Research programme
The project began with periodic Fibonacci structures modulo 9 and developed into a broader investigation of lifting, invariance, reconstruction and observable response under transformations. Current work separates rigorous mathematical results from broader hypotheses in Reconstruction Theory and Reconstruction Ontology.
Finite periodic structure
Fibonacci-derived modular structures, period towers, return laws, degeneracies and ternary organisation.
Transformations and lifts
Matrix groups, congruence levels, tangent lifts, order defects and adjoint transfer.
Identity through response
A developing conceptual framework asking what can be reconstructed from invariants and structured responses to change.
Current paper
Adjoint Transfer and Order-Lifting Dichotomies for 2 × 2 Matrices over Prime-Power Rings
Ivo Vajc · Independent researcher
The paper studies determinant-compatible lifts of invertible 2 × 2 matrices. In characteristic three, the affine order-defect mechanism yields an exact branching law for every non-scalar coarse state.
Reconstruction Theory
A central working idea is that an object need not be characterized by a single observed state. It may instead be characterized by a sufficiently rich family of responses to transformations. This motivates reconstruction classes, reconstruction signatures, observable and invisible directions, reconstruction depth, and reconstruction time.
Ω is used as a conceptual symbol for a structured terrain of possible states, transformations, observations and reconstruction relations. This is presently a research framework and philosophical interpretation—not a claim that a new physical field has been experimentally established.
Methods, verification & AI
Mathematical claims are developed through a combination of algebraic derivation, finite exhaustive computation, adversarial numerical audits and literature comparison. Computational verification is treated as an independent discovery and error-detection layer, not as a substitute for proof.
Use of artificial intelligence
Artificial intelligence, including ChatGPT, is used as a research-assistance tool in the project: for exploratory dialogue, formulation of hypotheses, code drafting and review, organisation of computational experiments, exposition, language editing, and literature-search assistance. Mathematical claims intended as results are not accepted solely because an AI system proposes them; they are subjected to explicit derivation, computational checks where applicable, and literature review. Responsibility for the published content and claims remains with the author.