IceCube observes a break near 30,TeV in the diffuse astrophysical neutrino spectrum. We interpret it as the photomeson ($p\gamma$) threshold. Accelerated protons on the soft X rays of accreting black holes through the $\Delta (1232)$ resonance. One kinematic relation sets the break energy from the target field’s lowest photon energy, the seed scale ${\epsilon }_0$. The measured break fixes ${\epsilon }_0\simeq 0.13$,keV and supplies the low-energy suppression no sum of falling power laws can produce. Building on the $\Delta (1232)$ identification of Khatee Zathul, Fang, Halzen, and Hooper and the single-source-class photo-pion fit of Winter, Fiorillo, and Buson, we give closed-form relations that invert the four broken-power-law fit parameters to the source physics with no remaining freedom, namely ${\gamma }_2=s$ and ${\gamma }_1=s-({\alpha }_x-1)$ ($s$, ${\alpha }_x$ the proton and target photon indices), and $E_{\rm br}\propto[(1+\bar z)\,\varepsilon_0]^{-1}$. The break width then measures the population’s uniformity. The total smearing is bounded to ${\sigma }_s\le 0.235$,dex (68% CL), no broader than redshift alone must make it, and the seed scale is the same across the sources to within a factor $$1.5, a constraint mean-spectrum fits do not provide. The model also predicts that below-break neutrinos come on average from higher redshifts than those above. The threshold also fixes the flavor and neutrino-antineutrino composition, including the energy-dependent ${\bar{\nu }}_e$ fraction and the Glashow-resonance discriminator computed in detail by Winter , matching current flavor data. Inverted source by source, the relation gives each resolved IceCube source its target photon scale, from the keV coronae of NGC 1068 and PKS 1424+240 to the $$20,eV jet of TXS 0506+056. That two-decade spread means they cannot supply the homogeneous break. It requires a separate, fainter population. KM3-230213A points to a warm-dust target, ${\epsilon }_0\simeq 0.02$,eV, unless cosmogenic.