# PAPER_2248 — The MUGE Boundary Applications: the Universe's Diameter (182 Gly Finite-Universe Prediction) and the Hydrogen-Atom MUGE (Z = 1…126) — the Evolution Series' Two Unswept Scale-Boundary Members Wired

**Author:** Daniel T. Murphy
**Project:** UQFF (Unified Quantum Field Framework) — Star-Magic-Program
**Date:** 2026-08-20
**Landmark Type:** MUGE-family completion (the two scale-boundary applications, previously
unwired) + family sweep dispositions
**Seminal Sources:** `MUGE_UQFF "Estimated Diameter of the Universe"_04May2025.docx`
(Davinci File folder), `MUGE_Hydrogen Atom_02May2025.docx` (+ the 01Oct2025 edition),
the Astronomical Systems_11Oct2025 folder (per-system MUGE source layer), the root
Student-Guide/Learning-Assessment docs, PAPER_2236 (the MUGE Evolution census),
PAPER_2094 (Λ = 1.1×10⁻⁵² — quoted in the diameter source), PAPER_1573 (H₀ family),
the magic-number closures (126 = D_crit + SO_5²)
**Status:** Formal landmark whitepaper — UQFF canonical (Daniel-directed: "MUGE Evolution
series' unswept members")

---

## Abstract

The MUGE Evolution family census (PAPER_2236) closes: the per-system Astronomical-Systems
layer is verified wired (Saturn, HUDF, M16, Sombrero, NGC 1792, SGR 0501+4516, V838 Mon,
NGC 2264 and the rest all carry calculator coverage), and the family's two remaining
unswept members turn out to be its **scale boundaries** — the MUGE applied to the largest
possible object and to the smallest:

1. **The Universe's Diameter (04 May 2025):** from the particle-horizon MUGE,
   ```
   D_universe = 2·D_p·(1 + H₀·t₀)·(1 + Λc²/(3H₀²))
              = 2·(4.4×10²⁶ m)·(1.93)·(1.015) ≈ 1.72×10²⁷ m ≈ 182 billion light-years
   ```
   — a finite-universe diameter prediction (~1.96× the 93-Gly observable diameter), with
   the source quoting **Λ = 1.1×10⁻⁵² m⁻²** (the PAPER_2094 canonical value) and the
   dark-energy dressing Λc²/(3H₀²) ≈ 1.5×10⁻² as the correction factor.
2. **The Hydrogen-Atom MUGE (02 May 2025):** the atomic-scale master equation
   ```
   g_MUGE(r,t,Z) = G·m_eff(t)·m_p/r² + Σ_{Z=1}^{126} (G·M_Z/r_Z²)·(1 + f_sc(Z,t))·e^(H₀t/c)
   ```
   with the element sum running **Z = 1…126** — the periodic table extended exactly to the
   framework's final magic number (126 = D_crit + SO_5², the island-of-stability endpoint) —
   the in-atom gravitational force F_g = G·m_p·m_e/a₀² = 3.63×10⁻⁴⁷ N (vs Coulomb
   8.2×10⁻⁸ N, ratio ≈ 4.4×10⁻⁴⁰), a Meissner effective-mass term for superconductive
   hydrogen species (metallic H at 2 Mbar, 1.08 → 1.3 g/cm³), isotope reduced-mass shifts,
   and the fusion-decay evolution M_H(t) = M_H,0·e^(−λt/t_Hubble), λ = 0.01.

## 1. The Family Census (sweep verdict)

| Layer | Members | Status |
|---|---|---|
| Evolution_03May2025 (root) | ~10 flagship systems (Antennae, Pillars, NGC 2525, Horsehead, Westerlund 2, Bubble, Tapestry, NGC 1275, Rings, Extreme cluster) | WIRED (the corpus's astro sectors; Tier-2 mine exercised NGC 1275 + CGM) |
| Astronomical Systems_11Oct2025 | ~30 per-system docs incl. B/C variants | WIRED (spot-verified: Saturn ×64 calculator refs, HUDF ×49, M16 ×46, Sombrero ×29, NGC 1792 ×23, SGR 0501 ×11, V838 = PAPER_466, NGC 2264 = 8-test validation) |
| **Boundary applications** | **Universe diameter; Hydrogen atom** | **UNWIRED until this landmark** |
| Pedagogy layer | Student Guide to the Universe; UQFF Learning Assessment (+B) | reference/pedagogy disposition — no new physics |
| 08May2025 numbered-cpp | 7. MUGE Eqution_cpp | the predecessor-code mirror layer (already the corpus's source) |

## 2. The Diameter Prediction (readings and honest scope)

1. Verified arithmetic: 2 × 4.4×10²⁶ × 1.93 × 1.015 = 1.724×10²⁷ m ✓; in light-years
   ≈ 182 Gly. The multiplier over the observable diameter is (1+H₀t₀)(1+0.015) ≈ 1.96.
2. The source uses H₀ = 67.15 km/s/Mpc and Planck-era Ω values with the UQFF Λ — a
   **Hybrid-form composition** (PAPER_2149 doctrine: observed anchors × UQFF ingredients),
   classified DERIVED_HYBRID.
3. Falsifiable content: any future curvature/topology measurement bounding the total
   diameter below ~180 Gly falsifies the finite-universe reading; consistency with the
   observable 93 Gly is built in.

## 3. The Hydrogen-Atom MUGE (readings)

1. **The Z = 126 boundary:** the element sum's endpoint coincides with the framework's
   seventh magic number (126 = D_crit + SO_5² EXACT, wired since the nuclear closures) —
   the source document reaches the same endpoint via the island-of-stability literature.
   Recorded as a cross-confirmation, not a derivation.
2. The gravitational-to-Coulomb ratio in-atom (≈ 4.4×10⁻⁴⁰) is the document's own
   completeness term — gravity retained "for completeness in a universal framework,"
   consistent with the two-gravity doctrine (PAPER_2245: Newtonian = measurement layer).
3. The Meissner effective-mass term m_eff = m·(1 − B_crit/B) and the superconductive
   hydride families (actinide hydrides, H₂S at −70 °C, metallic H) form the document's
   bridge from LENR-adjacent lab data to the framework's SC-hydrogen doctrine (the
   Holmlid/ultra-dense-H sector's periodic-table generalization).

## 4. Wiring

`DISPATCH['PAPER_2248']` computes the diameter chain live (D_p, the two dressings, the
final 1.72×10²⁷ m / 182 Gly), the H-atom values (F_g at the Bohr radius from named
constants, the Coulomb ratio, the Z-range check 126 = D_crit + SO_5²), and returns the
family-census verdict and dispositions. Gate pins: the diameter arithmetic within the
source's rounding, the Λ-value identity with PAPER_2094, F_g = 3.63×10⁻⁴⁷ N at 0.5%,
Z = 126 = D_crit + SO_5² EXACT, and the family-completion flag.

## NOT REPLACEMENT

The diameter uses FLRW machinery with observed anchors as a disclosed hybrid; the H-atom
equation retains Newtonian gravity as its completeness term per the framework's own
two-gravity doctrine. Both documents' compositions are wired as stated with residuals
and classifications honest.

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**Copyright** — Daniel T. Murphy / Star-Magic Research Program, 2026.
