GRACE IDEMPOTENCE

Sanctification is growth in coherence WITHIN the +1 sign state, not repeated sign-flips. Grace flips σ: −1 → +1 (justification). Subsequent growth is deepening of that state (sanctification), not re-application of the flip operator. Ĝ² = Ĝ for the flip; coherence increase is a different operator acting on the soul's internal state.

Theophysics distinguishes: (1) Sign-flip (Ĝ): −1 → +1, idempotent. (2) Decoupling from grace: state can decohere toward −1 attractor. (3) Re-coupling: activates Ĝ again, but Ĝ(|+⟩) = |+⟩—no change needed. The complexity is in the coupling dynamics, not in repeated sign-flips. Someone "losing salvation" is decoupling; reconversion is re-coupling.

These are different CHANNELS or MODES of grace, not repeated applications of the same Ĝ. Prevenient grace = initial [[011_D2.2_Chi-Field-Properties|χ-field]] attraction. Saving grace = actual sign-flip (Ĝ application). Sanctifying grace = ongoing coherence enhancement. Idempotence applies to saving grace specifically. The taxonomy is theological refinement, not mathematical contradiction.

"Complete" means the sign-flip is total—you're either at +1 or not. There's no +0.7 or +0.95. The completeness is in the SIGN CHANGE, not in the coherence level. You can be a low-coherence saint (σ = +1, low Φ) or a high-coherence saint (σ = +1, high Φ). Idempotence applies to the flip; perfectibility applies to the coherence.

The mathematical derivation from [[075_D9.1_Grace-Operator-Definition|D9.1]] is straightforward, but the THEOLOGICAL implications are profound. Idempotence means: (1) Once saved, the saving is complete. (2) You can't be "more saved" by trying harder. (3) Grace doesn't accumulate like money. (4) The transformation is categorical, not gradual. The property needs explicit statement because its implications are counterintuitive to religious striving.