On the Intractability of Chaotic Symbolic Walks: Toward a Non-Algebraic Post-Quantum Hardness Assumption

The paper’s PSPACE- and #P-hardness “proofs” are high-level sketches that omit the crucial isolation and no-return invariants needed for a valid many-one (and parsimonious) reduction. For PSPACE-hardness, the paper merely maps states to lattice points and edges to contractive affine maps with noise, then asserts an inversion equivalence without excluding spurious trajectories or proving layer-respecting behavior; see its Step 2–5 under 4.1 PSPACE-Hardness and the reliance on “≈” and noise to force rounding, with no quantitative margins or persistence of separation . For #P-hardness, it similarly claims a one-to-one mapping from DAG paths to SPIP trajectories, again without a proof that trajectories can neither merge nor spuriously arise from wrong choices under noise . The paper also uses an internally inconsistent rounding description (“floor rounding to the nearest integer”), further undermining soundness of the reductions . By contrast, the candidate model supplies a complete, quantified construction: a layered encoding with a single contractive matrix, carefully spaced grids, explicit isolation lemmas for wrong-layer and wrong-source transitions, and a no-return lemma with concrete parameter choices—together yielding a proper many-one reduction for reachability and a parsimonious reduction for counting.