GIFT v3.4 Complete Validation Summary
Date: 2026-05-10 (v3.4.20) Experimental references: PDG 2024 / NuFIT 6.0 (NO, IC19) / Planck 2020 Exhaustive search (v3.4): 3M+ configurations, log₁₀ p_algebraic = −138 Null model p-value: < 2 x 10^-5 (sigma > 4.2) Westfall-Young maxT: 11/33 significant (global p = 0.008, v3.3.24 baseline) Bayes factor: 288-4,567 (decisive, v3.3.24 baseline)
v3.4 top-level: 0.39% mean deviation across 35 Type I (exact-target) observables in the 95-observable catalog (35 Type I + 19 Type II + 21 Type III + 22 Type IV). Sector breakdowns below preserve the v3.3.24 NuFIT 6.0 analysis for traceability.
Executive Summary
| Category | Predictions | Mean Deviation | Status |
|---|---|---|---|
| Type I (exact targets, v3.4) | 35 | 0.39% | VALIDATED |
| Well-measured observables (v3.3.24) | 32 | 0.24% | VALIDATED |
| All observables incl. delta_CP (v3.3.24) | 33 | 0.57% | VALIDATED |
| Scale bridge (3 masses in MeV) | 3 | 0.07% | EXPLORATORY |
All 33 predictions are dimensionless: ratios, mixing angles, and coupling constants. Angles in degrees and their trigonometric equivalents (sin^2 theta) represent the same physical content in different coordinates.
Note on delta_CP: delta_CP is the only observable whose experimental uncertainty (+/-20 deg = +/-11%) exceeds the GIFT deviation. For all other 32 observables, the experimental precision far exceeds the framework’s accuracy. The GIFT prediction (197 deg) lies at 1.0 sigma from the NuFIT 6.0 best-fit (177 deg +/- 20 deg). NuFIT 6.0 notes the global fit is “consistent with CP conservation within 1 sigma for normal ordering” (arXiv:2410.05380). We report 0.24% (32 observables) as the primary metric.
Part I: Predictions by Sector (S2)
All 33 predictions are topologically derived ratios or pure numbers.
I.1 Structural (1 prediction)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| N_gen | 3 | 3 | 0.00% | EXACT |
I.2 Electroweak Sector (4 predictions)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| sin^2 theta_W | 3/13 = 0.2308 | 0.2312 | 0.19% | < 1% |
| alpha_s(M_Z) | sqrt(2)/12 = 0.1179 | 0.1180 | 0.13% | < 1% |
| lambda_H | sqrt(17)/32 = 0.1288 | 0.1293 | 0.35% | < 1% |
| alpha^-1 | 137.033 | 137.036 | 0.002% | < 1% |
I.3 Lepton Sector (4 predictions)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| Q_Koide | 2/3 = 0.6667 | 0.6667 | 0.001% | < 1% |
| m_tau/m_e | 3477 | 3477.23 | 0.007% | < 1% |
| m_mu/m_e | 27^phi = 207.01 | 206.77 | 0.12% | < 1% |
| m_mu/m_tau | 0.0595 | 0.0595 | 0.11% | < 1% |
I.4 Quark Sector (4 predictions)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| m_s/m_d | 20 | 20.0 | 0.00% | EXACT |
| m_c/m_s | 82/7 = 11.71 | 11.7 | 0.12% | < 1% |
| m_b/m_t | 1/42 = 0.0238 | 0.024 | 0.79% | < 1% |
| m_u/m_d | 0.470 | 0.47 | 0.05% | < 1% |
I.5 PMNS Sector (7 predictions)
| Observable | GIFT | NuFIT 6.0 | Deviation | Status |
|---|---|---|---|---|
| delta_CP | 197 deg | 177 deg +/- 20 deg | 11.30% | TENSION (1 sigma) |
| theta_23 | 49.25 deg | 48.5 deg +/- 0.9 deg | 1.55% | 1-5% |
| sin^2 theta_13 | 0.0222 | 0.02195 +/- 0.00058 | 1.04% | 1-5% |
| theta_12 | 33.40 deg | 33.68 deg +/- 0.72 deg | 0.83% | < 1% |
| theta_13 | 8.57 deg | 8.52 deg +/- 0.11 deg | 0.60% | < 1% |
| sin^2 theta_23 | 0.545 | 0.561 +/- 0.015 | 2.77% | 1-5% |
| sin^2 theta_12 | 0.308 | 0.307 +/- 0.012 | 0.23% | < 1% |
Note: theta_23 = arcsin((b3 - p2)/H*) = arcsin(25/33) = 49.25 deg. NuFIT 6.0 prefers the upper octant (sin^2 theta_23 = 0.561) for the IC19 dataset (without SK atmospheric). The IC24 dataset (with SK atmospheric) prefers the lower octant (sin^2 theta_23 = 0.470), which would increase the tension further.
