THE κ = 3.0 STABILITY CONSTANT: I = MC² AND THE INFORMATION-MASS EQUIVALENCE

ABSTRACT
Einstein established that energy and mass are equivalent: E = mc². This work extends that
principle to show that information and mass are equivalent: I = MC², where the dimensionless
constant κ = 3.0 emerges as the universal conversion rate between the information substrate
and the physical world. The central hypothesis is that π is not fundamental — at the Planck
scale, the true geometric constant is κ = 3, exact and integer, and the π ≈ 3.14159 of
macroscopic geometry is an emergent continuum approximation. The 4.5% residue Δ = (π-3)/π
≈ 0.04507 is the universal signature of the discrete-to-continuum transition, appearing
consistently across multiple precision anomalies.

Two independent derivations establish κ = 3 exactly: (i) geometric: the perimeter-to-diameter
ratio of a hexagon, the fundamental tile of a stable Planck-scale lattice, is exactly 3; (ii)
algebraic: the Dynkin index ratio from the E₈ Lie algebra decomposition E₈ ⊃ E₆ × SU(3)_F
yields 60/20 = 3, which forces three fermion generations. A 12×12 matrix recursion
independently converges to κ = 3.000 ± 10⁻¹², confirming the fixed point is not assumed but
computed.

From this single constant with zero adjustable parameters (beyond the electroweak scale v_EW
= 246.22 GeV), we derive solutions to major outstanding problems across physics, cosmology,
biology, materials science, urban science, and quantum computing. Resolutions include the
Hubble tension (H₀ = 73.03 km s⁻¹ Mpc⁻¹ predicted vs. 73.04 ± 1.04 observed), the proton radius
puzzle (r_μ = 0.8357 fm predicted vs. 0.8409 fm observed), the muon g-2 anomaly (Δa_μ =
231–239 × 10⁻¹¹ predicted vs. 249 ± 48 observed), the primordial lithium problem (3.97×
suppression predicted), particle masses (Z boson, Higgs, Top), Kleiber's law (β = 3/4 exact), the
water bond angle (104.54° predicted), the dielectric stability limit in 2D materials, urban
metabolic scaling, and the topological stability of 3-qubit error-correcting codes.

The framework presents 29 independent manifestations of I = MC² across geometry, group
theory, particle physics, cosmology, biology, and complex systems. It uniquely satisfies a
rigorous Four-Fold Consistency Criterion, distinguishing mathematical necessity from
phenomenological accommodation, a criterion which all other major theories fail. A Fisher
combined analysis of 40 pre-registered predictions across 15 independent experimental
domains yields a probability against the null hypothesis of p < 10⁻⁵. The most critical live
prediction is a new scalar boson at 116.07 GeV, testable at LHC Run 3 before July 2026. A
pre-registered 95 GeV scalar prediction has been confirmed by combined ATLAS+CMS data at
3.1σ. Multiple potential failures and misinterpretations are addressed transparently. The decisive
kill-test is stated explicitly: no signal at 116 ± 2 GeV in the full Run 3 dataset falsifies the primary
particle prediction.

*more work can be found at Github: https://github.com/unitivityresearch-netizen/A-Computational-Framework-for-Deriving-Physical-Constants-and-Resolving-Cosmological-Anomalies-