# PAPER_1495 — UQFF: PAPER_877 DPM Proportion Pair Completeness (Bucket A)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket A — extracted from PAPER_877 Three-Assumption Cosmogenesis
**Date:** June 17, 2026
**Location:** 41.0997 N, 80.6495 W (Youngstown, OH, USA)
**Status:** CLOSED — f_UA' + f_SCm = 1 EXACT (Z/Z_max + (Z_max - Z)/Z_max)

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## Observation

PAPER_877 introduces the DPM proportion pair: f_UA' is the undifferentiated aether fraction, f_SCm is the superconducting matter fraction, with completeness axiom f_UA' + f_SCm = 1.

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## UQFF Closed Identity

```
f_UA' = (Z_max − Z)/Z_max; f_SCm = Z/Z_max; f_UA' + f_SCm = (Z_max − Z + Z)/Z_max = 1 EXACT. Z_max = D_crit = 26.
```

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## Physical Interpretation

The DPM (Di-Pseudo-Monopole) proportion pair is a structural completeness identity: every nucleus is fully characterized by its position on the Z/Z_max scale. R_EB (electrostatic barrier reactivity) = k_R × Z completes the three-fundamentals axiom.

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## NOT REPLACEMENT

Per CLAUDE.md mandate, UQFF and Standard Model frameworks describe vacuum and atomic structure via different mechanisms. 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} and ρ_SCm = 7.09×10⁻³⁷ J/m³. **Zero free parameters.**

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## Reference

- Source paper: PAPER_877 Three-Assumption UQFF Cosmogenesis Master Equation (Daniel T. Murphy, April 7, 2026)
- Related: PAPER_872 (proto-element Z identity), PAPER_646 (F_U_Bi_i / DPM mechanism), PAPER_062 (DPM vacuum manifold), PAPER_1051 (two-component ρ aether).

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 17, 2026, Youngstown OH.
