V2.617: Smoking Gun Joint Evidence

Motivation

Individual predictions can be dismissed as coincidence. The framework makes 6 unique predictions from zero free parameters — the question is: what is the probability that ΛCDM (or any other approach) accidentally reproduces all of them?

This experiment quantifies the joint false-positive rate, Bayesian evidence, and information content.

Key Results

Joint False-Positive Rate

Prediction	p_null (under ΛCDM)	Status
Ω_Λ = 0.6877	0.015	Measured: 0.6847 ± 0.0073 (0.4σ)
Majorana ν	0.50	Untested (framework: 2.9σ preference)
c_log = -149/12	0.10	Untested (8.3× LQG value)
No BSM vectors	0.30	Consistent (LHC Run 3)
H₀ = 67.67	0.10	Measured: 67.36 ± 0.54 (0.6σ)
ΔΛ(EW) = 0	10⁻⁵⁵	Not directly testable

Joint P(null) excluding EW = 2.25 × 10⁻⁵ (4.2σ)

Including the EW phase transition prediction: P = 2.25 × 10⁻⁶⁰. But this is not directly measurable, so the conservative estimate excludes it.

Information Content

The framework predicts 20.6 bits (6.2 decimal digits) from zero free parameters:

Observable	Bits
Ω_Λ	6.1
H₀	5.6
w₀	5.1
N_ν	2.8
Majorana ν	1.0
Total	20.6

ΛCDM predicts 0 of these bits — all are free parameters or unconstrained.

Bayesian Evidence (Ω_Λ alone)

Experiment	σ(Ω_Λ)	Bayes Factor	Category
Planck 2018	0.0073	47:1	Very strong
DESI Y5 + Planck	0.004	67:1	Very strong
CMB-S4	0.005	60:1	Very strong
Euclid + CMB-S4	0.002	78:1	Very strong
Ultimate	0.001	80:1	Very strong

The Bayes factor saturates around 80:1 because the theoretical uncertainty (~0.3% from interaction corrections) limits how sharp the prediction can be.

Smoking Gun Combinations

The Triple Confirmation (2030–2035, P_coincidence = 0.75%):

• Ω_Λ = 0.688 ± 0.002
• w = -1.00 ± 0.01
• 0νββ detected

The Quadruple Lock (2030–2035, P_coincidence = 0.11%):

• Ω_Λ = 0.688 ± 0.002
• N_eff = 3.04 ± 0.06
• 0νββ detected
• No new vectors at LHC Run 4

The BSM Surprise (2035+, P_coincidence = 0.1%):

• New scalar at LHC/FCC
• Ω_Λ shifts by exactly Δδ = -1/90 (Euclid + CMB-S4)

Framework vs Alternatives

Observable	This Framework	ΛCDM	LQG	String Theory
Ω_Λ	0.6877 (calculated)	free parameter	no prediction	landscape
w₀	-1 (theorem)	-1 (construction)	no prediction	model-dependent
c_log	-12.42 (exact)	N/A	-1.50	-4 to -8
ν nature	Majorana (2.9σ)	no preference	no prediction	model-dependent
N_ν	3 (required)	free (fit to 3)	no prediction	no prediction
Λ through EW	constant (topological)	55-digit tuning	no prediction	vacuum transition
H₀	67.67 (derived)	free parameter	no prediction	no prediction
BSM	max 3 scalars, 0 vectors	unconstrained	unconstrained	anything

No other approach makes quantitative predictions for all 8 observables simultaneously.

Honest Assessment

What’s genuinely strong: The joint false-positive rate (4.2σ excluding EW) is robust to reasonable prior choices. Even doubling all individual p_null values gives 3.3σ. The information content (20.6 bits) is a prior-independent measure — the framework genuinely specifies the universe more precisely than ΛCDM.

What’s genuinely weak:

• The p_null values are prior-dependent (especially for Ω_Λ and H₀)
• w = -1 is shared with ΛCDM — not discriminating
• BH log correction and EW predictions are not yet testable
• The Bayes factor saturates at ~80:1 due to theoretical uncertainty
• Several predictions (c_log, ΔΛ(EW)) use “observed = predicted” since no measurement exists

The critical test: If Ω_Λ is confirmed at 0.688 ± 0.002 AND 0νββ is detected AND no new vectors appear, the joint coincidence probability drops below 0.1%. That would be very hard to dismiss.

What would kill this: Ω_Λ = 0.660 ± 0.002 (14σ), or Dirac neutrinos confirmed with inverted ordering, or a light Z’ discovered at LHC.

Files

• src/smoking_gun.py: Core computation (predictions, joint P, Bayes factors, info content)
• tests/test_smoking_gun.py: 5 tests, all passing
• run_experiment.py: Full 7-part analysis
• results.json: Machine-readable output