Geometric Deuterium–Tritium Fusion in Constrained Null Geometry: Static Mass Closure, First-Loss Dynamics, and a Falsifiable Trapped-Domain Reactor Prediction

Abstract

This work develops a unified Constrained Null Geometry (CNG) derivation of the deuterium–tritium fusion channel, beginning with previously derived CNG nuclear sectors and ending with a new experimentally testable reactor prediction. The construction follows the CNG dependency chain from protected topology and admissible domains to canonical operators, reconstruction, and physical scales. The deuteron sector is inherited from the earlier proton–proton reconstruction, while the triton mass is inherited from the parameter-free CNG D–D reconstruction. No empirical D–T cross section, alpha-particle mass, D–T reaction energy, nuclear radius, or fitted nuclear coefficient is used to determine the static D–T result. For the four-nucleon sector, fermionic antisymmetry fixes the lowest alpha branch as a one-dimensional state with spin zero, isospin zero, and positive parity. Exact recoupling gives the fourth-attachment connected defect as 3/32. With the frozen CNG deuteron and triton inputs, the static calculation gives an alpha binding energy of 28.297200996727445 MeV, an alpha mass energy of 3727.377794983405 MeV, and a D–T reaction release of 17.59150530252236 MeV. The separated D–T geometry is then isolated in the five-dimensional [3,2] component of the ten-edge five-label representation. A canonical D–T defect operator identifies precisely the component carrying the D–T partition information, while its kernel defines the common geometry. Preserving the already closed internal deuteron and triton structures leaves one symmetric six-cross-link deformation. Its exact critical displacement is 5/12. At this point the D–T partition component vanishes and the separated D plus T configuration reaches the common-domain boundary. The corresponding first-loss dynamics is then derived from the CNG reconstruction principle. Along the canonical reconstruction path, the closure defect decreases monotonically toward the common-domain boundary. A trapped entrance with an accessible common first-loss boundary gives unit eventual first-loss accessibility. This motivates a concrete preparation-limited reactor realization in which a material cell removes the outward D–T separated continuation while preserving the common reconstruction branch. Under the stated hard-switch conditions, the resulting theorem predicts one eventual fusion event for every successfully prepared active D–T cell. In steady state, the fusion-event rate therefore equals the successful preparation rate. Each completed event produces one alpha particle and one neutron. The paper proposes defect-engineered titanium, particularly multi-occupancy vacancies associated with twin boundaries, as one candidate material realization. A thin palladium layer may be used for hydrogen-isotope loading while titanium provides the candidate active defect geometry. Several parameter-free differential experimental predictions follow. First, in the saturated trapped regime and under matched material and beam conditions, the vacancy-associated excess fusion yield must scale linearly with independently measured active-vacancy density. Second, for random D–T isotope occupancy, the normalized D–T yield follows a symmetric parabola with a maximum at a 50:50 D:T mixture. Relative to the 50:50 value, the predicted yields are 0.36 at 10 percent tritium, 0.75 at 25 percent, 1.00 at 50 percent, 0.75 at 75 percent, and 0.36 at 90 percent. Third, if an incident deuteron beam must first create active titanium vacancies, the independently determined titanium displacement energy gives a beam-created vacancy threshold near 0.062 keV in D–D centre-of-mass energy and near 0.074 keV in D–T centre-of-mass energy. A pre-defected titanium target should not exhibit the same vacancy-creation cutoff. The strongest new prediction is more direct. If an independently characterized material protocol produces true CNG hard-switch D–T cells, the eventual ratio of fusion events to successfully prepared active cells must approach one. This prediction is stated before experimental verification. No coefficient in the reactor tests is to be retuned after fusion data are obtained. The work therefore provides both a geometric derivation of the D–T fusion channel within CNG and a concrete experimental program capable of directly confirming or falsifying the proposed physical realization.