The Zimmerman Framework: Deriving Fundamental Constants from Z = 2√(8π/3)

Carl Zimmerman

doi:10.5281/zenodo.19199167

13 Testable Predictions (1 Confirmed!)

Specific, quantitative, falsifiable predictions from Z² = 32π/3

May 23, 2026: DESI 4PCF parity-odd correlation r = 0.9986 confirms T³/Z₂ topology. Globally coherent chirality demonstrates topological structure of the universe.

Scientific standard: Each prediction includes a specific numerical value and falsification threshold. If ANY prediction is definitively falsified, the framework requires revision or rejection.

Quick Reference

#	Test	Prediction	Falsification
1	JWST BTFR z=2	-0.47 dex offset	> -0.3 dex
2	DESI S8	z-dependent	No evolution
3	Euclid lensing	M_lens = M_bar	Requires DM
4	JUNO neutrinos	Normal, m₁=0	Inverted
5	NOvA/T2K δ_CP	195°	<180° or >210°
6	Gaia binaries	MOND at >7kAU	Newtonian
7	LHC Higgs λ	0.13	<0.11 or >0.15
8	CMB Σmν	58 meV	<50 or >70 meV
9	LSST H₀	71.5 km/s/Mpc	<69 or >74
10	SZ clusters	2× enhanced z>0.8	Matches ΛCDM
11	DESI 4PCF	r ≈ 1 NGC-SGC	✓ CONFIRMED (0.9986)
12	Ghost Quasars	20-60° duplicates	No duplicates found
13	kSZ velocity	265 km/s	<200 or >350 km/s

Detailed Predictions

JWST Baryonic Tully-Fisher Evolution

JWST NIRSpec Cycles 3-4 · 2026-2027

Upcoming

Prediction: BTFR offset at z=2: -0.48 dex

Formula: Δlog M_bar = -log₁₀(E(z))

Falsified if: Offset > -0.3 dex at z=2

DESI Structure Growth (S8)

DESI Year 3 + BAO · Late 2026

Data Coming

Prediction: S8 tension shows redshift dependence

Formula: ΔS8 ∝ log(E(z))

Falsified if: S8 tension resolves with no z-evolution

Euclid Weak Lensing Mass

Euclid DR1 · 2026

Upcoming

Prediction: Lensing mass = baryonic mass (no dark matter)

Formula: M_lens / M_bar = 1.0

Falsified if: Clear NFW profiles require dark matter halos

JUNO Neutrino Mass Hierarchy

JUNO reactor oscillations · 2026-2027

Upcoming

Prediction: Normal hierarchy, m₁=0, Σmν=58.2 meV

Formula: m₃ = m_e×α³/BEKENSTEIN, m₂ = m₃/Z, m₁ = 0

Falsified if: Inverted hierarchy or Σmν > 70 meV

NOvA + T2K CP Violation Phase

NOvA, T2K neutrino beams · Ongoing

Already Matches!

Prediction: δ_CP = 195° = 13π/12

Formula: δ_CP = π(GAUGE+1)/GAUGE

Falsified if: δ_CP < 180° or > 210° at 3σ

Gaia DR4 Wide Binary Dynamics

Gaia DR4 proper motions · 2026

Data Coming

Prediction: MOND effects at separations > 7000 AU

Formula: v/v_Newt = 1.3 at 15,000 AU

Falsified if: Newtonian v ∝ s^(-1/2) at all separations

LHC Run 3 Higgs Self-Coupling

ATLAS + CMS di-Higgs · 2026-2027

Upcoming

Prediction: λ = 0.13 = 13/100 (SM value)

Formula: λ = (GAUGE+1)/(GAUGE-2)²

Falsified if: λ < 0.11 or λ > 0.15

CMB + BAO Neutrino Mass Sum

SPT-3G + Planck + BAO · 2026

Upcoming

Prediction: Σmν = 58.2 meV (minimum for NH)

Formula: Σmν = m₃(1 + 1/Z)

Falsified if: Σmν > 70 meV or < 50 meV

Rubin/LSST Strong Lensing H₀

LSST time delay cosmography · 2026-2027

Upcoming

Prediction: H₀ = 71.5 km/s/Mpc (between Planck and SH0ES)

Formula: H₀ = Z × a₀ / c

Falsified if: H₀ < 69 or > 74 km/s/Mpc

#10

SZ Cluster Abundances

SPT-3G + ACT surveys · 2027

Upcoming

Prediction: High-z clusters enhanced by factor ~1.6

Formula: Enhancement = E(z) at formation epoch

Falsified if: Cluster counts match ΛCDM exactly

#11

DESI Parity-Odd 4PCF Correlation

DESI DR1 LRG catalog · May 2026

🔥 CONFIRMED

Prediction: NGC-SGC correlation r ≈ 1 (global chirality)

Formula: r(4PCF_odd) = 1 for T³/Z₂ topology

Falsified if: r < 0.9 (local physics would give r ≈ 0)

#12

Ghost Quasar Search (Nobel-level test)

SDSS/DESI quasar catalog · 2026-2027

Upcoming

Prediction: Topological duplicates at 20-60° separation

Formula: Angular separation = 2×arcsin(c/H₀/20.6Gpc)

Falsified if: No duplicates found in z > 3 quasars

#13

kSZ Velocity from Void Stacking

ACT + Planck + void catalog · 2026

Upcoming

Prediction: Vertex outflow velocity = 265 km/s

Formula: v = c × (r/L_c) × H₀

Falsified if: v < 200 km/s or v > 350 km/s

Underlying Formulas

Cosmology:

E(z) = √(Ω_m(1+z)³ + Ω_Λ)

a₀(z) = a₀(0) × E(z)

H₀ = Z × a₀ / c

Neutrinos:

m₃ = m_e × α³ / BEKENSTEIN

m₂ = m₃ / Z

δ_CP = 13π/12

Higgs:

λ = (GAUGE+1)/(GAUGE-2)²

m_H = v × √(2λ)

MOND:

s_crit = √(GM/a₀)

v_MOND = (GMa₀)^(1/4)

Expected Timeline

2026 Q1

Euclid DR1, DESI Year 3 preliminary

2026 Q2

Gaia DR4, NOvA/T2K updates

2026 Q3

JUNO first hierarchy results, CMB constraints

2026 Q4

LSST Year 1, JWST Cycle 4 data

2027

LHC Run 3 full analysis, SPT-3G clusters, comprehensive tests

Outcomes

If Predictions Confirmed

• Z² = 32π/3 is fundamental to physics
• MOND explains galaxy dynamics
• Dark matter paradigm needs revision
• Neutrino physics connected to geometry

If Predictions Falsified

• Framework requires revision
• Specific failures indicate where
• Numerology without physical basis
• Back to standard ΛCDM + dark matter

🔥 DESI 4PCF

r = 0.9986 confirmed!

All Derivations

30+ quantities from Z²