CHAN CONSTANT f=14.26% - One Number Resolves 7 Cosmological Tensions - V=1-N^2/Ncrit^2 Theory - Lau Chi Man

*v2 Addendum: The Lau Echo Formula - A Quantitative Falsifiable Prediction* This v2 adds a quantitative prediction to v1 (DOI: 10.5281/zenodo.23725831). In Lau Theory, the vacuum has a fundamental lattice spacing *L_Lau = 5.04e-18 m* (T_crit = 1.85e15 K) and *CHAN CONSTANT f = 14.26% = 1826/12818*. A black hole does not form a singularity but undergoes a quantum bounce at L_Lau. The gravitational-wave echo delay time is: *Δt_echo = (4GM / c³) _ ln[ GM / (c² _ L_Lau) ]* Where G is gravitational constant, M is black hole mass, c is speed of light. L_Lau is fixed from cosmology, no free parameter. *Predictions:* - GW150914-like (62 M_sun): Δt_echo = 0.12 - 0.18 s after merger - 30 M_sun event: Δt_echo ≈ 0.06 s - M87_ (6.5e9 M_sun): Δt_echo ≈ 11 hours - Sgr A_ (4e6 M_sun): Δt_echo ≈ 20 minutes This delay must scale as M*ln(M). Search for this specific scaling in LIGO-Virgo-KAGRA O4/O5 data will provide a direct test. This is distinct from other echo models which treat reflectivity as a free parameter. With this addendum, one number L_Lau = 5.04e-18 m simultaneously explains 7 cosmological tensions (v1, chi2=2.5) and predicts GW echoes. *Author: Lau Chi Man, Independent Researcher, Hong Kong* *ORCID: 0009-0002-3521-8344* *Email: [email protected]*