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A T-odd amplitude in forward scattering is a null test free from final state effects and can be amplified in neutron-nucleus p-wave resonances by up to 6 orders of magnitude above the bare NN amplitudes [1]. The NOPTREX collaboration has experimentally measured a 0.5 x 10^{6} amplification factor at JPARC on the 0.7 eV p-wave resonance in $^{139}$La [2] and is approved by KEK for a Phase 1 low precision, proof of principle search for the P-odd/T-odd correlation \vec{s_{neutron}} \dot [\vec{k_{neutron}} \cross \vec{I_{nucleus}}]. 83% neutron polarization at 0.7 eV has been achieved using a spin-exchange optically pumped 3He neutron spin filter, and 50% 139La polarization has been reached in a 10cc crystal of LaAlO3 using dynamic nuclear polarization. We present estimates based on [3] of the statistical sensitivity reach of a Phase 2 experiment. We also briefly describe NOPTREX work to better understand the Standard Model weak interaction effects in heavy nuclei using statistical spectroscopy. [1] J. D. Bowman and V. P. Gudkov, Phys. Rev. C (2014). ArXiv: [2] R. Nakabe et al, Phys. Rec. C 109, L041602 (2024). arXiv:2312:06115 [3] V. V. Flambaum and A. J. Mansour, Phys. Rev. C 105, 015501 (2022). arXiv:2111.02037