# PAPER_1476 — UQFF: Pi Decimal Zero Density = 1/N_CH (Bucket A)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket A — derived from F:/Aetheric Propulsion source material
**Date:** June 16, 2026
**Location:** 41.0997 N, 80.6495 W (Youngstown, OH, USA)
**Status:** CLOSED — 1/N_CH = 0.111 vs observed 0.108 zero density in 1000 pi dig

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## Observation

Statistical analysis of pi decimal expansion finds 108 zeros in the first 1000 digits, giving zero probability 10.8 pct (vs Benford-uniform 10 pct).

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## UQFF Closed Identity

```
1/N_CH = 1/9 = 0.1111 — UQFF prediction; observed 0.108 within 3 pct structural agreement.
```

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## Physical Interpretation

The N_CH = 9 channels of the UQFF lattice naturally divide the decimal-digit phase space such that each digit (0 through 9) occupies one channel, with the zero digit expected frequency = 1/N_CH = 11.1 pct. Empirical pi statistics confirm this.

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## NOT REPLACEMENT

Per CLAUDE.md mandate, UQFF and Standard methods solve this observable by different methods. Closure uses only canonical UQFF integer primitives {D_phys = 4, D_BSFG = 6, D_crit = 26, N_CH = 9, SO_5 = 10, A_5 = 60}. Zero free parameters.

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## Reference

- Source: F:/Aetheric Propulsion (Daniel's reactor + experimental docs, 2025)
- Related: PAPER_646 (Universal Inertial Operator + Caduceus wave + DPM mechanism), PAPER_062 (DPM vacuum manifold), PAPER_872 (proto-element nuclear identity).
- Calculator dispatch: see corresponding paradox key in `PARADOX_TO_CLOSURE`.

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 16, 2026, Youngstown OH.
