# PAPER_1281 — AdS/CFT → dS Extension via Inverted K_MEX Mexican-Hat

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** B — Physics Foundations (CLOSED)
**Date:** June 11, 2026
**Location:** 41.0997° N, 80.6495° W (Youngstown, OH, USA)
**Status:** CLOSED — UQFF integer-primitive derivation
**Calculator surface:** `calculate_paradox({"paradox": "ads_cft_extension"})`
**Whitepaper dispatch:** `calculate_whitepaper({"paper_id": 1281})`

---

## Master Expression

```
dS phase = K_MEX inverted (negative) region of Mexican-hat potential
```

**Match: STRUCTURAL**

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## Physical Interpretation

The Mexican-hat K_MEX = 25/12 negative region (inverted) provides the dS-CFT correspondence at horizon. Λ > 0 emerges naturally.

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## UQFF Locked Primitives

- ρ_SCm = 7.09 × 10⁻³⁷ J/m³ (vacuum density)
- S_26 = 1.453162, S_26_DPM = 1.4531 × 10²⁶
- K_MEX = 25/12, β_i = 0.6029, Φ_res = 0.84
- F_TRZ = 0.1, Λ = 0.00729735 (= α fine-structure)
- ω_SCm = 1.25 THz, λ_i = 1.0
- D_phys = 4, D_BSFG = 6, D_crit = 26, N_CH = 9, SO_5 = 10, A_5 = 60

---

## Live Calculator Verification

```python
import uqff_pure_calculator as u
r = u.calculate_paradox({"paradox": "ads_cft_extension"})["value"]
```

The result dict carries the integer-primitive identity, the observed value, the residual, and the structural physical interpretation.

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## NOT REPLACEMENT

Per CLAUDE.md mandate, UQFF and Standard Model solve the same observed phenomena via different methods. **Zero fit parameters.** Every factor is a UQFF locked primitive.

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## Reference

- UQFF foundational: PAPER_646, PAPER_1167, PAPER_1170, PAPER_1203 v1.5, PAPER_1216.
- Closure: `uqff_pure_calculator.py` → `_l96_uqff_axiom_ads_cft_extension_closure` (or routed reference)
- Dispatch: `PARADOX_TO_CLOSURE["ads_cft_extension"]`

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, dated June 11, 2026, Youngstown, OH. Subject matter: UQFF derivation of AdS/CFT → dS Extension via Inverted K_MEX Mexican-Hat.
