No-Go Theorem and Conditional Uniqueness for the Universal Endpoint Gain in Quantum Traction Theory: Tier-K Preregistration v1.0

Abstract

Does a finite-capacity source law force the gravitational endpoint to be read at full gain? \[ \boxed{ \mathrm{A2+A5\!\text{-}\!X+A6+A7}\not\Rightarrow\chi_g=1, \qquad G_{\rm end}=\chi_gG_A,\quad 0\leq\chi_g\leq1, \qquad \mathrm{EFA\!\text{-}\!G1}\Longleftrightarrow\chi_g=1. } \] The sealed object is a no-go and conditional-closure preregistration: the core source axioms bound the endpoint-gain family, while the distinct Endpoint Faithfulness hypothesis fixes the gain-one branch for a prospective test. The stable citation target is the concept DOI 10.5281/zenodo.21955408. This content-frozen release addresses whether the universal gravitational endpoint gain, chi_g, is fixed by the source axioms of Quantum Traction Theory (QTT) or remains an independent replacement for Newton's constant. Within the declared class of pointwise local, real-linear, origin-preserving, SO(3)-equivariant source-to-laboratory cameras, the release constructs a countermodel family showing that A2 endurance dynamics, A5-X completed-event support, A6 finite-capacity bounds, and A7 2pi bundle closure do not entail chi_g = 1. These assumptions determine at most a scalar camera P_g = chi_g I/t_A; with the strongest two-sided capacity ceiling they restrict the gain to 0 <= chi_g <= 1. The family P_chi(J) = chi J/t_A preserves the source continuity law, completed-event support, capacity ceiling, and bundle closure while changing the observed coupling to G_end = chi G_A. The release then states the minimal conditional closure, EFA-G1 (Endpoint Faithfulness): a fully inclusive, target-blind gravitational camera maps a source-saturated endurance current to the saturated one-tick kinematic endpoint. Given the camera assumptions, EFA-G1 is equivalent to chi_g = 1. It is therefore frozen as an additional falsifiable physical hypothesis, not relabelled as a consequence of A2/A5-X/A6/A7. The accompanying Tier-K card preregisters a prospective test of this gain-one branch. Using the pre-freeze weak-sector anchor G_F = 1.16637859(59) x 10^-5 GeV^-2 and the frozen dimensionless constructor, the card fixes G_0 = 6.674300783009366 x 10^-11 m^3 kg^-1 s^-2 with an anchor-only standard uncertainty of 0.505839 ppm. Historical G determinations are ineligible as prospective evidence. GAIN-GREEN requires two independent post-freeze measurement classes, fixed covariance and eligibility rules, no retuning, and Bayes factor greater than 100 against the complete chi_g in [0,1] counterfamily under three frozen priors. Tier-K hard-evidence promotion additionally requires an endpoint-linked non-G holdout and standard-theory subtraction. The package includes the no-go theorem, conditional uniqueness theorem, preregistration card, one-page verdict certificate, canonical JSON payload, countermodel ledger, verification code, future-data template, SHA-256 manifest, and freeze certificate. Current status: TIER-K CANDIDATE; no hard-evidence claim.