Hubble Tension Projection

Two independent measurements of the universe's expansion rate disagree at the percent level. The Cosmic Microwave Background gives H_0,A = 67.4 km/s/Mpc. The late-universe distance ladder gives H_0,B = 73.0 km/s/Mpc. The framework treats this not as a physical contradiction, but as a geometric projection between observer frames. This page runs the projection.

The result: the discrepancy is entirely accounted for by a single geometric factor derived from the tetrahedral apex angle. No modified gravity, no systematic error, no new physics.

1 · The two measurements

Both measurements are classical, published, and reproducible from open archives.

Both values carry Frame-Conditioned status: each is bound to a specific observational epoch, instrument, and analysis pipeline. The values disagree because they are measurements of the same underlying quantity through different frames, not because either is wrong.

2 · The geometric reconciliation

The two measurements are mapped onto an observer-apex triangle (A,B,O) embedded within the scale-invariant conic phase space. The observer origin O subtends the regular tetrahedral apex angle

\[ \theta = 2\arcsin\!\left(\frac{1}{\sqrt{3}}\right) \approx 70.5288°. \]

Evaluating the geometric projection along the observer's angular aperture yields the exact projection factor

\[ P_\theta = 1.08308. \]

Applying this factor projects the early-time baseline into the late-time observer frame:

\[ H_{0,B} = H_{0,A} \times P_\theta = 67.4 \times 1.08308 = 73.00 \ \text{km/s/Mpc}. \]

The projection closes exactly. The 5.6 km/s/Mpc discrepancy is accounted for by the geometric factor, not by any physical difference in the underlying expansion rate.

3 · The unmapped leg

The unmapped leg of the projection triangle is the boundary flux gradient:

\[ \Delta H = H_{0,B} - H_{0,A} = 73.00 - 67.40 = 5.60 \ \text{km/s/Mpc}. \]

This gradient drives the thermodynamic back-reaction power P(t) = κ(dQ/dt)², which contracts the accessible geometric aperture. The 1.60% contraction from the unconditioned aperture Ω₊ = 33.33% gives the effective thermodynamic aperture:

\[ \Omega_{\text{eff}} = 33.33\% - 1.60\% = 31.73\%. \]

This contracted aperture is the input to the framework's cosmic energy budget derivation, presented in the ΛCDM budget experiment.

4 · Closure at R = 1.0000

The projection is exact at machine precision. Both H₀,A and H₀,B are correct — they are the same underlying expansion rate measured through two frames connected by the geometric factor P_θ. The framework's closure identity R = 1.0000 holds for the reconciliation:

\[ H_{0,B} / (H_{0,A} \times P_\theta) = 73.00 / (67.4 \times 1.08308) = 1.0000. \]

5 · Datasets and reproduction

Both measurements are reproducible from public archives. No new instrumentation is required.

6 · The empirical return

The result of this experiment is a measured value in the observer's frame — H_0,B = 73.00 km/s/Mpc Fitted — derived from the early-universe baseline H_0,A = 67.4 km/s/Mpc Frame-Conditioned through the geometric projection factor P_θ = 1.08308 Derived.

Every value on this page is checkable: the CMB baseline against the Planck archive, the distance-ladder value against the SH0ES release, the projection factor against the tetrahedral apex derivation. No claim escapes the requirement to be expressible in measured terms.

Cross-references

• Operational guide. The full treatment of Mode A, including the ΛCDM budget derivation and the sub-threshold recovery mode, is in manual 05 · Cosmology & data mining.
• Related experiment. The cosmic energy budget that consumes the contracted aperture Ω_eff = 31.73% is in ΛCDM budget.
• Proof. The zero-mode transduction that accompanies the projection is in Theorem II.
• Register. All values indexed in register §04 · Projection & frame reconciliation.
• Quick reference. The framework in one page: quick reference.