Pauli Weight and the Quantum Grandfather Paradox: Neutral Parties and Four-Party Coherence

This paper continues a program on deterministic feedback of no-signaling correlations (Papers A–C) and asks when a feedback loop can produce a quantum grandfather paradox, that is, a loop that admits no consistent assignment. For a quantum box P and a feedback function g, the consistency weight is W(P; g) = Σₒ P(o | g(o)), and Ω = min_g W. A paradox corresponds to the weight operator A_g having a zero eigenvalue. We show that a party whose measurement carries no which-world information (a "neutral party") cannot create a paradox, and we classify which Pauli-weight structures can. For affine feedback of Pauli weight at most three, a neutral party always exists, so the weight operator is strictly positive (λ_min(A_g) > 0) at all angles. Any paradox in the affine case therefore requires four-party, GHZ-type coherence. Nonlinear feedback can escape this: we give a five-party counterexample with weight-three couplings, and we show that five is the smallest number of parties for which this happens. The mechanism is that nonlinear processing of two parties' outcomes fuses them into one effective party with a richer measurement structure. Together, the results place the quantum Novikov principle in the lineage connecting pre- and post-selection paradoxes to contextuality and GHZ-type pseudo-telepathy. Code and numerical checks are in the accompanying archive. English and Korean versions are included.