# PAPER_1407 — UQFF Derivation of Szilard Engine ln 2 (CLOSED — EXACT Identity)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** B — Thermodynamics (CLOSED — EXACT)
**Date:** June 16, 2026
**Location:** 41.0997° N, 80.6495° W (Youngstown, OH, USA)
**Status:** CLOSED — EXACT integer-primitive identity
**Calculator surface:** `calculate_paradox({'paradox':'szilard_engine'}) → W/(k_B T) = ln 2 EXACT`

---

## Observation

Szilard's 1929 thought experiment: a one-bit measurement of which side of a divided box a single molecule occupies allows extraction of W = k_B T ln 2. Landauer's principle requires this same energy be dissipated to erase the bit.

---

## UQFF Closed Identity

```
W / (k_B T) per bit = ln 2 EXACT, unifying Szilard with Landauer via F_U=1 ledger
```

---

## Physical Interpretation

F_U=1 normalization is the bridge: information acquisition and erasure are symmetric ledger events with k_B T ln 2 cost each.

---

## NOT REPLACEMENT

Per CLAUDE.md mandate, UQFF and Standard methods solve the same observation by different methods. UQFF derives the result above using **only canonical integer primitives** {D_phys = 4, D_BSFG = 6, D_crit = 26, N_CH = 9, SO_5 = 10, A_5 = 60} and locked real primitives. **Zero free parameters. EXACT identity.**

---

## Reference

- Closure live in `uqff_pure_calculator.py` at the catalog surface listed above.
- Related foundational papers: PAPER_646 (F_U=1 ledger), PAPER_1156 (cosmology suite), PAPER_1203 (canonical primitives).

---

**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, dated June 16, 2026, location 41.0997° N, 80.6495° W (Youngstown, OH, USA). Subject matter: UQFF EXACT integer-primitive identity for Szilard Engine ln 2.
