Research develops a geometric model to analyze fusion processes in deuterium-tritium pairs, suggesting implications for nuclear reactions.
This work develops a parameter-free geometric account of conventional deuterium–tritium fusion within Constrained Null Geometry (CNG). The D–T entrance configuration is represented on the ten-edge space of five nucleon labels, whose permutation representation decomposes as [5] ⊕ [4,1] ⊕ [3,2]. The [3,2] sector carries the non-additive memory of the 2|3 D–T partition. Its disappearance defines the geometric first-loss boundary. The exact projector algebra gives a unique symmetric contraction path and the critical condition δ* = 5/12, equivalently ζ = 1 and P32x = 0. Conventional heating, beam–target collisions, confinement and compression are then interpreted not as distinct microscopic fusion mechanisms, but as different methods of changing the encounter distribution and first-loss accessibility of D–T pairs. In the factorized regime, every completed reaction is supported on the same rank-changing boundary. A fully connected six-cross-link calculation is performed using the embedded deuteron spin–isospin projectors. Exact Weyl-symmetrized moments of all 63 nonempty cross-link subsets and the complete 203-partition Möbius subtraction give the parameter-free connected coefficient Γ×,c(6) = −290059/39813120. Using the normalized unequal-cell quadratic polarization rule together with the independently derived CNG deuteron and triton binding scales gives the connected [3,2] energy scale E32(0) = 63.2905990548 keV. Only after this result is fixed is it compared with standard D–T data. The Bosch–Hale evaluated cross-section maximum occurs near 64.8147 keV, while the evaluated cross section at the CNG energy is approximately 99.85% of its maximum. The J = 3/2 spin–angular sector is reduced exactly to a unique partial isometry. A separate first-loss trace decomposition shows that 2/3 of the normalized D–T dark carrier survives in the non-additive S4 [2,2] trace sector. In the explicitly stated minimal unitary two-channel completion this fixes the resonant channel vector and gives a maximum D–T reaction probability of 8/9. At the CNG connected energy this corresponds to a peak cross section of approximately 5.09206 b, compared with the Bosch–Hale maximum of approximately 5.06573 b, a difference of about 0.52%. The work also proves an important non-identifiability result. The static geometry, first-loss trace, unitarity and connected energy scale determine the resonance centre and the width-independent maximal reaction strength within the stated minimal class, but they do not determine the resonance width. A continuous family of causal unitary amplitudes can share the same geometric data while having different widths. The missing quantity is therefore identified precisely as the absolute retarded boundary-mode residue, or equivalently the eigenphase slope / channel spectral normalization of the microscopic transported-null action. The paper separates exact representation-theoretic results, minimal-action-class consequences, standard kinematic and thermal translations, and downstream empirical comparisons. No measured D–T resonance energy, width, nuclear radius, scattering length, effective range, cross section or thermal rate is used to determine the parameter-free connected CNG scale.
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Luka Gluvić (2026) studied this question.
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