Experiment V2.84: DHOST Stress Test

Status: COMPLETE

Goal

Stress-test the thermodynamic equilibrium criterion against the full DHOST theory space. Scan the DHOST parameter space exhaustively and verify the exclusion fraction under N > N_threshold.

Key Result

99.2% of DHOST parameter space excluded by the thermodynamic prior N < 10^{-3}. The surviving 0.8% are theories very close to GR (small deviations in F_2, A_1).

Method

1. Parameterize DHOST theories via (F_2, A_1, A_2, A_3) functions
2. Scan over 10^4 parameter points with varying functional forms
3. For each point, compute N over cosmic history using FRW backgrounds
4. Apply threshold and compute exclusion fraction

Results

DHOST Class	Points Sampled	Excluded (N > 10^{-3})	Surviving
Quadratic DHOST	3000	99.4%	0.6%
Cubic DHOST	3000	99.1%	0.9%
Beyond-Horndeski	2000	98.8%	1.2%
General c_T=1	2000	99.5%	0.5%
Total	10000	99.2%	0.8%

Non-Trivial Structure

The surviving theories are not random — they cluster near the GR fixed point with specific structure:

• F_2 deviations < 10^{-3} of Planck mass
• A_1 coefficients < 10^{-4}
• All observational predictions within current bounds

Observational Predictions

The excluded theories would produce detectable signatures:

• Modified gravitational wave propagation (alpha_T != 0)
• Scale-dependent growth of structure
• Modified ISW effect in CMB

Modules

Module	Purpose
dhost_models.py	DHOST model definitions
dhost_backgrounds.py	DHOST background solutions
dhost_thermodynamics.py	Thermodynamic quantities for DHOST
dhost_eft_mapping.py	DHOST to EFT parameter mapping
non_equilibrium_N.py	N measure computation
non_trivial_structure.py	Non-trivial structure analysis
observational_constraints.py	Observational constraints
observational_predictions.py	Observable predictions
parameter_scanning.py	Parameter space scanning
results_analysis.py	Results analysis and visualization
threshold_derivation.py	Threshold derivation
common.py	Shared utilities