A7U: Distributed Planck Bundles, Intrinsic Space Fluctuations, and the No-Pure-Particle Theorem

A7U is a parameter-free extension of Quantum Traction Theory's bundled-existence axiom A7. Canonical A7 says each active world-cell address closes a fixed 2π modular budget and carries a complete Planck bundle. A7U removes the last hidden-sector ambiguity: the complement of any local visible particle is not an arbitrary unseen substance, but the visible modular share of the other A5-entangled co-members of the same w-bundle. The full distributed bundle is exactly pure; every strict laboratory subsystem is exactly mixed. The headline theorem is the no-pure-particle theorem: a laboratory can prepare states with arbitrarily high operational purity in an accessible subspace, but no single elementary particle is ever the complete pure object. Exact purity belongs only to the full distributed Planck bundle. This gives QTT a parameter-free replacement for collapse-model rates, environmental spectral-density knobs, pointer-basis selection rules, ultraviolet regulators, zero-point counterterms, and arbitrary geometry-noise amplitudes. Space fluctuations are reframed as zero-sum modular-share reshuffling across w-co-members. In the ordinary local-readout sector these fluctuations are capacity-bounded, local-marginal preserving, and unable to deliver free energy, but they appear as vacuum stress fluctuations, Casimir boundary shifts, residual purity floors, and low-redshift cosmological drift anisotropies. Engineered w-address information transfer, if discovered, is treated as a future frontier sector rather than a falsifier of distributed existence. The paper provides: (i) the formal axiom A7U.1–A7U.5; (ii) the no-pure-particle theorem; (iii) a reduction-to-A7 theorem ensuring corpus-loyal extension of every prior QTT result; (iv) a correlation-safe Shapley modular-share formula; (v) two conjectures on the variational floor (uniform positive, closed form), with the closed-form floor identified as the load-bearing target for the next paper; (vi) capacity-correct space/vacuum/Casimir fluctuation bounds; (vii) a six-step falsifier ladder with the headline empirical edge "no exact pure particle, ever"; and (viii) a published-data test target identified in the Arndt-group Talbot–Lau matter-wave interferometry corpus. The empirical falsifier: any certified ontic-pure laboratory single-particle state falsifies A7U. Current best certified single-system purities are O(0.999), well above the regime where A7U predicts a residual floor.