Not a Tired-Light Model: Affine Geometric Stretch with Local Remission and Conserved Energy Lmax_v11: Photon-Stretch Geometry, Affine-Parameter Cosmology Fundamental Affine Parameter Ψ(d,Φ,B) = 1 - d/Lmax(Φ,B) Ψ measures the remaining geometric span available to a photon relative to the local affine limit. All observable quantities derive from Ψ. (1) Interaction & Survival ρI(d,Φ,B) = E0/d · Ψ Psurv = Ψ Lmax(Φ,B) = 72 Gly · (1 - Φ/c² - βB·B²/B0²) t = d/c Note: Φ = local gravity, B = magnetism. Voids → Lmax ≈ 72 Gly. Clusters → Lmax ↓. (2) Redshift & Distance 1 + z = 1/Ψ d(z) = Lmax · z/(1 + z) t = d/c Redshift measures geometric dilation relative to Lmax. Gravity suppresses Lmax; voids preserve it. (3) Light Path d = d0 · (1 + κ + κΦ + κB) t = d/c κΦ = gravity stretch. κB = magnetic twist. Path terms are averaged over field variations. (4) Flux / Dimming F = L0/(4πd²) · Ψ² Geometric spreading and affine dilation are both controlled by Ψ. (5) Angular Size θ = Dphys/d d already includes κΦ and κB corrections. Time-averaged fields preserve angular sharpness. (6) Edge Condition Ψ(d = Lmax) = 0 Psurv(d = Lmax) = 0 tmax = Lmax/c The affine boundary is not uniform. Clusters ≈ 71 Gly. Voids ≈ 76 Gly. (7) Lensing Deflection α = 4GM/(c²b) + αB Mass bends the path and contributes to Φlocal, reducing Lmax. Magnetic fields contribute αB. (8) Lens Equation β = θ - (dls/ds)(α + αB) dls and ds already include κΦ and Φlocal effects. (9) Magnification μ = 1 / |(1 - κlens - κB)² - γ²| Fobs = μL0/(4πd²) · Ψ² Magnification, shear, and affine dimming remain coupled through κlens, κB, and Lmax. (10) Local Remission Llocal = 1 - ηεβB Atomic-scale remission behaviour. βB provides the bridge between local processes and global Lmax structure. (11) Conservation η = 1 ⇒ Nγ,out ≥ 0 Energy is conserved. Photons are continually absorbed and re-emitted, with wavelength and path evolution governed by local Φ and B conditions. Not a Tired-Light Model: Affine Geometric Stretch with Local Remission and Conserved Energy Lmax_v11 attributes cosmological redshift and flux dimming to progressive geometric dilation of the photon’s electromagnetic field as it approaches a finite affine-parameter limit \(L_{\max}(\Phi,B)\). The governing quantity is the remaining span so that \(1+z=1/\Psi\) and flux scales with \(\Psi^2\). Unlike classic tired-light proposals, which remove energy from the photon itself, the framework maintains strict energy conservation (Eq. 11: \(\eta=1\implies N_{\gamma,\rm out}\ge0\)). Photons are continually absorbed and re-emitted; wavelength and path evolution are set by the local gravitational potential \(\Phi\) and magnetic field \(B\). Any residue that appears at the affine boundary is treated as a non-radiative geometric contribution, not an irreversible energy sink. The dual-frame construction further separates a local “birth” redshift (recovering standard GR/SR factors) from the transit stretch, keeping the accounting closed while preserving the raw observational catalogues.