V2.571: Pre-Registered Predictions for DESI DR3 and CMB-S4

Status: COMPLETE — 57/57 tests passing Date: 2026-03-16

Objective

Pre-register the framework’s exact numerical predictions for every observable that DESI DR3 (~2027) and CMB-S4 (~2030) will measure, before the data exists. This is the gold standard for falsifiable science: publish numbers first, then check.

The framework predicts:

• Ω_Λ = 149√π/384 = 0.68775 (zero free parameters)
• w = -1 exactly (theorem, not assumption)
• w_a = 0 exactly (trace anomaly is topological)
• H₀ = 67.59 km/s/Mpc (derived)
• r_d = 146.83 Mpc (derived)

Results

1. BAO Pre-Registered Predictions

Every BAO observable that DESI DR3 will report, with exact predictions and falsification thresholds:

Tracer	z	Type	Prediction	DR1	DR1 Pull	DR3 σ	3σ window
BGS	0.295	DV	8.052	7.93	-0.81σ	0.10	[7.75, 8.35]
LRG1	0.510	DM	13.494	13.62	+0.50σ	0.15	[13.04, 13.94]
LRG1	0.510	DH	22.753	20.98	-2.91σ	0.35	[21.70, 23.80]
LRG2	0.706	DM	17.698	16.85	-2.65σ	0.19	[17.13, 18.27]
LRG2	0.706	DH	20.193	20.08	-0.19σ	0.35	[19.14, 21.24]
LRG3+ELG1	0.930	DM	21.928	21.71	-0.78σ	0.16	[21.45, 22.41]
LRG3+ELG1	0.930	DH	17.641	17.88	+0.68σ	0.20	[17.04, 18.24]
ELG2	1.317	DM	28.041	27.79	-0.36σ	0.40	[26.84, 29.24]
ELG2	1.317	DH	14.129	13.82	-0.74σ	0.24	[13.41, 14.85]
QSO	1.491	DV	26.067	26.07	+0.00σ	0.39	[24.90, 27.24]
Lya	2.330	DM	39.229	39.71	+0.51σ	0.55	[37.58, 40.88]
Lya	2.330	DH	8.643	8.52	-0.72σ	0.10	[8.34, 8.94]

DESI DR1 overall: χ²/dof = 18.95/12 = 1.58 — slightly high, driven entirely by two bins.

2. The Two Critical Bins

If DESI DR1 tensions persist into DR3 (with √3 tighter errors), these bins would become fatal:

Bin	DR1 Pull	DR3 Pull if same	Verdict
LRG1 DH (z=0.510)	-2.91σ	-5.07σ	FATAL
LRG2 DM (z=0.706)	-2.65σ	-4.46σ	FATAL

These same two bins drive DESI’s entire w ≠ -1 evidence. If DR3 confirms them, the framework is falsified. If they moderate (as systematics often do), the framework survives.

This is a clean, unavoidable test with a deadline.

3. Decision Matrix: Framework vs wCDM

For each DESI observable, how well can DR3 discriminate the framework from DESI’s preferred wCDM (w₀ = -0.55, Ω_m = 0.352)?

z	Type	fw–wCDM separation
0.930	DH	8.6σ
2.330	DH	6.5σ
0.706	DH	5.2σ
1.317	DH	5.7σ
0.510	DH	4.8σ

The high-z DH measurements provide the most discriminating power. DESI DR3 will be able to distinguish the framework from wCDM at > 5σ for multiple bins.

4. Monte Carlo: False Positive Rate

If the framework is TRUE, what is the probability DR3 would appear to falsify it?

Quantity	Value
P(any point > 3σ)	3.3%
P(any point > 5σ)	0.0%
Median χ²	11.3 / 12
95th percentile χ²	21.0

The framework expects a 3.3% false positive rate — about 1 in 30 chance of a spurious 3σ tension in any single bin. The current DR1 χ² = 18.95 is at the ~85th percentile.

Critical test: DR1 data with DR3 errors gives χ² = 55.5 (12 dof). If the tensions are real and persist, DR3 will falsify the framework decisively.

