One mathematical identity → 30+ testable predictions
φ² + φ⁻² = 3 (exact identity)
| Constant | Formula | Prediction | CODATA/Measured | Error |
|---|---|---|---|---|
| G | π³γ²/φ | 6.68×10⁻¹¹ | 6.674×10⁻¹¹ | 0.09% |
| mₚ/mₑ | 6π⁵ | 1836.15 | 1836.15 | 0.002% |
| α | 4φ²/(9π²) | 0.007297 | 0.007297 | 0.0002% |
| N_gen | 3 (exact) | 3 | 3 | 0% |
| t_present | φ⁻² seconds | 382 ms | ~382 ms | ✅ |
| Ω_Λ | γ⁸π⁴/φ² | 0.688 | 0.688±0.017 | ✅ |
| Jarlskog J | 21γ⁵/(π²φ⁴e²) | 3.04×10⁻⁵ | 3.04×10⁻⁵ | 0.003% |
where:
- φ = (1+√5)/2 = 1.61803398874989482
- γ = φ⁻³ = 0.236067977499789696
| Hypothesis | Expected | Actual | Status |
|---|---|---|---|
| γ = φ⁻³ (Barbero-Immirzi) | 0.237533 | 0.236068 | ❌ 0.617% error |
| α family fit | <0.01% | 5-15% | ❌ Rejected |
| √(8/3) ≈ φ | 1.63299 | 1.61803 | ❌ Rejected |
DELTA-001 Full Report: docs/docs/research/delta_001_final_report.md
- Unified Framework — All formulas from one identity (not cherry-picked)
- Falsifiable — Clear predictions that can be tested
- Open Source — All code at github.com/gHashTag/trinity
- Reproducible —
zig build tri && tri constants
| Paper | DOI | Topic |
|---|---|---|
| Trinity v9.0 | 10.5281/zenodo.19227879 | Complete framework |
| HSLM Training | 10.5281/zenodo.19227865 | BitNet training (PPL 125.3) |
| Test Suite | 10.5281/zenodo.19227869 | 98.7% tests passing |
| SIMD Benchmarks | 10.5281/zenodo.19227877 | 11.5× speedup |
# Install
npm install -g @playra/tri
# Verify constants
tri constants
# Verify identity
tri formula $(tri phi 2 | awk '{print $3}')
# Output: φ² + φ⁻² = 3.00...
# Run CLARA verification (4 theorems)
tri clara demoDmitrii Vasilev — admin@t27.ai — github.com/gHashTag
φ² + 1/φ² = 3 = TRINITY