V2.475: Theoretical Error Budget — How Precisely Does the Framework Predict Ω_Λ?

Status: COMPLETE — Theory-limited at 1.2%, dominated by graviton mode count

The Question

The framework claims “zero free parameters.” But every prediction has theoretical uncertainty. How precisely does the framework actually predict Ω_Λ — and what dominates the error?

Central Prediction

Ω_Λ = 0.6877 ± 0.0082 (theory) vs Planck 0.6847 ± 0.0073 (obs)

Tension: 0.28σ — fully consistent.

Error Budget

Source	ΔΩ_Λ	Fractional	Variance share	Reducible?
Graviton mode count	±0.0075	1.1%	82.3%	Yes
Non-perturbative α (QCD/EW)	±0.0034	0.5%	17.5%	Yes
α_s value (analytical vs lattice)	±0.0003	0.05%	0.2%	Yes
Higher-order δ (Adler-Bardeen)	±0.00007	0.01%	0.0%	No (exact)
Massive field decoupling	~10⁻⁶⁴	—	0.0%	No
Curvature corrections	~10⁻¹²¹	—	0.0%	No

Total: ±0.0082 (1.2%), prediction band [0.680, 0.696].

The hierarchy is extreme

The graviton mode count alone accounts for 82% of the total variance. Non-perturbative α corrections add 17.5%. Everything else is negligible — the trace anomaly δ is exact by the Adler-Bardeen theorem, mass corrections are suppressed by (H₀/m)² ~ 10⁻⁶⁴, and curvature corrections by (H₀/M_Pl)² ~ 10⁻¹²¹.

Discrete Graviton Mode Test

n_grav	Ω_Λ	Pull (σ)	Viable?
0 (no graviton)	0.665	-2.8	No
2 (physical TT)	0.734	+6.7	No
5 (traceless sym)	0.716	+4.2	No
8	0.699	+1.9	Yes
10 (symmetric h_μν)	0.688	+0.4	Yes
12	0.677	-1.0	Yes
15	0.662	-3.1	No

Only n_grav ∈ {8, 10, 12} are viable. The theory prediction n=10 (symmetric tensor components D(D+1)/2 for D=4) sits at the sweet spot.

Theory vs Experiment

Experiment	Year	σ_Ω (obs)	σ_Ω (theory)	Status
Planck 2018	2018	0.0073	0.0082	Theory > Experiment
DESI Y1	2024	0.0060	0.0082	Theory > Experiment
DESI Y3	2027	0.0040	0.0082	Theory > Experiment
DESI Y5	2029	0.0030	0.0082	Theory > Experiment
Euclid + CMB-S4	2032	0.0015	0.0082	Theory > Experiment

The framework is ALREADY theory-limited. Planck’s observational precision (0.0073) exceeds the framework’s theoretical precision (0.0082). Improving experiments won’t help until the graviton mode counting is resolved.

What This Means

The honest picture

1. “Zero free parameters” is correct but incomplete. The framework has no adjustable parameters, but its prediction carries ±1.2% theoretical uncertainty, dominated by the graviton mode count.

2. The framework is theory-limited, not data-limited. Even with current Planck data, the observational error bar (0.0073) is smaller than the theoretical one (0.0082). The bottleneck is resolving n_grav, not collecting more data.

3. Three numbers matter; three don’t. The error budget has a sharp hierarchy:

   • n_grav (82% of variance) — must be resolved
   • α non-perturbative corrections (17.5%) — needs QCD lattice computation
   • α_s value (0.2%) — essentially resolved
   • δ, mass, curvature (<0.01% combined) — exact or negligible

4. The prediction band [0.680, 0.696] comfortably contains Planck’s 0.6847. The framework is consistent with all current data.

What would sharpen the prediction

Resolving the graviton mode count from first principles would reduce the total uncertainty from 1.2% to 0.5% (dominated by non-perturbative α). A proper lattice QFT computation of α with interaction corrections would bring it to ~0.05%. At that point, the framework would predict Ω_Λ to ±0.0003 — testable by Euclid + CMB-S4.

What would falsify the framework

If future measurements pin Ω_Λ outside [0.680, 0.696] at 3σ, the framework is falsified regardless of n_grav. If the graviton mode count is independently determined (e.g., from black hole entropy or gravitational wave observations) and it’s not 8-12, the framework fails.

Files

• src/error_budget.py: All 6 error sources, combined budget, discrete n_grav test, precision comparison, falsification forecast
• tests/test_error_budget.py: 32 tests, all passing
• run_experiment.py: Full analysis with 8 phases
• results.json: Machine-readable results