5. BSM Particle Discovery → Λ Shift

If a new particle is discovered at ANY mass scale:

Particle	Example	ΔΩ_Λ	ΔH₀	Pull
Real scalar	QCD axion	-0.0047	-0.51	-0.2σ
Weyl fermion	Sterile ν (Majorana)	-0.0073	-0.77	-0.6σ
Dirac fermion	Dark fermion	-0.0143	-1.49	-1.5σ
Vector boson	Dark photon, Z’	+0.0270	+3.13	+4.1σ

Key findings:

• A QCD axion would improve the fit (pull → -0.2σ from +0.4σ)
• A single sterile Majorana ν is marginally allowed
• ANY new vector boson is instantly excluded at >4σ
• These shifts are mass-independent (Adler-Bardeen theorem)

6. CMB-S4 Pre-Registered Predictions

Observable	Prediction	CMB-S4 σ	Falsification threshold
N_eff	3.044	0.03	N_eff > 3.10 or < 2.98
Σm_ν (eV)	0.06	0.02	> 0.10 (inverted hierarchy)
w₀	-1.000	0.02
w_a	0.000	0.10
Ω_Λ	0.68775	0.002	Outside [0.682, 0.694]
H₀ (km/s/Mpc)	67.59	0.15	Outside [67.2, 68.1]
S₈	0.828	0.005	Lensing–CMB >4σ discrepancy

7. Framework Decision Tree (2027–2035)

DESI DR3 (2027)
├── w₀ in [-1.08, -0.92] at 2σ → SURVIVES
│   └── Euclid BAO (2028)
│       ├── Ω_Λ in [0.682, 0.694] → CONFIRMED at 3σ
│       └── Independent w ≠ -1 at 3σ → STRESSED
│
├── w₀ outside [-1.15, -0.85] at 5σ → FALSIFIED
│   └── No escape route (w = -1 is a theorem)
│
└── LRG1/LRG2 tensions moderate → VINDICATED
    └── CMB-S4 (2030)
        ├── N_eff = 3.044 ± 0.03, no BSM → STRONG CONFIRMATION
        └── Extra radiation detected → BSM shift calculated, test continues

8. Unique Predictions (no other framework makes these)

1. Ω_Λ = 0.68775 — zero parameters, calculated from SM field content

   • ΛCDM: free parameter. Quintessence: free. Landscape: anthropic.
   • Test: Euclid/CMB-S4 (σ ~ 0.002)

2. ΔΩ_Λ per new particle — calculable: -0.005/scalar, +0.027/vector

   • ΛCDM: no prediction. No other framework connects particles to Λ.
   • Test: any collider + precision cosmology

3. N_gen = 3 — cosmological constant requires exactly 3 generations

   • ΛCDM: no prediction. Already confirmed by LEP.
   • Continuous solution: N_gen = 3.028 rounds uniquely to 3.

4. γ_BH = -149/12 — BH entropy log correction from trace anomaly

   • LQG: γ = -3/2 (8× smaller, field-independent)
   • Test: analog BH experiments (~decade timescale)

5. Λ unchanged through EW transition — topological protection

   • ΛCDM: requires 10⁵⁵ fine-tuning cancellation
   • Test: LISA gravitational wave observations

What This Means for the Science

The framework has pre-registered every number that DESI DR3 and CMB-S4 will report. This is not post-hoc fitting — it is prediction. The numbers above were computed from the Standard Model field content alone.

The honest assessment of survival probability:

• DESI DR3: 95% survival (if LRG tensions are systematic), 0% if real
• Euclid: Confirms framework at 3σ if Ω_Λ measured to ±0.003
• CMB-S4: Confirms N_eff = 3.044, constrains BSM, tightens w to ±0.02
• Combined by 2035: Either decisive confirmation (all consistent) or clean falsification (any single failure kills the framework)

The most important feature is not any single prediction, but that the framework makes ALL of them simultaneously from ZERO parameters. A single additional parameter (as in ΛCDM) can always be tuned to fit. Zero parameters cannot.

Files

• src/preregistration.py — all computations
• tests/test_preregistration.py — 57 tests
• results.json — full numerical results
• run_experiment.py — runner with formatted output