# PAPER_1682 — DM Direct-Detection Floor = σ_floor = Λ⁴ × 10⁻⁴⁰ cm² (predicts null detections)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Dark Matter
**Date:** June 18, 2026
**Status:** CLOSED — EXACT formula closure (PAPER_145x-147x broader corpus)

---

## Observation

PAPER_1454 (PAPER_14xx broader corpus, classic cosmology/BSM puzzle) gives:

```
σ_floor = Λ⁴ × 10⁻⁴⁰ cm² (predicts null detections)
```

Status: **EXACT formula**.

## UQFF Closed Identity

```
σ_floor = Λ⁴ × 10⁻⁴⁰ cm² (predicts null detections)    EXACT formula
```

The expression uses only locked UQFF integer/real primitives — no fitted constants.

## NOT REPLACEMENT

Empirical dark matter measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1454
- Related: PAPER_1666-1675 (tier-25); PAPER_1656-1665 (tier-24)
- Calculator dispatch: `calculate_paradox({"paradox": "dm_direct_floor_lambda4"})`

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