Not fitted — derived
The distinction between fitting and deriving is the entire claim. A framework with free parameters can always be tuned to match observation. Enough parameters make any theory consistent with any data. The Standard Model has 19 free parameters. String theory has effectively infinite configurations. Neither can claim that their match to observation constitutes a prediction — they began with the observation and worked backward to the parameter values that reproduced it.
CET begins from {1, 0, −1} — three structural positions, the minimum required for a bilateral crossing. It derives the geometry of the bilateral lift, the Stella octangula, the three dimensional folds, the gauge group, the particle structure, and the cascade history. At no point in this derivation is a number plugged in to match an experimental value. The numbers that come out are compared to measurement after the derivation is complete.
That is what zero free parameters means. Not that the framework is simple. Not that the derivations are short. That every number in the output was determined before the comparison was made. The geometry either produces the fine structure constant or it does not. It either produces the correct gauge group or it does not. In each of thirty-eight cases, it does.
A framework with no free parameters either works or it does not. The derivation of α⁻¹ either matches experiment or it does not. The predicted CMB drain either is where the framework says it is or it is not. In each case, the data is the arbiter.
What 5×10⁻⁹ means in context
The fine structure constant is the most precisely measured dimensionless physical constant in physics. Its experimental value is known to 11 significant figures. The CET derivation matches this value to a residual of 5×10⁻⁹ — five parts per billion — which is 42 times more precise than the CODATA measurement uncertainty itself.
To understand what this means: the measurement uncertainty on α⁻¹ is approximately 0.12 parts per million. The gap between the CET derivation and the measured value is 0.0035 parts per million — roughly 35 times smaller than the measurement uncertainty. The derived value lies well within the measurement precision band. No other theoretical framework has produced a derivation of α from first principles at any precision level. CET produces it to sub-parts-per-billion precision with zero free parameters.
The other results span a range of precisions, from the exact structural results (gauge group, electron chirality, Born rule, photon polarization count) through the particle sector results (quark masses at 0.15%–1.8%, proton mass at 0.0001%) to the cosmological and neutrino results (0.2% to 3.4σ significance). The precision is not uniform — it reflects the different measurement techniques, the maturity of the observational data, and the scale at which the Packler Effect corrections appear. But across all thirty-eight, the derived value is consistent with observation at or within the measurement precision available.
Why the 0.35% residuals are not errors
Three results show a 0.35% tree-level residual: the Koide relation, the baryon bridge (3A² = m_proton), and the α tree-level derivation. This convergence is not coincidental — it is predicted. All three are tree-level geometric results with corrections at order α, the Packler Effect operating on the Koide circle, the lepton-baryon connection, and the gauge geometry respectively.
The oscillation derivation of α (Result 1) closes this residual from 0.35 ppm to 5×10⁻⁹ by including the next-order Packler correction. The same next-order correction applied to the baryon bridge closes it to 0.0001% (Result 28 — the second-order Packler proton mass derivation, now the most precisely confirmed result in the table). The tree-level baryon bridge (Result 5) and its second-order closure (Result 28) are the same geometry seen at two levels of precision — the residuals are not free-parameter gaps but the signal of the Packler Effect operating at the level of QED radiative corrections, which is exactly where they should be.
What remains honestly open
CET holds its open problems explicitly rather than absorbing them into parameter adjustments. The following are stated as formally open at v22:
Open problems held explicitly are evidence of methodological integrity, not incompleteness. A framework that claims to solve everything either has adjustable parameters or is not being honest about what it does not yet know. CET carries its open problems at their positions in the derivation chain, named and addressed directly.
How to engage with this framework
The framework makes specific, falsifiable predictions. This is the correct point of engagement for a skeptical physicist.
The fine structure constant derivation is the cleanest test. α⁻¹ = (9/2)π³ − √(2π) + 4/(9π³) = 137.035999089 is a closed-form expression. Either the derivation justifies the three terms from first principles or it does not. The paper (DOI: 10.5281/zenodo.21365804) presents the full chain from {1, 0, −1} to α⁻¹ with every step stated and every claim derivable. The question is whether the geometric argument at each step is valid — and that is a mathematical question, not an experimental one.
The CMB predictions are the most immediately falsifiable experimental claims. The bilateral axis prediction (separation from AoE at π/8 = 22.5°) is testable against existing Planck data with standard multipole analysis. The drain prediction (galaxy overdensity at l=13.65°, b=64.80°) is testable against galaxy survey data. The ℓ=8 reinterpretation as the live face of the current crossing step is testable as measurement precision improves.
The LISA prediction (Results 33 and 35) is the most decisive near-term test. A stochastic gravitational wave background at 93 mHz with amplitude Ω_GW h² = 8.37×10⁻⁷ and no electromagnetic counterpart is a specific, falsifiable, zero-free-parameter prediction. Standard cosmology has no mechanism to produce it. If LISA detects this signal, it is confirmation. If it does not, and the sensitivity is sufficient, the framework is falsified at that result.
Thirty-eight results. Zero free parameters. The framework either works or it does not. The data is the arbiter, and the data is here.