Theory of Relational Field Induction (TRFI)

Space V3 absolute static discrete lP=1.616e-35 m tau=c^4/G. Time intensity It d tau=dt/It. Particles knots: photon Tw=0 reflex, electron Tw=1 toroidal, quark Tw=2-3 dense spherical chvar. L=alpha Tr(I^2)+gamma|grad I|^2 delta L/delta I=0 gives It=1+rs/r e^{-r/R}. Gravity a=c^2 grad It/It. Icrit=lP/RH=1.224e-61 a0=c H0/2pi=1.083e-10 vs 1.20e-10 H0=2pi a0/c=70.0/77.5 brackets Hubble tension. BTFR M=v^4/G a0 slope 4.0 vs 3.98±0.12. Black hole recycler Tw_c=Ne=1.5e23 bounce jet HI >90% beyond 1e3 rs. Discrete space V3 with Planck length $l_P=1.616e-35$ m, tension $\tau=c^4/G$, memory field $I_{\mu\nu}$. Lagrangian $L=\alpha Tr(I^2)+\gamma|\nabla I|^2$. From $\delta L/\delta I=0$: $I_t(r)=1+r_s/r \cdot e^{-r/R}$, $R=N_e l_P/2\pi=3.86e-13$ m, $N_e=1.5e23$ Gravity defined originally as:$a=c^2 \nabla I_t/I_t$, $a_{\parallel}=|a|\cos\theta$ (change of speed $dv/dt$), $a_{\perp}=|a|\sin\theta$ (change of angle $d\theta/ds$) — Appendix A original. Newton limit $r\ll R$: $a=GM/r^2$. MOND limit $r\gg R$: $a=0.5 a_N+0.5\sqrt{a_N^2+4a_N a_0}$, $a_0=cH_0/2\pi=1.083e-10$ m/s2. Core Prediction (falsifiable, derived from TRFI, no free parameter): Critical twist $Tw_c=N_e=1.5e23$. Black hole stores $Tw_{BH}$. When $Tw_{BH}>Tw_c$, bounce $det(I)\to-det(I)$ at $\rho\to\rho_P=5.155e96$ kg/m3 must release excess twist. Cheapest neutral release: proton $Tw=3$ + electron $Tw=1$ = HI ( $Tw=4$ closed). Charged $Tw=1$ alone leaves $I_{\theta\phi}$ field with cost $L_{ann}=\beta I_{\theta\phi}^2$. $r_{trans}=10^3 r_s \cdot (M/6.5e9 M_{sun})$ $f_{HI}(r)=1-e^{-r/r_{trans}}$, $>90\%$ for $r>2.3\times10^3 r_s$ $n_e(r)=n_0/(1+k n_0 r/v) \sim 1/r$ due to annihilation $dn/dt=-k n^2$ Observational status (Appendix D): M87 jet within 1000 $r_s$ already observed as pair plasma: "hot plasmas injected at 7 $r_s$, M87 jet likely composed of pair plasma, most radio photons within 1000 $r_s$" (2025 AASTeX draft) Nuclear spectrum of M87 shows HI, HII lines Jet composition leptonic vs hadronic still listed as "longstanding mystery" (MDPI 2025) JWST NIRCam 0.90-3.56 micron images show kpc jet (Livingston et al 2025) EHT Movie Campaign March-April 2026 + ngEHT 86/230/345 GHz plasma composition program will test this Magnetic trapping / Antimatter echo (Appendix C):$B(r)=B_0(r_s/r)^3$, Penning trap between $r_s$ and $10^3 r_s$, $\mu=m v_{\perp}^2/2B$ invariant. $\tau_{echo}\sim10^3 r_s/c \cdot B_{max}/B_{min}$: hours-days for Sgr A*, months-years for M87*. Predicts 511 keV ring + circular polarization sign change. Falsification:If ALMA/VLA deep 21cm 0.3-3 kpc along jet shows <10% HI and pure synchrotron continues, TRFI falsified. If $n_e$ does not decay as $1/r$, TRFI falsified. Contents: Main PDF: TRFI Ultimate V12 ORIGINAL (gravity, bounce, constants) Appendix A: gravity as speed+angle change Appendix B: HI prediction derivation Appendix C: magnetic trapping / echo Appendix D: existing observational hints Test Proposal: ngEHT/EHT/ALMA/JWST Constants: $l_P$, $R$, $N_e$, $\rho_P$, $a_0$, $I_{crit}=1.224e-61$, $H_0=70$ (local)/77.5 (CMB) km/s/Mpc.