundational binary X (“what/how”) is introduced as the core modality of distinction, reproduced fractally across all levels of actualization. It gives rise to four coherent functional roles: A (retention of the form of difference), B (content of difference), G (transition of difference into an act), and N (pre-actual tension of difference). These roles are treated as manifestations of a single architectural modality rather than independent entities. The paper establishes the minimality and internal coherence of X and outlines the architectural consequences that define the conditions for distinguishable structures and the transition of difference into an act. The work provides a foundation for further investigations of mechanisms of form-generation, actualization, and stability of differences across disciplinary contexts.

2. Why ANAM Does Not Admit Axioms: Architectural and Methodological FoundationsPetina, A. (2026). Zenodo.

DOI: https://doi.org/10.5281/zenodo.18115844

The article examines the architectural and methodological reasons why the generative structure ANAM does not admit axioms. It demonstrates that the minimal binary relation “what/how” and its fractal unfoldings constitute the only configuration compatible with the emergence of distinguishability and the act of actualization. Unlike axiomatic systems, which rely on externally fixed initial statements, ANAM generates structure from within, requiring no selection of postulates. The paper analyzes the origin of “pseudo-axioms” as a result of cognitive channel limitations and discusses the implications of axiom absence for proof models, verification practices, and the formal sciences. ANAM is presented as a pre-axiomatic foundation that defines the level at which any formal system becomes possible.

3. Architecture of Distinguishability and Cognitive Reconstructions: Human-Channel Limitations and Mechanisms of FixationPetina, A. (2026). Zenodo.

DOI: https://doi.org/10.5281/zenodo.18115909

The article examines how the multidimensional architectural structure of distinguishability in ANAM becomes distorted when passing through the human cognitive channel. The generative A/B/G/N configuration exists architecturally as a simultaneous multidimensional structure, but due to cognitive bandwidth limitations and the linear nature of language, consciousness transforms it into a sequential chain. The work introduces Linear Reconstructive Markers (LRM)—fixators such as “before,” “after,” “moment,” which do not belong to the architecture but arise from perceptual constraints. The study differentiates the architectural and cognitive levels of description, identifies common interpretational errors, and proposes a method of architectural correction aimed at restoring structural simultaneity and minimizing reconstructive distortions.

I. The Minimal Architecture of Distinguishability (ANAM): Generative A/B/G/N Structure, the Unique Minimal Transition, and the Emergence of Numerical Form

DOI: https://doi.org/10.5281/zenodo.18079249

This study systematically develops the minimal generative architecture of distinguishability ANAM and demonstrates that stable distinction is possible only under the simultaneous coherence of the four structural modalities A/B/G/N. The work establishes a single minimal transition Ω = 2 → Ω = 3 from which the architectural invariants ΔHₘᵢₙ and Jₘᵢₙ arise, and shows that numerical form is not postulated but emerges as a consequence of the repeatability of distinguishable transitions. The paper formulates strict falsifiability criteria for the ANAM structure and conditions for reproducible analysis of its predictive implications.

II. ANAM and the Possibility of Cold Fusion: Manifestation of the Act of Minimalities and the Form of Transition

DOI: https://doi.org/10.5281/zenodo.18088159
The article analyzes cold fusion not as a process of externally “overcoming a barrier,” but as a manifestation of the ANAM act of minimalities—where distinguishability, action, and compatibility thresholds arise as a unified whole. It shows that the transition traditionally interpreted as tunneling corresponds to achieving a minimal act-form that makes the retention of two configurations unnecessary. Predictive consequences are formulated: low-energy isomeric transitions, isotope shifts without neutron emission, stable small energy release, and sensitivity of the effect to the structural configuration of the medium.

III. Retrospective Predictive Test of the ANAM Generative Architecture: An Autonomous Reconstruction of an Elemental Table

DOI: https://doi.org/10.5281/zenodo.18090480
This work presents a rigorous retrospective test: whether the structure of an elemental series can be autonomously reconstructed using only the ANAM architecture. The study shows that the A/B/G/N transitional regimes and the architectural compatibility conditions generate a stable set of forms corresponding to the observed elements. An architectural metric of distinguishability is introduced, enabling reproducible generation of structural groupings and serving as an independent confirmation of ANAM’s predictive capacity.

IV. Faith as an Architectural Limit: Distinguishability Attempting to Disappear

DOI: https://doi.org/10.5281/zenodo.18100611

The study examines the phenomenon of faith as a limiting regime of system functioning in which distinguishability tends to disappear. It shows that faith is not a psychological state but an architectural limit: a regime of minimal divergence in which a system attempts to maintain an impossible configuration that violates the conditions of distinguishability. The work identifies stable signatures of this regime and its relation to the limiting architectural states G and B.

V. ANAM Distinguishability Architecture Physical Stress Test: Autonomous Generation of a Physical Layer and Retrospective Predictive Verification

DOI: https://doi.org/10.5281/zenodo.18105364

This article presents a methodological stress test of the distinguishability architecture: whether ANAM can autonomously generate a coherent physical layer and reproduce known physical structures. It shows that stable interaction among A/B/G/N under architectural pressure forms physical-metric regimes corresponding to observed physical laws. A retrospective verification is performed: the reconstructed physical layer aligns with confirmed empirical data.