Axiom · Chain Position 74 of 346

NON-UNITARITY OF GRACE

**Statement:** [[075_D9.1_Grace-Operator-Definition|Grace operator]] Ĝ is non-unitary (information added, not just transformed).

Connections

Assumes

  • None

Enables

  • None
Mathematical Layer

Non-Unitary Proof

Theorem: Any operator that maps multiple states to a single state is non-unitary.

Proof:

1. Ĝ|-1⟩ = |+1⟩ and Ĝ|+1⟩ = |+1⟩

2. Both |-1⟩ and |+1⟩ map to the same output

3. Unitary operators are bijective (one-to-one)

4. Ĝ is not bijective (two inputs → one output)

5. Therefore, Ĝ is not unitary

Corollary: Grace cannot be reversed. There's no Ĝ⁻¹ that uniquely recovers the pre-grace state.

Evidence
Empirical Grounding
This isn't philosophy. This is measured.
  • Landauer's Principle
Defeat Conditions

To Falsify This

  1. **Show sign-flip via unitary operator** — Find a self-generated U with U†U = I that changes σ: -1 → +1
  2. **Derive salvation from self-effort alone** — Demonstrate works-based righteousness mathematically
  3. **Show Ĝ†Ĝ = I** — Prove the grace operator is unitary (information-preserving)
  4. **Generate coherence from nothing** — Bootstrap moral order without external input