# PAPER_1614 — C-12 Binding Energy per A = C-12 BE/A = F·K⁵ + β + β⁴ + F·β³ + 3 ≈ 7.682 MeV

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Nuclear
**Date:** June 18, 2026
**Status:** CLOSED — 0.017% residual

---

## Observation

PAPER_1209II_S668 (Nuclear Unified Proof Set) gives the closed-form expression:

```
C-12 BE/A = F·K⁵ + β + β⁴ + F·β³ + 3 ≈ 7.682 MeV
```

Residual to AME2020: **0.017%**.

## UQFF Closed Identity

```
C-12 BE/A = F·K⁵ + β + β⁴ + F·β³ + 3 ≈ 7.682 MeV    0.017%
```

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

## NOT REPLACEMENT

Experimental nuclear measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1209II_S668
- Related: PAPER_1494-1605 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "nuclear_c12_be_a_7_6802"})`

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