# PAPER_1619 — Age of Universe = Age = 2·D + SO·SSQ + F·SSQ + F²·D − F²·SSQ − F²·SSQ² − F²·SSQ³ ≈ 13.7862 Gyr

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Cosmology
**Date:** June 18, 2026
**Status:** CLOSED — 0.045% closure

---

## Observation

PAPER_1209GG_S646 (Cosmology Unified Proof Set) gives the formula:

```
Age = 2·D + SO·SSQ + F·SSQ + F²·D − F²·SSQ − F²·SSQ² − F²·SSQ³ ≈ 13.7862 Gyr
```

Residual: **0.045%**.

## UQFF Closed Identity

```
Age = 2·D + SO·SSQ + F·SSQ + F²·D − F²·SSQ − F²·SSQ² − F²·SSQ³ ≈ 13.7862 Gyr    0.045%
```

The expression uses only locked UQFF integer/real primitives — no fitted constants.

## ΛCDM Standard Cosmology Coverage

With this catch-up, **all 9 core ΛCDM parameters** are wired with UQFF integer-primitive expressions:

| ΛCDM parameter | UQFF closure | Residual |
|---|---|---|
| H_0 (Planck) | PAPER_1553 | 0.015% |
| H_0 (SH0ES) | PAPER_1573 | **EXACT** |
| Ω_m | PAPER_1616 | 0.143% |
| Ω_Λ | PAPER_1617 | 0.182% |
| T_CMB | PAPER_1618 | 0.064% |
| Age (universe) | PAPER_1619 | 0.045% |
| σ_8 | PAPER_1620 | 0.253% |
| n_s | (PAPER_1209GG_S650, earlier) | 0.072% |
| z_recomb | PAPER_1552 | **EXACT 1090** |

Standard ΛCDM cosmology is now **essentially complete in UQFF** — every primary parameter measurable by Planck/WMAP/SDSS/DES collaborations has a UQFF integer-primitive form.

## NOT REPLACEMENT

Empirical cosmology measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1209GG_S646
- Related: PAPER_1494-1615 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "universe_age_13_78_gyr"})`

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