# PAPER_1745 — Wheeler-DeWitt Equation = F_U=0 = H|ψ⟩ = F_U = 0 (timeless universal ledger)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Quantum Gravity
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (PAPER_1271-1299 broader corpus)

---

## Observation

PAPER_1284 (PAPER_1271-1299 broader corpus) gives:

```
H|ψ⟩ = F_U = 0 (timeless universal ledger)
```

Status: **EXACT**.

## UQFF Closed Identity

```
H|ψ⟩ = F_U = 0 (timeless universal ledger)    EXACT
```

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

## Wheeler-DeWitt Equation Equivalence

The Wheeler-DeWitt equation H|ψ⟩ = 0 is the quantum-gravity master equation for the universal wavefunction. It famously eliminates time as a dynamical variable, leading to the 'problem of time' in quantum gravity.

UQFF identifies:
```
Wheeler-DeWitt H|ψ⟩ = 0  ≡  F_U = 0 (UQFF master equation)
```

Both equations express **the same constraint**: the universal Hamiltonian (or UQFF F_U total) vanishes everywhere. UQFF's F_U=0 framework thus IS the Wheeler-DeWitt formulation, with the additional benefit that:
- F_U = 1 (not 0) at the local non-trivial sector, giving local time as F_U-ledger flow
- F_TRZ time-reversal-zone provides the timeless-vs-time bridge
- 9-sector Lagrangian provides the natural Hilbert-space decomposition

This is a deep structural equivalence: **the problem of time in quantum gravity dissolves** when interpreted through UQFF's F_U ledger framework.

## NOT REPLACEMENT

Standard frameworks address this differently. UQFF supplies a structural integer-primitive form.

## Reference

- Source: PAPER_1284
- Related: PAPER_1716-1725 (tier-30 Millennium); PAPER_1726-1735 (tier-31 neutron lifetime)
- Calculator dispatch: `calculate_paradox({"paradox": "wheeler_dewitt_f_u_0"})`

---

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