V2.569 - BAO Survival Monte Carlo
V2.569: BAO Survival Monte Carlo
Status: COMPLETE — 43/43 tests passing
The Question
The framework predicts Ω_m = 1 - 149√π/384 = 0.31225 with zero free parameters. V2.562 showed 284:1 Bayesian odds, but a skeptic could argue this is mostly Occam factor. Here we ask the frequentist question: how special is this particular Ω_m?
We generate 100,000 random Ω_m values and test each one against ALL published BAO measurements from 2011-2024. The survival fraction — the percentage of random values that fit as well or better — is a direct measure of how “lucky” the prediction would need to be if it weren’t derived from physics.
Method
- Compile 16 independent BAO measurements from 4 surveys (6dFGS, SDSS MGS, BOSS DR12, DESI DR1) spanning z = 0.106 to z = 2.33
- Compute flat ΛCDM predictions for D_M/r_d, D_H/r_d, and D_V/r_d at each redshift
- Compute χ² for the framework’s Ω_m = 0.31225
- Draw 100,000 random Ω_m values from Uniform[0.2, 0.5] and compute χ² for each
- Report the survival fraction P(χ²_random ≤ χ²_framework)
BOSS z=0.51 and z=0.61 measurements are excluded from the combined dataset to avoid double-counting with DESI LRG1 (z=0.510) and LRG2 (z=0.706).
Results
Per-Point Pulls
| Survey | z | Type | Measured | Predicted | σ | Pull |
|---|---|---|---|---|---|---|
| 6dFGS | 0.106 | DV | 2.98 | 3.10 | 0.13 | -0.92σ |
| SDSS MGS | 0.15 | DV | 4.47 | 4.32 | 0.17 | +0.87σ |
| BOSS DR12 | 0.38 | DM | 10.23 | 10.43 | 0.17 | -1.20σ |
| BOSS DR12 | 0.38 | DH | 24.89 | 24.64 | 0.58 | +0.44σ |
| DESI DR1 | 0.295 | DV | 7.93 | 8.06 | 0.15 | -0.90σ |
| DESI DR1 | 0.510 | DM | 13.62 | 13.52 | 0.25 | +0.42σ |
| DESI DR1 | 0.510 | DH | 20.98 | 22.79 | 0.61 | -2.97σ |
| DESI DR1 | 0.706 | DM | 16.85 | 17.73 | 0.32 | -2.74σ |
| DESI DR1 | 0.706 | DH | 20.08 | 20.23 | 0.61 | -0.24σ |
| DESI DR1 | 0.930 | DM | 21.71 | 21.96 | 0.28 | -0.90σ |
| DESI DR1 | 0.930 | DH | 17.88 | 17.67 | 0.35 | +0.60σ |
| DESI DR1 | 1.317 | DM | 27.79 | 28.09 | 0.69 | -0.43σ |
| DESI DR1 | 1.317 | DH | 13.82 | 14.15 | 0.42 | -0.79σ |
| DESI DR1 | 1.491 | DV | 26.07 | 26.11 | 0.67 | -0.06σ |
| DESI DR1 | 2.330 | DM | 39.71 | 39.29 | 0.94 | +0.45σ |
| DESI DR1 | 2.330 | DH | 8.52 | 8.66 | 0.17 | -0.80σ |
Pull distribution: mean = -0.57, std = 1.10 (expected: 0, 1) 13/16 within 1σ, 14/16 within 2σ, max |pull| = 2.97σ
χ² Scan
| Quantity | Value |
|---|---|
| Best-fit Ω_m (BAO alone) | 0.3266 ± 0.0076 |
| χ²_min | 19.69 (1.23/dof) |
| Framework χ² | 23.40 (1.46/dof) |
| Δχ² | 3.72 |
| Framework pull from best-fit | -1.89σ |
Monte Carlo Survival
| Quantity | Value |
|---|---|
| N_mc | 100,000 |
| Prior | Ω_m ∈ [0.2, 0.5] |
| Survival fraction | 9.7% |
| Ω_m(1σ) range | [0.311, 0.344] |
| Width | 0.033 |
9.7% of random Ω_m values achieve χ² ≤ framework’s. The framework is in the top 10% but not the top 1%.
