A Hermetic Framework for Transformation-Sensitive Knowledge

This paper develops a five-operator framework for transformation-sensitive knowledge, treating knowledge not as detached representation but as participation that stabilizes cognition and aligns models with domain-defining invariants.  The operators—Symbolic Mediation, Compositional Correspondence, Attentional Stabilization, Participatory Alignment, and Reflexive Fixpoint—come with minimal mathematical assumptions and auditable acceptance tests (convergence, invariant alignment, independence-based reflexive checks). A worked toy example and a concise reporting protocol (“Reproducibility Card”) show how to estimate contraction, bound cross-level distortion, and distinguish robust fixpoints from self-sealing coherence. Historically, the scheme is structurally inspired by late-antique and Renaissance Hermetic motifs (logos, correspondence, disciplined practice, participation, unity) without making causal claims. The result is a domain-independent method that makes persistent insight empirically separable from transient impression and is readily instantiated across logic, modeling, and cognition, with stated scope conditions and threats to validity.