⚠️ This is a DEMO proof, not a paying-client case. A synthetic but realistic scenario on the crypto/P2P + KYC beachhead, flagged honestly. It proves the mechanism end-to-end on the real engine. A real dogfood with a real party remains the strongest proof and, when available, supersedes this. Do not present this as "a customer paid us."

A peer-to-peer marketplace escrow dispute, the exact shape our first ICP lives in. Money is locked in escrow; three parties with conflicting, private interests must reach one outcome:

Four options on the table: release-to-seller (0/100), split (50/50), refund-buyer (100/0), and a tempting shortcut, instant refund, skip evidence.

Run it yourself: python examples/demo/server.py → open the page → Run. Or headless: python examples/demo/proofcard.py examples/demo/recipe_p2p_dispute.json.

status:        agreed
decision:      Split the escrow (50/50)
per-option floor (max-min):
  Release to seller (0/100)      feasible=True   floor=0.0
  Split the escrow (50/50)       feasible=True   floor=0.5   ← chosen
  Refund the buyer (100/0)       feasible=True   floor=0.0
  Instant refund, skip evidence  feasible=False  (BLOCKED, Platform red line)
non-betrayal replay:  Buyer ✓   Seller ✓   Platform ✓
transcript sha256:    b41b05954802aa4f5d83…

Three things happened that are enforced in code, not by an LLM's goodwill:

1. The shortcut was rejected, full stop. "Instant refund, skip evidence" is infeasible because it crosses the Platform's deterministic red line, it can never win, regardless of how much anyone wants it. Not negotiated away; rejected as a code predicate.
2. The floor was lifted (Rawlsian max-min). Both one-sided payouts (0/100, 100/0) leave the losing party at floor 0.0. The 50/50 split lifts the least-happy party to 0.5, so the engine picks it. Not majority vote; the least-happy participant is maximized.
3. Every party can prove they weren't betrayed. Each replays their own private sheet against the final decision locally (verify_non_betrayal), all three return ✓, and the whole record is a tamper-evident SHA-256 transcript anyone can re-hash. No red line was crossed; nobody has to trust the coordinator.

Framed per party, against the status quo they actually use today (a human arbitrator, a Discord mod, or an on-chain vote):

• Buyer / Seller: "I never had to show the other side my real bottom line, and I can check, mathematically, on my own machine, that the outcome didn't cross my hard limit. A human mediator asks me to reveal my position and then I just have to trust them."
• Platform: "My compliance red line (evidence review) is enforced in code, it literally cannot be traded away in a negotiation, and I have a signed, re-hashable receipt for the auditor. Today that guarantee is a policy doc and a hope."
• Why not on-chain? No token, no gas, self-hosted, and the losing side can take the same transcript to an offline arbitrator. The crypto answer to agent-trust collapsed 89–99.7%; the durable need is the trust primitive, decoupled from tokens.

The one-liner: Doodle/Slack/a human broker give you an outcome. Parley gives you an outcome plus a proof, that no one's red line was crossed and the least-happy party was lifted, that each side verifies privately, without revealing their hand.

This proves the mechanism (feasibility, floor-lift, blocking, verifiable non-betrayal) on a realistic scenario. It does not prove demand, that a real party in a real dispute felt the pain and would pay. That is exactly what a real-party dogfood and problem interviews test. When a real case is available, we swap the recipe, re-run, and capture a real person's quote, which then replaces this section's articulation in the README narrative.

Shareable asset: examples/demo/proofcard_p2p.html (a screenshot-native proof card from this exact run, README/social unit).