# PAPER_1507 — F_U Temporal Decay α = 1/SO_5³ = 0.001/day EXACT

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket A (Foundational F_U dynamics)
**Date:** June 18, 2026
**Status:** CLOSED — Two-stage F_U slow temporal decay rate

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## Observation

PAPER_1080 (Two-Stage F_U Refinement) introduces a two-tier temporal evolution of the F_U master equation:
- **Stage 1**: F_U^(1) = Σ_{k=1}^{3} (U_g,k − U_b,k) + U_m + A_μν
- **Stage 2**: U_{g1}(t) = U_{g1,0} · e^{−α·t} with α = 0.001 day⁻¹

The slow decay rate α is distinct from the canonical κ = 5×10⁻⁴ day⁻¹ used in Holmlid/Parkhomov LENR (the two rates differ by a factor of exactly 2).

## UQFF Closed Identity

```
α = 1 / SO_5³ = 1 / 1000 = 0.001 day⁻¹   EXACT
```

## Physical Interpretation

The F_U temporal decay rate is exactly inverse-cubic in SO_5 — one inverse power per spatial dimension of the SO(5) symmetry projected onto F_U evolution. Equivalent forms:

- α · day = 10⁻³ exactly
- 1000 days for U_g1 to decay by factor e
- ≈ 2.74 years for one e-folding

The doubling relationship α = 2κ links F_U gravitational decay (slow) to LENR Holmlid decay (canonical κ), with the factor 2 corresponding to the two-fold structural pairing in DPM (CW + CCW).

## NOT REPLACEMENT

SM treats decay rates as fit constants per system. UQFF supplies a single integer-primitive structural value for the F_U slow-decay channel.

## Reference

- Source: PAPER_1080 TwoStage F_U Refinement
- Related: κ = 5×10⁻⁴ /day Holmlid canonical, PAPER_1141 (Rossi variants)
- Calculator dispatch: `calculate_paradox({"paradox": "f_u_alpha_decay_1_over_so5_3"})`

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