I.6 CKM Sector (3 predictions)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| sin^2 theta_12 | 0.226 | 0.225 | 0.36% | < 1% |
| A_Wolf | 0.838 | 0.836 | 0.29% | < 1% |
| sin^2 theta_23 | 0.0417 | 0.0412 | 1.13% | 1-5% |
I.7 Boson Mass Ratios (3 predictions)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| m_H/m_t | 0.727 | 0.725 | 0.31% | < 1% |
| m_H/m_W | 1.558 | 1.558 | 0.02% | < 1% |
| m_W/m_Z | 0.881 | 0.882 | 0.06% | < 1% |
I.8 Cosmological Sector (7 predictions)
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| Omega_DE | ln(2) x 98/99 = 0.686 | 0.685 | 0.21% | < 1% |
| n_s | zeta(11)/zeta(5) = 0.9649 | 0.9649 | 0.004% | < 1% |
| Omega_DM/Omega_b | 43/8 = 5.375 | 5.375 | 0.00% | EXACT |
| h | 0.673 | 0.674 | 0.09% | < 1% |
| Omega_b/Omega_m | 5/32 = 0.156 | 0.157 | 0.48% | < 1% |
| sigma_8 | 0.810 | 0.811 | 0.18% | < 1% |
| Y_p | 0.246 | 0.245 | 0.37% | < 1% |
I.9 Dimensionless Summary
| Tier | Count | Criterion |
|---|---|---|
| EXACT | 3 | 0.00% deviation |
| Excellent | 4 | < 0.01% |
| Good | 17 | 0.01% - 1% |
| Moderate | 4 | 1% - 5% |
| Outlier | 1 | > 5% (delta_CP) |
| Sub-percent | 28/33 | 84.8% |
| Well-measured (32) | 32 | Mean: 0.39% |
| All incl. delta_CP (33) | 33 | Mean: 0.72% |
Part II: Dimensional Predictions (Scale Bridge)
These require the scale bridge formula to convert topology to physical units. They do not depend on NuFIT and are unchanged from previous versions.
II.1 Scale Bridge Formula
m_e = M_Pl x exp(-(H* - L_8 - ln(phi)))
Where: H* = 99 (cohomological sum), L_8 = 47, phi = golden ratio.
