The Principle of Convergent Inaccessibility: A Structural Cosmological Limit to the Derivability of Free Parameters

The Principle of Convergent Inaccessibility (PIC) proposes that every physical theory constructed entirely within the observable domain of the universe necessarily contains a non-empty set of free parameters that cannot be derived from the theory itself. The inaccessibility of these parameters is interpreted not as a contingent limitation of knowledge, but as a structural consequence of the causal separation between a pre-Big Bang convergent cosmological phase (S⁻) and the observable divergent phase (S⁺). The paper introduces a state space endowed with causal decomposition, defines informational compression and projection operators, and develops an axiomatic system based on PIC-1..3. By combining Shannon's Data Processing Inequality with the geodesic incompleteness established by the Penrose-Hawking singularity theorems, a lemma of irreversible informational loss is formulated, leading to a semi-formal theorem concerning the structural existence of an irreducible residue Λ. Within the proposed framework, the free parameters of physics are interpreted not as mere theoretical gaps but as observable traces of a causally inaccessible cosmological phase. The principle further suggests that no theory constructed exclusively within S⁺ can completely eliminate such parameters. PIC is presented as a speculative proposal in structural cosmology and as a possible new fundamental limit to physical knowability.