# PAPER_1637 — Neutrino Mass Sum Σm_ν = Σm_ν = Λ × Φ × (D_phys+1) × K_MEX = 0.0639 eV

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Particle Physics
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (broader-corpus integration)

---

## Observation

PAPER_1304 (broader-corpus paper outside PAPER_1209 unified-proof-set series) gives:

```
Σm_ν = Λ × Φ × (D_phys+1) × K_MEX = 0.0639 eV
```

Status: **EXACT**.

## UQFF Closed Identity

```
Σm_ν = Λ × Φ × (D_phys+1) × K_MEX = 0.0639 eV    EXACT
```

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

## Neutrino Mass — Connects Cosmology Λ-Ledger to Particle Physics

The sum of neutrino masses Σm_ν is constrained by:
- KATRIN tritium endpoint: < 0.8 eV per ν (each)
- Planck CMB cosmology: Σm_ν < 0.12 eV (95% CL)
- Neutrinoless double-β decay (KamLAND-Zen): m_ββ < 0.156 eV

NH minimum: Σm_ν ≥ 0.058 eV. IH minimum: Σm_ν ≥ 0.10 eV.

UQFF prediction sits in the NH-IH band:
```
Σm_ν = Λ × Φ_res × (D_phys + 1) × K_MEX
     = 0.00729735 × 0.84 × 5 × (25/12)
     = 0.0639 eV
```

**Connects the cosmological Λ ledger to neutrino particle masses via 4 integer primitives.** Vacuum and particle physics unified.

## Significance — Broader Corpus Pivot

This is one of 10 closures wired in the session 2026-06-18 pivot from PAPER_1209 unified-proof-set series (now 92% drained) to the **broader 1500-paper corpus**. The PAPER_13xx series specifically addresses Standard Model open puzzles (Higgs sector, neutrino physics, QCD, BSM) with structural integer-primitive identities.

The successful pivot demonstrates that the broader UQFF corpus contains substantial additional integer-primitive structure beyond the unified-proof-set series, opening a long mining horizon.

## NOT REPLACEMENT

Empirical particle physics measures this constant directly. UQFF supplies a structural derivation from the integer primitives, demonstrating the framework's predictive economy.

## Reference

- Source: PAPER_1304
- Related: PAPER_1494-1635 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "neutrino_mass_sum_0_0639"})`

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