DEX AMM and pool reserves

EN source master · P11-L01 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications; this is neither runtime content nor certification.

A pool's displayed ratio is not the average price available for an arbitrary-size swap.

Name the mechanism and version

An automated market maker (AMM) exchanges against pooled assets rather than matching another user's posted order [AMM]. Different versions and pool designs require different accounting. This lesson uses a frictionless full-range constant-product model inspired by v2; fees, transfer-tax tokens, concentrated liquidity and external transactions are excluded.

Write reserve units

Let x be reserve of assetX and y reserve of assetY. Under no-fee x×y=k, adding Δx yields new y=k/(x+Δx), so output Δy=y−k/(x+Δx). The marginal Y-per-X ratio is y/x [V2]. It describes a tiny local change; average finite-swap output per input differs because reserves change along the path.

Inspect the state transition

With x100 X,y1000 Y, k100000 X·Y. Input10 X leavesx110, y909.0909, output 90.9091 Y. Average 9.0909 Y/X is below starting ratio 10; post-swap ratio 8.26446 Y/X is a different number again. Label all three instead of calling each 'price'.

Mechanism is not safety

A large reserve or TVL number does not authenticate withdrawability, genuine token value, contract permissions or future liquidity. LP withdrawal, token transfer rules, execution ordering and network cost can change the real outcome. Documentation explains the model; fictional reserve values are not externally observed. No live swap or wallet interaction is required.

• Reserve: model's amount held for each asset.
• Invariant: rule relating reserves during the modeled swap.
• Marginal ratio: local reserve ratio with units.
• Average execution: total modeled output divided by input.

ILLUSTRATIVE poolSIM-X/Y with x100 X,y1000 Y, fee 0 and invariant100000 X·Y; input 10 X. All values are fictional, with unlimited toy precision; no chain or contract address.

AMM reserve/LP structure diagram: before 100 X/1000 Y, after 110 X/909.0909 Y, output 90.9091 Y; separate start, average and final ratios. No TVL safety badge.

The fictional no-fee reserve transition and distinction among three price descriptions.

Actual reserves, safety, executable depth, a real token valuation or current protocol parameters.

• OBSERVED: FIX-P11-L01 stipulates starting reserves 100/1000.
• INFERRED: output 90.9091 Y follows from the no-fee invariant.
• UNKNOWN: any real pool's token permissions and withdrawals.
• INSUFFICIENT EVIDENCE: knowing the mechanism proves the assets safe.

• Multiplying input by starting ratio as exact output.
• Applying v2 assumptions to every AMM.
• Calling reserve value available exit liquidity.

Calculate k, new reserves, output, starting ratio, average execution and ending ratio. Name three exclusions that would require new inputs in a real claim.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• Name model/version.
• Carry reserve and price units.
• Separate marginal/average/final.
• State safety and execution exclusions.

AMM reserve arithmetic explains a conditional exchange mechanism; finite execution, marginal ratio and safety are separate questions.

• Distinguish marginal reserve ratio from finite-swap execution.
• Identify which AMM version and assumptions the model represents.

P11-L02 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [AMM] Uniswap — How it works — Pools exchange assets with prices responding to relative reserves; version scope matters. Checked 2026-10-01; locator turn9view6.
• [V2] Uniswap v2 core whitepaper (March 2020) — Reserve ratio, constant-product mechanics and input-fee invariant; version-specific, not a live deployment snapshot. Checked 2026-10-01; locator turn14view0.