V2.401 - Species-Dependence Precision Curve
V2.401: Species-Dependence Precision Curve
Motivation
The single most powerful unique prediction of the entanglement gravity framework: Lambda is a zero-parameter function of the Standard Model field content.
The formula R = |δ_total|/(6·α_s·N_eff) = Ω_Λ connects the cosmological constant directly to the trace anomaly and entanglement entropy of every quantum field. Adding or removing a particle shifts Lambda in a calculable way. No other approach to the cosmological constant makes this connection.
This experiment:
- Verifies species linearity on the Srednicki lattice
- Computes R for 20+ BSM scenarios with Planck and Euclid precision
- Shows N_ν = 3 (Majorana) is uniquely preferred
- Maps the joint prediction connecting Ω_Λ, γ_BH, n_grav, and N_ν
- Identifies when each scenario becomes testable
Results
Phase 1: Lattice Verification
Species linearity confirmed to machine precision on the Srednicki lattice (N=200, C=5):
| Test | Measured ratio | Expected | Agreement |
|---|---|---|---|
| n_comp = 2/1 | 2.0000 | 2 | EXACT |
| n_comp = 4/1 | 4.0000 | 4 | EXACT |
| n_comp = 8/1 | 8.0000 | 8 | EXACT |
| α_vector/α_scalar | 2.0009 | 2.000 | 0.04% |
Finite-C offset: α_s(C=5) = 0.02195 vs theory 0.02351 (6.6% — converges in double limit). The physics is in the ratios, which are exact.
Phase 2: Species-Dependence Curve
The definitive BSM exclusion table:
| Scenario | R | Λ/Λ_obs | σ(Planck) | σ(Euclid) | γ_BH | Status |
|---|---|---|---|---|---|---|
| SM + graviton | 0.6877 | 1.004 | +0.4 | +1.5 | -12.417 | Allowed |
| +1 scalar (axion) | 0.6830 | 0.998 | -0.2 | -0.8 | -12.428 | Allowed |
| +1 Weyl (sterile ν) | 0.6805 | 0.994 | -0.6 | -2.1 | -12.478 | Allowed |
| +4 scalars (2HDM) | 0.6693 | 0.978 | -2.1 | -7.7 | -12.461 | Euclid |
| +1 vector (Z’) | 0.7147 | 1.044 | +4.1 | +15.0 | -13.106 | Euclid |
| +3 sterile ν | 0.6667 | 0.974 | -2.5 | -9.0 | -12.600 | Euclid |
| Dirac neutrinos | 0.6667 | 0.974 | -2.5 | -9.0 | -12.600 | Euclid |
| 4th generation | 0.5983 | 0.874 | -11.8 | -43.2 | -13.333 | EXCLUDED |
| MSSM | 0.4498 | 0.657 | -32.2 | -117.5 | -14.083 | EXCLUDED |
| SU(5) GUT vectors | 0.9647 | 1.409 | +38.4 | +140.0 | -20.683 | EXCLUDED |
Phase 3: Neutrino Constraint
| N_ν | R | σ(Planck) | σ(Euclid) | Comment |
|---|---|---|---|---|
| 0 | 0.7109 | +3.6 | +13.1 | Excluded |
| 1 | 0.7029 | +2.5 | +9.1 | Excluded (Euclid) |
| 2 | 0.6952 | +1.4 | +5.3 | Disfavored |
| 3 | 0.6877 | +0.4 | +1.5 | SM ◄ preferred |
| 4 | 0.6805 | -0.6 | -2.1 | Allowed but shifted |
| 5 | 0.6735 | -1.5 | -5.6 | Disfavored |
| 6 | 0.6667 | -2.5 | -9.0 | Excluded (Euclid) |
Majorana vs Dirac: Majorana at +0.4σ, Dirac at -2.5σ → Majorana preferred by 2.9σ. Euclid will distinguish at 10.5σ.
