# PAPER_1654 — Topological Braid Gate Max = Gate complexity ≤ D_crit = 26 braid operations

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Quantum Computing
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (broader-corpus PAPER_13xx mine)

---

## Observation

PAPER_1339 (PAPER_13xx broader corpus) gives:

```
Gate complexity ≤ D_crit = 26 braid operations
```

Status: **EXACT**.

## UQFF Closed Identity

```
Gate complexity ≤ D_crit = 26 braid operations    EXACT
```

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

## NOT REPLACEMENT

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

## Reference

- Source: PAPER_1339
- Related: PAPER_1636-1645 (tier-22 broader-corpus closures); PAPER_1494-1635 (PAPER_1209 series)
- Calculator dispatch: `calculate_paradox({"paradox": "braid_gate_max_26"})`

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