> ## Documentation Index > Fetch the complete documentation index at: https://docs.inkwell.finance/llms.txt > Use this file to discover all available pages before exploring further. # Matching mechanism > How Dagon finds a clearing price through ciphertext alone. Walrasian tâtonnement, evaluated entirely on encrypted values. > **CONFIDENTIAL & PROPRIETARY © 2026 Inkwell Finance, Inc. All Rights Reserved.** > > This document is for informational purposes only and does not constitute legal, tax, or investment advice, nor an offer to sell or a solicitation to buy any security or other financial instrument. Any examples, structures, or flows described here are design intent only and may change. How do you find a fair price when no one — not the operator, not a matcher, not an observer — is allowed to see anyone else's order? ## The problem At clearing, the engine needs to find a single price *p* such that aggregate demand at *p* equals aggregate supply at *p*. In a normal order book this is done by sorting and matching quotes. In Dagon nothing can be sorted because nothing can be decrypted. The orders are encrypted curves, not encrypted quotes. ## The answer Walrasian tâtonnement: the engine bisects over a price range, evaluates aggregate demand and supply at each midpoint, narrows the range toward whichever side is heavier, and repeats. After a small, fixed number of iterations the remaining price range is tight enough to use as the clearing price for the batch. Every step is evaluated on ciphertexts. The engine never learns whether demand exceeded supply at any given midpoint — it computes both aggregates as encrypted values and uses encrypted comparisons to steer the next iteration. ## Why bisection The search is a fixed-depth algorithm: no branching on plaintext, no early exit. That makes it compile cleanly into a straight-line FHE circuit with predictable multiplicative depth, deterministic runtime, and no side-channel leakage from iteration count. A batch takes the same wall-clock regardless of which bracket the true clearing price falls in. In principle a closed-form clearing price exists at the crossing. Computing it directly would require division by encrypted unknowns (numerically fragile) and branches on encrypted sign tests (expensive). Fixed-depth bisection trades optimality per iteration for determinism and predictability — the right trade for an FHE circuit. ## Output semantics At the final iteration the graph emits an encrypted clearing price, a per-lane encrypted fill for each side, and a one-bit convergence flag. The clearing price becomes public once the operator's re-encryption step releases it. The per-lane fills remain private to each participant, decryptable only through a proxy re-encryption from the participant's session key. Nothing in the graph exposes who matched with whom, at what size, or against which curve shape. The book stays encrypted from submit through clearing through settlement. ## Two views of the same search The interactive walkthrough at [dagon.so/how-it-works#mechanism ↗](https://dagon.so/how-it-works#mechanism) shows the bisection through two complementary visualizations: * **Rail view** — the price range narrowing toward a single point across iterations. * **Merge view** — demand and supply curves approaching a single crossing. Both views animate against the same trace. Drag the scrubber in the header to step through the search. ## See also How the engine fits a whole batch's curves into a compact FHE layout before the search runs. Step through the bisection at your own pace. Rail + merge views animate together.