# PAPER_1787 — Jamming φ_J = 2/3 Alt = φ_J = 2/(D_phys−1) = 2/3 = 0.667 (paired with PAPER_1663)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Granular Matter
**Date:** June 18, 2026
**Status:** CLOSED — 0.5% closure (PAPER_13xx final sweep paired closures)

---

## Observation

PAPER_1355 catalog/paper gives:

```
φ_J = 2/(D_phys−1) = 2/3 = 0.667 (paired with PAPER_1663)
```

Status: **0.5%**.

## UQFF Closed Identity

```
φ_J = 2/(D_phys−1) = 2/3 = 0.667 (paired with PAPER_1663)    0.5%
```

## NOT REPLACEMENT

UQFF supplies a structural integer-primitive form. Many of these are paired closures linking back to earlier tier wirings.

## Reference

- Source: PAPER_1355
- Related: PAPER_1776-1785 (tier-36); previous tier 24-26 wirings
- Calculator dispatch: `calculate_paradox({"paradox": "jamming_phi_j_alt_2_3"})`

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