x/emission

Code: chain/x/emission (see DECISIONS.md for why module code lives under chain/x/ rather than here).

Purpose

LCV has a fixed total supply of 10,000,000,000 LCV — nothing is ever minted after genesis. The 12% "staking rewards" allocation (1,200,000,000 LCV) is pre-funded into a module account (staking_rewards) at genesis. x/emission is the only thing that ever moves coins out of that account: every block it computes how much reward is due under an exponential decay curve and transfers that amount — never mints it — into the fee_collector account, where x/distribution's existing BeginBlocker picks it up and allocates it to the block proposer, bonded validators/delegators, and the community pool exactly as it does with transaction fees.

x/mint stays enabled (per the global spec) but is pinned to 0% inflation at genesis (InflationMin = InflationMax = InflationRateChange = 0), so it mints exactly zero coins every block — x/emission is the sole source of new-to-circulation staking rewards.

Decay curve

Let t be seconds elapsed since params.start_time (the genesis time, unless a genesis file explicitly overrides it), P = params.total_reward_pool, and H = params.half_life_seconds. Define:

lambda = ln(2) / H
rate(t) = lambda * P * e^(-lambda*t)          // instantaneous reward rate at time t
emitted(t1, t2) = P * (e^(-lambda*t1) - e^(-lambda*t2))   // closed-form integral of rate(t) from t1 to t2

emitted(0, ∞) = P: the curve asymptotically emits the entire pool but never exceeds it, and every block only ever transfers emitted(t_prev, t_now) for the actual elapsed wall time since the previous block (t_prev is persisted as LastEmissionTime), so the exact formula is used rather than a per-block-average approximation — no drift accumulates regardless of block time variance.

Default half_life_seconds is 2 years, chosen so that by year 10 (5 half-lives), 1 - 0.5^5 ≈ 96.9% of the pool has been emitted, matching the "10-year decaying emission" description in the top-level spec while leaving a long tail beyond that horizon rather than a hard cliff to zero.

All arithmetic (e^-x via a Taylor series, the pool multiplication) is done in cosmossdk.io/math.LegacyDec (arbitrary-precision fixed-point), never float64, so every validator computes bit-identical results — see chain/x/emission/keeper/decay.go.

State

• Params (0x00 key p_emission): mint_denom, staking_rewards_account, total_reward_pool (math.Int), half_life_seconds, start_time.
• LastEmissionTime (key last_emission_time): unix seconds up to which rewards have already been transferred; advances every block regardless of whether the computed amount was positive, so a chain halt/restart never double-pays for the downtime window once it resumes (the gap is paid out once, in the first block after restart).

Messages

• MsgUpdateParams (governance/authority-gated): updates all params atomically. Changing total_reward_pool or half_life_seconds takes effect only for time elapsed after the change (the closed-form integral is always evaluated between LastEmissionTime and the current block using the current params, so a mid-course correction doesn't retroactively rewrite past emissions).

BeginBlock

Runs immediately after x/mint and before x/distribution in app/app_config.go's beginBlockers order (mint stays first purely so both "issuance-shaped" modules are grouped together; the only ordering constraint that actually matters is emission-before- distribution). Each block:

1. Compute due = emitted(LastEmissionTime - start_time, now - start_time).
2. Clamp due to the staking_rewards account's actual balance (never errors on a depleted pool — emissions just stop).
3. Advance LastEmissionTime to now unconditionally.
4. If due > 0, SendCoinsFromModuleToModule(staking_rewards, fee_collector, due).

Invariants

• The staking_rewards module account never receives a Minter/Burner permission (app/app_config.go); it can only be drawn down by this module's SendCoinsFromModule call, and its genesis balance is fixed by the allocation script (scripts/genesis/) — so total LCV supply is invariant across the lifetime of the decay curve regardless of how emission plays out.
• emitted(t1, t2) < total_reward_pool for any finite t2 (strict asymptote), enforced by construction of the closed-form formula, not by a runtime check.

CLI note: hand-written params query command

lcvd query emission params is served by a hand-written command (chain/x/emission/client/cli/query.go) rather than the one AutoCLI would otherwise generate. See modules/feemarket/SPEC.md for the full explanation — the same AutoCLI/gogoproto-customtype gap applies here.

Limitations

• The Taylor series in expNeg is capped at 300 terms; this comfortably covers any lambda*t value corresponding to centuries of chain uptime at the default 2-year half-life; SPEC intentionally doesn't try to make this unbounded, since a value that large would indicate a params or clock bug worth surfacing rather than silently absorbing.
• Governance can change total_reward_pool upward via MsgUpdateParams with no on-chain check against the staking_rewards account's actual balance — the BeginBlock balance clamp means this can't overpay, but it also means a misconfigured increase silently has no effect once the account is exhausted rather than erroring. A future revision could add an explicit invariant comparing total_reward_pool against the funded balance at MsgUpdateParams time.