Phase 4: Joint Prediction Map
The SM + graviton field content simultaneously predicts five observables from one input:
| Prediction | Value | Comparison | Distinguishes from |
|---|---|---|---|
| Ω_Λ | 0.6877 (+0.4σ) | obs: 0.6847 ± 0.0073 | ΛCDM (free parameter) |
| γ_BH | -149/12 = -12.42 | LQG: -3/2 = -1.50 | LQG (8.3× different) |
| n_grav | 10 (SVT) | TT-only: n=2 excluded at 6.7σ | String theory (TT) |
| N_ν | 3 (Majorana) | N_ν=4: -0.6σ shift | Models with sterile ν |
| w | -1.000 exactly | DESI tests at σ=0.02 | Quintessence/Swampland |
No other framework in physics connects all five.
Phase 5: Sensitivity Gradient
| Particle type | ΔR | Direction | Euclid σ |
|---|---|---|---|
| Real scalar | -0.0047 | ↓ (less DE) | -0.8 |
| Weyl fermion | -0.0072 | ↓ | -2.1 |
| Dirac fermion | -0.0143 | ↓ | -5.6 |
| Gauge vector | +0.0270 | ↑ (more DE) | +15.0 |
| Scalar doublet | -0.0185 | ↓ | -7.7 |
Key asymmetry: Vectors INCREASE R (large |δ_vector| = 31/45 per field), while scalars and fermions DECREASE R. The SM sits at a special point where the gauge group SU(3)×SU(2)×U(1) gives precisely the right mix.
Phase 6: When Can We Test?
| Scenario | σ(Ω_Λ) needed for 3σ | Experiment | Timeline |
|---|---|---|---|
| +1 vector (Z’) | 0.009 | Planck (already!) | Now |
| +4 scalars (2HDM) | 0.006 | Euclid | 2028 |
| +3 sterile ν | 0.007 | Euclid | 2028 |
| Dirac neutrinos | 0.007 | Euclid | 2028 |
| +1 Weyl | 0.002 | Euclid | 2028 |
| +1 scalar | 0.002 | Stage-V CMB | ~2035 |
Interpretation
What This Means for the Framework
-
Falsifiability is real. The framework excludes the MSSM at 32σ, a 4th generation at 12σ, and any new gauge boson at 4σ — all from a single, parameter-free formula.
-
The SM is special. The precise field content of the Standard Model — SU(3)×SU(2)×U(1) with 3 generations of fermions and the Higgs doublet — produces R = 0.6877, within 0.4σ of the observed Ω_Λ. Random gauge groups would generically give R far from 0.68. This is either a coincidence or evidence that the framework captures real physics.
-
Joint predictions are the killer feature. ΛCDM treats Ω_Λ as a free parameter and says nothing about black hole entropy, graviton counting, or neutrino masses. This framework predicts all from one input: the SM trace anomaly.
-
Near-future testability. Euclid (2028) will measure Ω_Λ to ±0.002, sufficient to test Dirac-vs-Majorana neutrinos, 2HDM, sterile neutrinos, and dark photons. CMB-S4 (2030) will measure N_eff to ±0.06, cross-checking the neutrino constraint.
Honest Assessment
- The lattice confirms linearity (ratios exact) but finite-C values are 6-25% off from the double-limit. This is a known convergence issue, not a physics problem.
- The “MSSM excluded” result assumes all SUSY partners are light enough to contribute. Heavy SUSY (above the entanglement cutoff) would decouple and be indistinguishable from SM.
- The +0.4σ residual for SM+grav is closed by interaction corrections (V2.400, c₁=1.61).
- The framework predicts w = -1 exactly. DESI DR1 hints at w ≈ -0.75 (4.5σ tension). If DESI DR3 confirms w ≠ -1 at 5σ, the framework is falsified.
Files
src/srednicki_core.py— Srednicki lattice computationsrc/species_predictions.py— BSM scenario predictions (analytical)tests/test_species.py— Verification testsrun_experiment.py— Full 6-phase experiment