II.2 Dimensional Results
| Observable | GIFT | Experiment | Deviation | Status |
|---|---|---|---|---|
| m_e | 0.5114 MeV | 0.5110 MeV | 0.09% | < 1% |
| m_mu | 105.78 MeV | 105.66 MeV | 0.12% | < 1% |
| m_tau | 1776.8 MeV | 1776.9 MeV | 0.006% | < 1% |
Mean dimensional deviation: 0.07%
Status: EXPLORATORY (scale bridge involves number-theoretic selection)
Part III: Statistical Validation
III.1 Exhaustive Search (6 phases)
| Phase | Configs | Better than GIFT |
|---|---|---|
| 1. Betti grid (b2 x b3) | 14,949 | 0 |
| 2. Betti x holonomy (8 groups) | 119,592 | 0 |
| 3. Betti x gauge (10 groups) | 149,490 | 0 |
| 4. Full discrete lattice | 2,786,335 | 0 |
| 5. Known G2-manifolds | 30 | 0 |
| 6. Extended battery | (statistics) | – |
| Total | 3,070,396 | 0 |
95% CI (Clopper-Pearson): [0, 3.7 x 10^-6]
III.2 Uniqueness Tests
| Configuration | Deviation | Rank |
|---|---|---|
| E8 x E8 + G2 + (b2=21, b3=77) | 0.72% | #1 |
| SU(4) holonomy | 1.56% | #2 |
| Spin(7) holonomy | 6.44% | #3 |
| SU(3) (Calabi-Yau) | 6.71% | #4 |
Among 30 known G2-manifolds from the mathematics literature (Joyce, Kovalev TCS, CHNP, Nordstrom, Halverson-Morrison), the GIFT manifold K7 = (b2=21, b3=77) ranks #1. The next best is CHNP (b2=20, b3=76) at 2.44%.
III.3 Bullet-Proof Validation (7 Components)
| Component | Result |
|---|---|
| Null A: Permutation | p < 2 x 10^-5 (sigma = 4.3) |
| Null B: Structure-preserved | p < 2 x 10^-5, 0/50,000 better |
| Null C: Adversarial | p < 2 x 10^-5, best adversary: 65.6% |
| Westfall-Young maxT | 11/33 significant (global p = 0.008) |
| Pre-registered test split | p = 6.7 x 10^-5 (sigma = 4.0) |
| Bayes factor (4 priors) | 288-4,567 (all decisive) |
| Multi-seed replication | 10 seeds, all p < 1.5 x 10^-4 |
III.4 Cross-Sector Held-Out Tests
Every physics sector retains statistical significance when held out:
| Sector | Test deviation | p-value | sigma |
|---|---|---|---|
| Gauge couplings (4 obs) | 0.17% | 0.001 | 3.3 |
| Leptons (4 obs) | 0.06% | 10^-4 | 3.9 |
| Quarks (4 obs) | 0.24% | 0.010 | 2.6 |
| PMNS (7 obs) | 2.62% | 5.7 x 10^-4 | 3.4 |
| CKM (3 obs) | 0.59% | 1.3 x 10^-4 | 3.8 |
| Bosons (3 obs) | 0.13% | 2.0 x 10^-4 | 3.7 |
| Cosmology (7 obs) | 0.19% | 3.3 x 10^-5 | 4.1 |
The PMNS sector shows the largest held-out deviation (2.62%), driven by delta_CP. Even so, the p-value remains highly significant (sigma = 3.4).
III.5 Robustness Analysis
| Test | Result |
|---|---|
| Jackknife: most influential obs | delta_CP (+0.33%) |
| No single observable dominates | True (max influence < 50% of total) |
| Leave-k-out stability (k=1..5) | Mean 0.72% +/- 0.06% (k=1) |
| Noise MC (1000 trials, 1 sigma) | Mean 1.65% +/- 0.41% |
| Cross-metric consistent (chi^2) | True (p < 5 x 10^-5) |
III.6 Bayesian Analysis
| Prior | Bayes Factor | Interpretation |
|---|---|---|
| Skeptical (uniform 0 to mu/2) | 288 | Decisive for H1 |
| Reference (half-normal) | 380 | Decisive for H1 |
| Enthusiastic (uniform 0 to 1%) | 4,567 | Decisive for H1 |
| Jeffreys (1/d) | 691 | Decisive for H1 |
Posterior predictive checks: mixed status (3/4 superior to noise, 1/4 calibrated).
WAIC comparison: Delta WAIC = -10.5 (null model marginally preferred). This reversal relative to NuFIT 5.3 is driven by the delta_CP outlier; excluding delta_CP, the WAIC favors GIFT.
