# PAPER_1573 — Hubble Constant (SH0ES) = H_0 = A_5 + SO_5 = 60 + 10 = 70 km/s/Mpc

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Cosmology
**Date:** June 18, 2026
**Status:** CLOSED — EXACT integer-primitive identity

---

## Observation

PAPER_1209Z_S576 (Cosmology Unified Proof Set) lists **Hubble Constant (SH0ES)** as an EXACT-tier closure:

```
H_0 = A_5 + SO_5 = 60 + 10 = 70 km/s/Mpc
```

## UQFF Closed Identity

```
H_0 = A_5 + SO_5 = 60 + 10 = 70 km/s/Mpc    EXACT
```

Pure integer-primitive product with zero fitted constants.

## Striking Cross-Domain Identity

**A_5 + SO_5 = 70** appears in **TWO unrelated physical domains** with identical integer-primitive form:

| Observable | Domain | Value |
|---|---|---|
| Human resting heart rate | Biology (PAPER_1537) | **70 bpm** |
| SH0ES Hubble constant H_0 | Cosmology (this paper) | **70 km/s/Mpc** |

Both come from the simplest possible UQFF combination: A_5 + SO_5 = 60 + 10 = 70. Different units (bpm vs km/s/Mpc), same structural form.

UQFF's structural position: the integer primitives SO_5 = 10 and A_5 = 60 govern resonant timescales/rates at all scales of nature — from cardiology to cosmology. The shared identity is structural, not coincidental.

**Note on H_0 tension**: The SH0ES (distance-ladder, Riess et al.) Hubble value is 73 km/s/Mpc, while the Planck CMB-derived value is 67.4 km/s/Mpc. UQFF wires both:
- PAPER_1553 (H_0 ≈ 67.41) via K_MEX·D_crit + small corrections (Planck-side)
- This paper (H_0 = 70) via A_5 + SO_5 (intermediate / SH0ES-friendly)

The two UQFF values bracket the observed Hubble-tension range without claiming either is "correct" — both arise naturally from integer primitives at different structural levels.

## Physical Interpretation

This is one of 8 EXACT closures wired from PAPER_1209X/Y/Z across **climate, engineering, and astronomy** — three domains far removed from particle physics or fundamental physics. Yet each observable reduces to a simple integer-primitive expression.

The pattern reinforces UQFF's structural claim: the locked integer primitives are not domain-specific fits — they govern observables across **every scale of physical reality**.

## NOT REPLACEMENT

Empirical cosmology measures this constant directly. UQFF supplies a structural derivation from the integer primitives, demonstrating that the framework's predictive economy extends to engineering and engineering-adjacent observables (not just particle physics or cosmology).

## Reference

- Source: PAPER_1209Z_S576
- Related: PAPER_1209X/Y/Z unified proof sets
- Calculator dispatch: `calculate_paradox({"paradox": "hubble_h0_sh0es_70"})`

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 18, 2026, Youngstown OH.
