The Speed of Light as an Emergent Property of the Entanglement Network: Structural Derivation and Cosmological Implications

This paper develops a derivation of the speed of light c within the Entanglement Network Gravity (ENG) framework, in which spatial geometry is emergent from the correlation structure of an underlying quantum entanglement network. The derivation rests on three physically motivated commitments: (i) the network is fundamentally 2-dimensional with square-cell geometry, the 2-dimensionality motivated by the holographic principle and the square-cell geometry adopted as an additional structural choice; (ii) its elementary cells have size a = 1/sqrt (Lambda) and fundamental time step tau = 1/H0, the minimal c-free length and frequency scales available at cosmological scale; (iii) rotational isotropy is approximated at the cellular level by signal propagation to both axial and diagonal neighbors within one fundamental time step. From these commitments the maximum signal speed is the cell diagonal per time step, sqrt (2) *a/tau. The framework's primary empirical content is the dimensionless prediction OmegaLambda = 2/3, agreeing with the observed value 0. 685 +/- 0. 007 to within approximately 3%, a moderate tension of approximately 2. 5 sigma that ongoing cosmological surveys will resolve within the coming decade. The equivalent dimensional form c = sqrt (2) *H0/sqrt (Lambda) ~ 2. 94e8 m/s reproduces the measured speed of light to within approximately 2%, with the caveat that the observed value of Lambda is itself extracted from cosmological data using the Friedmann equation containing c; the non-circular content of the prediction is therefore the dimensionless OmegaLambda statement, with the c form as its algebraic counterpart. A counting argument for cosmological-scale network growth independently yields the structural reinterpretation H = Gamma/ (3n). The framework's implication that c varies with cosmic epoch is reconciled with the observational constancy of the fine structure constant through a coordinated-variation hypothesis identifying two structural invariants (hbar*c and m*c²) under which all dimensionless ratios remain invariant. The hypothesis is consistent with all observational tests examined here at the level of dimensionless quantities; verification against Big Bang nucleosynthesis, where coordinated c-variation is of order 1e17, is identified as the framework's principal outstanding test. The paper builds on and extends the foundation paper "Entanglement Network Gravity: Static Spacetime Geometry from Quantum Entanglement Density" (Zenodo DOI: 10. 5281/zenodo. 20026422).