A Finite-Reservoir Mechanism for the STAR Transverse-Momentum Correlation Dip

When shared finite support suppresses momentum correlations STAR's low-energy gold-collision data show a dip in transverse-momentum correlations. How can shared microscopic support suppress the motion of particle pairs without requiring a matching loss of average particle energy? This paper develops a finite-reservoir mechanism and connects its source fluctuations to the measured pair signal: \[\boxed{\Delta K_{st}=\Phi_{st}a_sa_t\frac{\operatorname{Var}(L)-Mf(1-f)}{M(M-1)}.}\] The source has M effective binary slots, occupied count L, and mean occupation f. The factors as and at convert source occupation into species momentum, while Φst counts accepted pairs sharing that support. A deficit of occupation fluctuations produces a negative pair contribution. Uniform allocation of J occupations over S slots gives an exact realization: \[\boxed{\operatorname{Cov}(X_i,X_j)=-\frac{f(1-f)}{S-1},\qquad i\ne j.}\] The paper derives coupled energy and baryon-number fluctuations, species correlations, exact selected-event estimators, and a finite-time memory law. Under the stated linear-response and independent-relaxation conditions, a three-particle relation cancels both the response amplitude and relaxation factor: \[\boxed{\frac{H_3^2}{(-H_2)^3}=\frac{4(1-2f_0)^2(S-1)}{f_0(1-f_0)(S-2)^2}.}\] Here H2 and H3 are the source contributions after division by the respective same-domain pair and triple fractions, with S > 2 and nonzero pair denominator. This provides a test beyond the inclusive dip: the pair and triple measurements must describe the same prepared population. An opening mathematical map identifies the QTT dependencies: A2 endurance, A6 finite capacity, and A7 completed-source accounting. The inherited color scale is held at 444.25315096 MeV. A disclosed, data-led comparison evaluates four branches against STAR's public centrality tables without optimizing continuous dip coefficients. The 444 MeV candidate gives RMS logarithmic discrepancies of 0.108 for seven central ratios and 0.126 across 42 ratios, versus 0.359 and 0.180 for independent-source scaling. All competing branches and the unfavorable 3 GeV stress result are retained. The mathematical results are conditional theorems; the empirical comparison is a discovery audit, not a significance claim or a completed microscopic selection of the Au+Au source. The next discriminants are identified-species covariance, the pair/triple relation, and independently fixed collision evolution and response. The reconstruction package includes the proofs, numerical inputs, exact-arithmetic checks, four-branch calculations, and provenance. Source dependencies: QTT main book; finite-reservoir Boltzmann framework; color-kernel theorem; Access Law. Experimental input: STAR HEPData tables. Stable paper link: 10.5281/zenodo.23066809.