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

When shared finite support suppresses momentum correlations A dip in particle-pair momentum correlations can occur while average particle momenta remain ordinary. This paper derives how shared finite source support produces that effect and how to distinguish its population law using two-, three-, and four-particle measurements. \[{Δ Kₛₜ=Φₛₜa_sa_tVar(L)-Mf(1-f)/M(M-1).}\] Here M is the source support, L its occupied count, f its mean loading, and Φst the fraction of accepted species pairs sharing that support. The response factors as and at convert source occupation into momentum. A deficit of occupation fluctuations fixes the source anticorrelation; fixed total occupation gives an exact realization: \[{c_2=-f(1-f)/S-1.}\] The fourth-order theorem provides a second, response-cancelling test even where the third source moment vanishes. At fixed half loading, for even S ≥ 4, independent identical domains and the stated linear response, \[{ H_4/H_2^2=6/S-3.}\] The measured connected fourth cumulant must first include the exact correction for quadruples split between two source domains: \[H_2=K_2/Φ_2, H_4={K_4-3(Φ_4+Q₂₂-Φ_2^2)H_2^2}{Φ_4}.\] The domain fractions and pair-partition weight Q22 are defined in the paper. With positive fractions and nonzero pair denominator, the ratio removes the common linear response and the specified independent relaxation. An exact counterexample shows why omitting the partition correction would infer the wrong source size. The framework also derives coupled energy and baryon fluctuations, finite-time memory, species-centered tests, and an all-orders selected-record generating functional. A two-window counterexample identifies the additional measurements needed to determine support without confusing it with population fluctuations. The inherited QTT color scale stays fixed at 444.25315096 MeV. In the disclosed four-branch discovery comparison, its candidate gives RMS logarithmic discrepancies of 0.108 across seven central ratios and 0.126 across all 42 ratios, versus 0.359 and 0.180 for independent-source scaling. The unfavorable 3 GeV stress result and all competing branches remain in the record. These are discovery scores, not significance estimates. The conditional theorems are proved; a full empirical STAR explanation requires the independently determined Au+Au population, response and joint covariance. The PDF opens with the source equation, axiom cards and reader orientation. The reconstruction archive preserves the earlier proofs and discovery inputs and adds 1,960 exact/arithmetic checks for the new results. 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.