Structural Compressibility

Formal Definition

For a fixed encoding E and description language U, a pattern x is structurally compressible when its Kolmogorov complexity K_U(x) plus a declared constant c > 0 is still less than the length of its exhaustive description |E(x)| — informally, the pattern carries regularity rather than being random noise.

Because K_U is defined relative to a fixed description language U and Kolmogorov complexity is not generally computable, A2 is a definitional criterion — a way of recognising compressible regularity — not an executable decision rule in the repository.

Status: an interpretive postulate

A2 is one of five interpretive postulates (research hypotheses, dated 2025-12-23), not a proven law. It supplies conceptual vocabulary and organizes narrative work, and must not be read as an empirically established law of cosmology, consciousness, or identity.

In the ASH Model

Under controlled symmetric bit-flip noise the state occupancy converges to uniform, whose Hamming-weight marginal is exactly Binomial(9, ½) (mean 4.5, variance 2.25) — a generic finite-hypercube baseline that non-ASH controls also reproduce, not an ASH-specific result. With XOR transforms and no noise the dynamics stay confined to a 16-state code orbit (weights {0, 4, 8}) and do not converge (TV ≈ 0.73 from the binomial). The bell-shaped histogram is therefore a control baseline, not a demonstration that A2 holds of reality.

What ASH does provide as an exact form of compressibility is structural: the 512-vertex state space F₂⁹ is organized by a rank-4 [9,4,4] transform code of just 16 codewords (weight enumerator {0:1, 4:14, 8:1}), and code-orbit averaging is an exact idempotent projection T (T² = T) onto functions constant on 16-element orbits. These are specified deterministic computations — a compact, deterministic rule set — not empirical evidence that A2 holds of physical reality.