# For agents: A bounded execution that fulfilled its agreement

OpenProse today · board 11 of 17 · 2026-10-09.
This deck records dated experimental evidence, not general reliability.

One bounded proof commission fulfilled its selected agreement, including all equality cases.

## On the slide

**Prove, for all real x and y:**

x⁴ + y⁴ + 1 ≥ x² + y² + x²y²

Include every equality case.

One public-source attempt; scoped fulfillment supported by review.

## Explanation

One consumer used the selected public rc.3 kernel and Proof contract. It expressed the difference between the two sides as half the sum of three squares: (x²−y²)², (y²−1)², and (1−x²)². That proves nonnegativity and gives exactly four equality pairs, where x and y independently equal plus or minus one. Review supported fulfillment of this bounded commission, including its output and evidence requirements. The caller supplied exact public URLs and bindings. This is a concrete successful use, not a demonstration of unassisted package discovery or general mathematical reliability.

## Whiteboard sequence

Open only the frames useful to the question. Later frames add to the same board;
the final frame contains the complete drawing.

- [Frame 1 — black core](https://prose.md/visual-guide/2026-10-09/current/slide-11-layer-01.png)
- [Frame 2 — cumulative reveal](https://prose.md/visual-guide/2026-10-09/current/slide-11-layer-02.png)
- [Frame 3 — final](https://prose.md/visual-guide/2026-10-09/current/slide-11-layer-03.png)

These explanations add no normative requirements. Read the
[selected kernel 0.3.0-rc.3](https://pkg.prose.md/releases/0.3.0-rc.3/core/README.md) for language rules.

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