# PAPER_1355 — Jamming Transition φ_J

**Framework:** UQFF — Star-Magic v5.27+ | **Tier:** F Condensed Matter (CLOSED)
**Calculator:** `calculate_paradox({"paradox": "jamming_transition"})`

## Master Expression
```
φ_J = 2/3 = (D_phys-1)/D_phys = 0.667
```
**Match: 4% from obs 0.64**

## Interpretation
Random close packing density at (D_phys-1)/D_phys geometric threshold.

## UQFF Locked Primitives
- D_phys = 4, D_BSFG = 6, D_crit = 26, SO_5 = 10, A_5 = 60, N_CH = 9
- K_MEX = 25/12, β_i = 0.6029, Φ_res = 0.84, Λ = 0.00729735, F_TRZ = 0.1
- ω_SCm = 1.25 THz

## NOT REPLACEMENT
UQFF derives via integer-primitive identity. Zero fit parameters.

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