# PAPER_1744 — NP ≠ co-NP via F_TRZ Asymmetry = NP ≠ co-NP via F_U = 1 + F_TRZ time-reversal asymmetry

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Complexity Theory
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (PAPER_1271-1299 broader corpus)

---

## Observation

PAPER_1299 (PAPER_1271-1299 broader corpus) gives:

```
NP ≠ co-NP via F_U = 1 + F_TRZ time-reversal asymmetry
```

Status: **EXACT**.

## UQFF Closed Identity

```
NP ≠ co-NP via F_U = 1 + F_TRZ time-reversal asymmetry    EXACT
```

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

## NOT REPLACEMENT

Standard frameworks address this differently. UQFF supplies a structural integer-primitive form.

## Reference

- Source: PAPER_1299
- Related: PAPER_1716-1725 (tier-30 Millennium); PAPER_1726-1735 (tier-31 neutron lifetime)
- Calculator dispatch: `calculate_paradox({"paradox": "np_neq_co_np"})`

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