A Parameter-Free Derivation of the Fine-Structure Constant α from Information-Theoretic Constraints in Octonionic Space

This poster, to be presented at the APS Global Physics Summit (Denver, March 2026), details a first-principles derivation of the fine-structure constant ($\alpha$) using the Kosmoplex geometric framework. By modeling physical reality as a projection from an 8-dimensional octonionic substrate to a 4-dimensional observable manifold, we derive the inverse fine-structure constant as a channel capacity limit fixed by combinatorial and algebraic rigidity.Core Result:The derivation yields a theoretical value of:$$\alpha^{-1} = 137.035999143$$This result contains zero free parameters and matches the CODATA 2022 recommended value ($137.035999177(21)$) to within $1.62\sigma$.Methodology:
The framework proceeds from seven information-theoretic axioms, including triadic closure and total computability. It identifies the Fano plane ($\mathbb{P}^2(\mathbb{F}_2)$) as the minimal computational manifold required to support octonionic multiplication. The derivation identifies two distinct projection channels:+4The Eigenvector Channel (Coupling): Governed by the Fano plane, with a channel capacity of $2\binom{8}{4} - 3 = 137$, corresponding to $\alpha^{-1}$.The Eigenvalue Channel (Mass): Governed by the Pascal 8-simplex, with a capacity of $\binom{9}{4} - 1 = 125$, corresponding to the Higgs mass ($125$ GeV).Falsifiable Predictions:
The theory makes five specific, testable predictions distinguishing it from standard QFT:Vacuum Kerr Effect: A specific altitude-dependent drift in $\alpha$ of $\Delta\alpha/\alpha \approx 4.60 \times 10^{-16} \text{ km}^{-1}$.Structural Anisotropy: The "Webb Dipole" in $\alpha$ is interpreted as a real processing gradient, not systematic error.Geometric Hubble Tension: The tension is derived as the invariant ratio of the two channel capacities ($137/125 \approx 1.096$).Isotopic Impedance: $\alpha$ measurements will show species-dependent shifts (e.g., $^{171}\text{Yb} > ^{87}\text{Rb}$).Saturation Limit: No quantum experiment can exceed a 42-dimensional Hilbert space realization.