Collective Uncertainty and the Sign-Dual Pair: A Heisenberg-First Reconstruction of Paired Quantum Structure
Collective Uncertainty and the Sign-Dual Pair Collective Uncertainty and the Sign-Dual Pair: A Heisenberg-First Reconstruction of Paired Quantum Structure Entropy Condensation Theory (ECT) — Extended Framework 2025 Abstract This paper develops a Heisenberg-first reconstruction of a sign-dual theory of paired quantum structure. The central claim is that the mathematically natural object in a paired system is not the isolated marginal particle but the conserved two-body object. The key insight driving the entire paper is this: the Heisenberg uncertainty principle is not eliminated in a paired system — it is reorganized. Uncertainty is not destroyed; it is redistributed from the pair-axis variables into the complementary sector. When the canonical algebra is written only in local variables $(x_1, p_1)$ and $(x_2, p_2)$, uncertainty appears to prohibit simultaneous localization of the physically r...