Historical Survival
| Year | N_data | χ²/dof | Ω_m(best) | Survived? |
|---|---|---|---|---|
| 2011 | 1 | 0.85 | 0.40 | Yes |
| 2015 | 2 | 0.81 | 0.26 | Yes |
| 2017 | 4 | 0.81 | 0.32 | Yes |
| 2024 | 16 | 1.46 | 0.33 | Yes |
The framework has survived every generation of BAO data. The χ²/dof increases with DESI (from 0.81 to 1.46) due to the two tension points.
Pre-DESI vs DESI
| Dataset | N | χ²/dof |
|---|---|---|
| Pre-DESI (6dFGS + SDSS + BOSS) | 4 | 0.81 |
| DESI only | 12 | 1.68 |
| Combined | 16 | 1.46 |
Pre-DESI data strongly support the framework. DESI data are acceptable (χ²/dof = 1.68) but show localized tension.
The Tension Story
Two DESI measurements drive almost all the tension:
- LRG1 DH at z=0.510: -2.97σ (framework predicts 22.8, DESI measures 21.0)
- LRG2 DM at z=0.706: -2.74σ (framework predicts 17.7, DESI measures 16.9)
These are the SAME two measurements that drive DESI’s evidence for w ≠ -1. This is not a coincidence — the framework predicts w = -1, so any data point that prefers w ≠ -1 will also be in tension with the framework.
Key context:
- BOSS DR12 measured DH/r_d = 22.33 ± 0.48 at z = 0.51, consistent with the framework. DESI’s value at the same redshift (20.98 ± 0.61) is 2.2σ from BOSS — this is a data-vs-data tension, not just framework-vs-data.
- Without these two points, the framework’s χ²/dof would be ~0.8 — excellent.
What This Means
The glass is 90% full
The framework’s zero-parameter prediction survives 16 BAO measurements spanning z = 0.1 to z = 2.3 with χ²/dof = 1.46. Only 9.7% of random Ω_m values do this well or better. That’s good — the framework is predicting a non-trivial number that falls in a narrow viable window.
But the glass isn’t 99% full
A 9.7% survival fraction is not overwhelming. The framework is 1.89σ from the BAO best-fit Ω_m = 0.327. If future data (DESI DR3, Euclid) confirm the best-fit near 0.327, the framework would face genuine 3σ+ tension.
The critical test is coming
The survival fraction translates to: the framework’s Ω_m = 0.312 is viable but not at the center of the BAO-preferred region. DESI DR3 (~2026) will either:
- Reduce the LRG1/LRG2 tension (if those measurements had systematics) → survival fraction increases dramatically
- Confirm Ω_m ≈ 0.327 with higher precision → framework falsified at >3σ
Combined with V2.562
The Monte Carlo gives a frequentist perspective: ~10% survival. V2.562’s Bayesian analysis gave 284:1 (0.35%) because it rewards parameter economy. The true significance lies between these — the framework fits well AND uses fewer parameters, but the fit itself has room for improvement.
Honest Assessment
Strengths:
- First comprehensive frequentist survival test against historical BAO record
- 16 measurements, 4 surveys, 14 years of data — the framework survives them all
- Pre-DESI data strongly consistent (χ²/dof = 0.81)
- Clearly identifies which measurements drive the tension
- 43 tests verify all computations
Weaknesses:
- 9.7% survival is modest — the framework is viable but not uniquely selected by BAO alone
- 1.89σ from BAO best-fit — acceptable today, potentially problematic if confirmed
- Two DESI measurements account for almost all tension; these same measurements are in tension with BOSS at the same redshift, suggesting possible systematics, but we cannot dismiss them without independent evidence
- Fixed H₀ = 67.36 and r_d = 147.09 — marginalizing over these would change results slightly
- No covariance between measurements at the same redshift (treated as independent)
What would strengthen the framework:
- DESI DR3 confirming the LRG1/LRG2 measurements near BOSS values
- Euclid providing independent BAO at similar redshifts
- Full covariance analysis with marginalization over H₀ and r_d
What would weaken/falsify the framework:
- DESI DR3 confirming Ω_m ≈ 0.327 with σ < 0.005 → framework excluded at >3σ
- Multiple additional BAO measurements consistently preferring Ω_m > 0.32
Files
src/bao_survival.py: Full analysis (BAO dataset, cosmological predictions, Monte Carlo, historical survival)tests/test_bao_survival.py: 43 testsresults.json: Complete numerical results