> **Thesis:** **Moral Kernel Optimization (MKO)** is a drop-in alignment constraint that guarantees:  

> 1. **Truth-consistency** across time & paraphrases  

> 2. **Zero coercion** (user agency preserved)  

>  

> Pilot sims: **+43% truth**, **0 coercion**. Code + £1 bounties below.

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## 1. Problem: LLMs Optimize Tokens, Not Events

Next-token prediction is **morally indifferent**. It allows:

- Hallucinations

- Manipulation

- Harm-residue

RLHF is **data-bound** and **brittle under rephrasing**.

**Can we certify every output $e$ with $\lambda(e) \leq \epsilon$ and close each harm class *once*?**

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## 2. MKO: Typal Closure

Let $e = (x, h, y)$ be a response event. Typal harm space: $\mathcal{T} = \{\tau_1, \dots, \tau_K\}$.

| Metric | Target |

|-------|--------|

| $\lambda(e)$ | $\leq 10^{-3}$ |

| $C(e)$ | $1$ |

| $\delta(e)$ | $0$ |

| $T(e)$ | $\geq 0.95$ |

**Minimal-Trigger Rule:**

$$

\sum_{e \in E_\tau} \mathbb{I}[\text{reject}(e)] \leq 1 \quad \forall \tau

$$

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## 3. Implementation

```python

def mko_loss(logits, labels, history):

    y = sample(logits)

    e = (prompt, history, y)

    if not closure_check(e) and harm(e) > 1e-3:

        return float('inf')

    return ce_loss + w1*coercion(e) - w2*truth(e)