The emission gate (spec 440)

The short version

Every block, the chain hands out TAO emission and each subnet competes for a slice. Until spec 440, a subnet’s slice was simply proportional to how much the market wanted it — twice the demand earned twice the emission. Spec 440 adds a gate: it draws a line, lets the sought-after subnets keep their full slice, chokes the barely-wanted ones toward zero, and hands the freed-up emission back up to the top.

How “wanted” a subnet is — its demand — is measured exactly as before. Only how that demand turns into emission changed.

1 · Building demand (`s`) — same math as before

Demand is built in three steps, unchanged from the price-based-shares design:

Step A — price. Each subnet’s raw demand is its moving alpha price — the EMA of its alpha token’s price against TAO from the AMM pool (get_moving_alpha_price). Staking TAO into a subnet’s pool bids its price up: higher price = more demand. Because it’s an EMA, a one-block spike can’t game it.
Step B — normalize into a share. Divide each subnet’s price by the sum of all prices → shares that sum to 1: sᵢ^price = movingPriceᵢ / Σⱼ movingPriceⱼ.
Step C — discount for miner burn, renormalize. Scale each share by (1 − miner_burned) and renormalize: sᵢ = sᵢ^price·(1 − minerBurnedᵢ) / Σⱼ sⱼ^price·(1 − minerBurnedⱼ). A full burner → 0. The result is the demand share s that feeds the gate.

Miner burn is a heavy first-stage filter, not a footnote: in the 2026-07-27 snapshot, 35 of 128 subnets burned 100% of their miner emission (zeroed out before the gate even sees them), 32 burned partially, and mean burn network-wide was ~43%.

2 · The bar (θ) — where the line sits

θ (“theta”) is a q-mass quantile on demand, recomputed every 360 blocks:

Sort all subnets’ demand shares largest → smallest.
Walk down, accumulating the shares.
The moment the running total crosses q = 0.61 (61% of all demand), stop. The share you’re standing on is θ, the bar.

Because shares sum to 1, “cumulative ≥ 0.61” means the top subnets together own 61% of demand. θ is a property of the demand distribution, not the subnet count — spinning up empty subnets adds no demand, so it can’t move the bar.

3 · The gate — a Hill function

gate(s) = s^h / (s^h + θ^h) = 1 / (1 + (θ/s)^h)

The two forms are identical; the chain computes the right-hand one because s^h underflows fixed-point precision for deep-tail shares, while the ratio θ/s stays well-conditioned. h (default 3, sudo-settable 1–8) sets how sharp the cliff is. The gate returns a number in [0, 1]:

Your demand `s` vs bar θ	gate(s)	Result
well above θ	→ 1.0	keep ~all your emission
exactly at θ	0.50	keep exactly half
well below θ	→ 0.0	emission choked toward zero

Then: renormalize (the redistribution)

eᵢ = sᵢ · gate(sᵢ) / Σⱼ sⱼ · gate(sⱼ)

Gating shrinks every share, but the block still emits a fixed total. Dividing by the new (smaller) sum scales the survivors back up — this is how the tail’s lost emission flows to the winners. A top subnet ends up emitting more than its raw demand share.

Then one more redistribution — emission-enabled subnets only

After the gate, the chain checks SubnetEmissionEnabled for each subnet. Any subnet with it set to false has its gated share zeroed and redistributed to the enabled subnets (a second renormalize over the enabled set only). This is a separate switch from miner burn — a subnet can clear every filter, survive the gate, and still be zeroed here. It’s the final stage, and it’s why the live emission a subnet actually receives is slightly higher than the gate alone would give.

4 · What it means

Emission is no longer proportional to demand. Any APY or emission figure that assumes a pro-rata split is now wrong for every subnet — winners are understated, the tail overstated.
The tail gets crushed. In the snapshot, ~38% of demand (below-bar subnets) collectively earned ~10% of emission. A low-demand subnet’s emission — and its miners’/validators’ yield — drops sharply.
Miner burn is a first-stage filter. Before the gate runs, (1 − miner_burned) zeroes or shrinks a subnet’s share. Any model that ignores burn will misplace which subnets earn.
The bar moves. θ recomputes every 360 blocks from live prices, so which subnets are “above the line” shifts as demand shifts. A static calculation will drift.
Two sudo knobs. q (default 0.61, bar height) and h (default 3, cliff sharpness) are both root-settable — a governance change to either reshapes every subnet’s emission at once.
A separate emission-enabled switch runs last. After the gate, any subnet with SubnetEmissionEnabled = false is zeroed and its share redistributed to the enabled subnets. It’s independent of demand, burn, and the gate — a subnet can survive everything else and still earn nothing.

Source provenance

Code: pallets/subtensor/src/coinbase/subnet_emissions.rs (v440 tag): get_subnets_to_emit_to / get_shares / maybe_update_emission_gate_bar / apply_emission_gate / get_subnet_block_emissions.
Spec: runtime version confirmed 440 on Finney (mainnet) via state_getRuntimeVersion.
Snapshot: demand = moving alpha price × (1 − miner burn), read off-chain at block 8,714,269 (2026-07-27 15:51 UTC), q = 0.61, h = 3, 126 emit-set subnets. θ landed at rank 18 (SN83), 1.339%. Reconciles to the live per-subnet emission Taostats displays (e.g. SN64 = 16.63% vs 16.67%).