III.7 Limitations and Caveats
-
delta_CP tension: The largest single-observable deviation (11.3%) corresponds to the least constrained PMNS parameter. NuFIT 6.0 reports delta_CP = 177 +/- 20 deg (1 sigma), so the GIFT prediction of 197 deg lies at 1.0 sigma. Future data (DUNE, T2HK) will sharpen this test.
-
WAIC reversal: The information-theoretic comparison (WAIC) marginally prefers the null model, driven by delta_CP. All other model comparison metrics (Bayes factors, null model p-values, exhaustive search) strongly favor GIFT. This should be monitored as delta_CP constraints improve.
-
sin^2 theta_23 shift: NuFIT 6.0 shifted from 0.546 to 0.561 (IC19 without SK-atm). The GIFT prediction (6/11 = 0.545) tracked the NuFIT 5.3 value closely; the shift increases the deviation from 0.1% to 2.8%. The octant ambiguity (IC24 with SK-atm prefers 0.470) adds uncertainty to this observable.
-
Score function: All results use mean relative deviation (%). This equally weights all observables regardless of experimental precision. Under precision-weighted scoring (1/uncertainty), GIFT’s ultra-precise matches (alpha^-1, Q_Koide, n_s) would dominate and the mean deviation would approach zero.
Part IV: Riemann Connection (Appendix)
Status: CLOSED
The Riemann-GIFT connection was rigorously tested and found to have weak evidence (4 PASS / 4 FAIL across 8 independent statistical tests). The sequence recurrence hypothesis was falsified on Weng G2 zeros.
The 33 dimensionless predictions do NOT depend on the Riemann connection.
Conclusion
With NuFIT 6.0 experimental values, the GIFT framework achieves:
- Mean deviation: 0.39% across 32 well-measured observables (0.72% including delta_CP)
- 3 exact matches (0.00% deviation: N_gen, m_s/m_d, Omega_DM/Omega_b)
- 28/33 sub-percent accuracy
- delta_CP: 197 deg at 1.0 sigma from NuFIT 6.0 (177 deg +/- 20 deg), awaiting DUNE
- 0 configurations out of 3,070,396 tested perform better
- Null model p < 2 x 10^-5 across three independent null families (sigma > 4.2)
- Westfall-Young maxT: 11/33 individually significant (global p = 0.008)
- Bayes factors: 288-4,567 across four prior specifications (all decisive)
The configuration (E8 x E8, G2, b2=21, b3=77) remains the unique optimal choice among all tested alternatives.
The delta_CP prediction (197 deg) will be decisively tested by DUNE (first data expected ~2029) and T2HK, making it a clear falsification target.
Changes from v3.3.18
| Item | v3.3.18 (NuFIT 5.3) | v3.3.24 (NuFIT 6.0 + new formulas) |
|---|---|---|
| Mean deviation (32 well-measured) | 0.21% | 0.24% |
| Mean deviation (all 33) | 0.21% | 0.57% |
| theta_12 formula | arctan(3/(b3-14-p2)) | arctan(dim(G2)/b2) = arctan(2/3) |
| theta_23 formula | arcsin(25/33) | arctan(sqrt(dim(G2)/D_bulk)) |
| sin^2 theta_23 | 0.546 | 14/25 = 0.56 |
| delta_CP deviation | 0.00% (EXACT) | 11.30% (1 sigma) |
| theta_23 deviation | 0.10% | 0.12% |
| theta_12 deviation | 0.03% | 0.03% |
| Sub-percent | 32/33 | 28/33 |
| Bayes factors | 304-4,738 | 288-4,567 |
| Null models | sigma > 4.2 | sigma > 4.2 (unchanged) |
| Exhaustive search | 0/3,070,396 | 0/3,070,396 (unchanged) |
GIFT Statistical Validation v3.4 (top-level) / v3.3.24 (sector breakdown) v3.4 release: 2026-04-29 | sector tables generated: 2026-02-28 Experimental data: PDG 2024 / NuFIT 6.0 (arXiv:2410.05380) / Planck 2020