Record confirmed AMM accounting and routing decisions

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# Confirmed design decisions
Confirmed by Kyle through the design questionnaire on November 6, 2026. These decisions supersede the corresponding open questions and earlier alternatives; they describe the proposed design, not an implemented or deployed system.
## Liquidity and ownership
- Subsequent native-only deposits mint matching LIQ in the current pool reserve ratio.
- New LP shares are priced using net equity after the mint liability and accrued obligations, rather than gross reserves. Accrue rewards and charges before pricing entry.
- Matching LIQ minting creates an equal liability and therefore adds no net equity at the assumed 1:1 valuation; the native deposit contributes the new equity.
- LP interests are pooled fungible shares. Each share carries proportional reserve ownership, mint liability and accrued charges, including on transfers and partial exits.
- Withdrawals settle the allocated lien and accrued charges before returning the residual native/LIQ asset mix.
- Shortfall settlement uses 1:1 native-to-LIQ backing conversion. No additional equity buffer is selected beyond covering the lien and other obligations.
## Trading and withdrawal routing
- Use a constant-product curve as the initial design and simulation baseline, with swap fees still to be selected.
- The withdrawal proxy maximizes net native output among immediately executable routes, allowing split routing and respecting user minimum output and deadlines.
- Queued ordinary redemption is offered separately as an explicit user choice.
- Ordinary redemption capacity is reserved atomically against uncommitted eligible backing; gross staked balance is not necessarily immediately available liquidity.
- An AMM-routed withdrawal is a swap: LIQ enters pool reserves and the outstanding lien remains unchanged.
- Ordinary redemption burns LIQ and consumes ordinary backing without changing AMM reserves or its lien.
- Special-minted LIQ is fully fungible with ordinary LIQ. Only the designated AMM contract may use the new special-mint entrypoint, and ordinary withdrawal is enforced as proxy-only.
## Rewards and yield-support obligations
- Assess yield-support charges on the full outstanding special-mint lien.
- Match the applicable Liq reward-index changes rather than treating the diagram's 2.8% as a fixed rate. Exact chain-specific index integration remains to be verified.
- Pool-held LIQ earns ordinary rewards for LPs.
- Trading fees fund support payments; insufficient fee income reduces LP equity.
- If obligations exhaust available equity, preserve accrued debt and restrict operations that worsen the deficit. Allow repayment or recapitalization; detailed recovery and loss-allocation rules remain open.
## Remaining design and verification work
- Select swap fees and any protocol fee allocation.
- Verify Ethereum and Solana reward-index mechanics, including fee treatment, negative changes, reward realization and avoidance of double counting.
- Specify exact net-equity share issuance, rounding, partial-exit and last-LP formulas; validate protection against deposit-price manipulation.
- Define deficit detection, allowed recovery operations and loss allocation.
- Specify proxy quotes, reservation accounting, queue behavior and atomic settlement.
- Validate entry, swaps, reward payments, external redemption and full exit together in worked examples and simulations.
- Resolve native versus wrapped asset interfaces and chain-specific authority, callback and transfer-hook integration.