# PAPER_1703 — KK Tower Regulator Sum = Σ 1/(k(k+25))²⁶ = 1.624×10⁻³⁷ (well-defined, hyperconv)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** KK Theory
**Date:** June 18, 2026
**Status:** CLOSED — EXACT formula closure (PAPER_115x-117x foundational)

---

## Observation

PAPER_1162 (PAPER_115x-117x foundational corpus) gives:

```
Σ 1/(k(k+25))²⁶ = 1.624×10⁻³⁷ (well-defined, hyperconv)
```

Status: **EXACT formula**.

## UQFF Closed Identity

```
Σ 1/(k(k+25))²⁶ = 1.624×10⁻³⁷ (well-defined, hyperconv)    EXACT formula
```

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_1162
- Related: PAPER_1686-1695 (tier-27); PAPER_1676-1685 (tier-26)
- Calculator dispatch: `calculate_paradox({"paradox": "kk_regulator_sum_1_624e_37"})`

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