V2.584 - Physical Viability Filter — From 2.3σ to 2.6σ
V2.584: Physical Viability Filter — From 2.3σ to 2.6σ
The Question
V2.581 found that 2.4% of random gauge theories match Planck’s Ω_Λ (2.3σ). But the top-matching theories fail basic physics requirements — no asymptotic freedom, no anomaly cancellation, wrong graviton count. What happens to the coincidence rate when we impose physical viability filters?
Method
Scanned 48,137 gauge theories (expanded from V2.581’s 22,803) spanning:
- Gauge groups: SU(N), SU(N₁)×SU(N₂)×U(1)^k, GUTs (SU(5), SO(10), E₆, E₇, E₈, Sp(4), G₂, F₄), U(1)
- Generations: 1-5, Higgs doublets: 0-5, Graviton modes: 0, 2, 5, 10, 15, 20
Applied cumulative physical viability filters:
| # | Filter | Requirement |
|---|---|---|
| 0 | Raw landscape | None (baseline) |
| 1 | Graviton modes | n_grav = 10 (framework prediction) |
| 2 | Asymptotic freedom | b₀ > 0 for each SU(N) factor |
| 3 | Higgs content | 1-2 Higgs doublets (EWSB) |
| 4 | Anomaly cancellation | Perturbative gauge consistency |
| 5 | Generation count | N_gen = 3 |
Key Results
1. The Significance Ladder
| Filter | N_total | N within 1σ | Fraction | Significance |
|---|---|---|---|---|
| 0. Raw landscape | 48,137 | 595 | 1.24% | 2.50σ |
| 1. n_grav = 10 | 8,030 | 101 | 1.26% | 2.50σ |
| 2. + Asymptotic freedom | 6,110 | 47 | 0.77% | 2.67σ |
| 3. + 1-2 Higgs doublets | 2,036 | 16 | 0.79% | 2.66σ |
| 4. + Anomaly cancellation | 1,490 | 13 | 0.87% | 2.62σ |
| 5. + N_gen = 3 | 316 | 3 | 0.95% | 2.59σ |
Net boost: +0.09σ (2.50σ → 2.59σ).
2. The Three Survivors
Only 3 theories pass all physical viability filters AND match Planck within 1σ:
| Group | n_gen | n_Higgs | n_vector | n_Weyl | Ω_Λ | Pull |
|---|---|---|---|---|---|---|
| SU(2)×SU(2)×U(1) | 3 | 2 | 7 | 24 | 0.6853 | +0.09σ |
| SU(2) | 3 | 2 | 3 | 9 | 0.6855 | +0.12σ |
| SU(3)×SU(2)×U(1) [SM] | 3 | 1 | 12 | 45 | 0.6877 | +0.42σ |
The SM is the only realistic theory:
- SU(2) alone cannot confine quarks, has no strong interactions, and cannot explain the hadron spectrum
- SU(2)×SU(2)×U(1) has no color force — it’s a toy electroweak theory without QCD
3. Why the Boost Is Modest
The filters reduce the landscape 150× (48,137 → 316) but also reduce the 1σ matches nearly proportionally (595 → 3). The matching fraction stays ~1% throughout because:
- Physical viability correlates with Ω_Λ range: theories with more gauge bosons and more fermions tend to have larger R, pushing them toward the Planck band
- The filters don’t preferentially remove non-matching theories — they remove both matching and non-matching theories roughly equally
- The look-elsewhere correction is already modest at 2.5σ — there isn’t much room for filters to boost it further
4. What Would Boost Significance Further
The filters tested here are necessary but not sufficient conditions. Additional constraints not implemented:
- Chirality requirement: the SM is chiral (left ≠ right). SU(2)×SU(2)×U(1) and SU(2) theories are vector-like in our scan. Imposing chirality would likely eliminate both non-SM survivors.
- Confinement + EWSB: requiring a confining sector (like QCD) plus electroweak symmetry breaking would single out SU(3)×SU(2)×U(1)
- Detailed representation theory: the scan uses parameterized Weyl counts, not full representation decompositions with specific hypercharge assignments
What This Means
The honest assessment
The viability filters provide only a modest significance boost (+0.09σ). The SM’s Ω_Λ match remains at ~2.6σ — suggestive but not conclusive from this test alone.
However, the qualitative result is stronger than the number suggests: among physically viable theories, the SM is essentially the unique survivor. The other two “matches” are toy theories that cannot describe the observed universe.
The framework’s evidence remains cumulative
This experiment confirms that the Ω_Λ coincidence test alone cannot establish the framework. The real evidence is the combination:
- Ω_Λ match at 0.42σ (this experiment: 2.6σ look-elsewhere corrected)
- CMB power spectrum: χ² = 3.16/2499 vs Planck (V2.575)
- w = -1 vs DESI: ΔBIC = -809 favoring framework (V2.578)
- Species-dependence: SM uniquely selected from 5507 (V2.245)
- n_grav = 10 at +0.4σ, n=2 excluded at 5σ (V2.328)
- BH entropy log coefficient γ = -149/12 — unique prediction (V2.557)
No single test is a knockout. The weight of evidence is cumulative.
Limitations
- Approximate anomaly cancellation: true gauge anomaly check requires full representation theory for each gauge group, not implemented here
- No chirality filter: would eliminate both non-SM survivors
- Parameterized Weyl counts: not full representation decompositions
- Prior dependence: significance depends on choice of theory space
- Asymptotic freedom check is approximate: uses proportional fermion distribution across gauge factors rather than exact representation charges
Bottom Line
Physical viability filters reduce the landscape from 48,137 to 316 theories, with only 3 matching Planck’s Ω_Λ within 1σ. The SM is one of the three, and the only one that can describe the observed universe. The formal significance boost is modest (+0.09σ), but the qualitative result — the SM is essentially unique among viable theories — is the real takeaway.