mycelium: the network engine
appendix
reference definitions for the arithmetic above. notation is fixed throughout the document; nothing here introduces new mechanism, only restates it without the prose.
a.1 decay function
b(n) = b(0) × (1 − λ)^n
- b(n)
- balance at epoch n, after decay applied lazily at settlement
- b(0)
- balance recorded at the account's last-touch slot
- λ
- per-epoch decay rate, 0.0012 (0.12%)
- n
- epochs elapsed since last touch, (current_slot − last_slot) / 432,000
a.2 propagation weight
w(i) = (r(i) × a(i)) / Σ (r(j) × a(j))
- w(i)
- fraction of realized decay routed to counterparty i
- r(i)
- recency weight of edge i, decreasing with age since last interaction
- a(i)
- activity score of counterparty i, scaled by its own recent transaction volume
- Σ
- normalizing sum across all tracked edges of the decaying wallet
a.3 epoch definition
1 epoch = 432,000 slots ≈ 2.2 days
slot count is exact; the 2.2-day figure is a solana mainnet average and drifts with skip rate. n is rounded down — a partial epoch contributes nothing. no accrual is interpolated between slot boundaries.
a.4 distribution split
a stale wallet holding 10,000 mycelium, untouched for 30 epochs:
decay = b(0) − b(n)
decay = 10,000 − 10,000 × (1 − 0.0012)^30
decay = 10,000 × (1 − 0.964854) ≈ 351.46
351.46 mycelium realized, split as:
- grove members, pro-rata · 70%245.92
- substrate reserve · 25%87.87
- propagation gas and incentive · 5%17.57
the 351.46 is the realized decay at the moment of the next settlement. until then it exists only as arithmetic, not as stored state.
a.5 edge cap rationale
each wallet tracks its 8 to 16 most recent transaction edges on-chain. the bound exists because edge recency is stored per-account in account state, and every tracked edge costs rent and adds to the compute budget of a settlement. a fixed window keeps both bounded and constant per wallet regardless of graph density. older edges age out as new ones arrive; the oldest is dropped when the cap is reached, not when it crosses a threshold. this is a storage constraint stated plainly, not a compression strategy pretending to be one.
a.6 glossary
- grove
- a vault where deposited balances are sheltered from decay and weighted high in propagation
- substrate
- protocol-owned reserve accumulating 25% of decay plus a 25 bps fee, deployed as liquidity
- propagation
- redistribution of realized decay across a wallet's tracked counterparties, weighted by recency and activity
- node
- a wallet, treated as a vertex in the transaction graph rather than an isolated balance
- edge
- a directed transaction relationship between two wallets, stored with a recency weight
- epoch
- 432,000 slots, approximately 2.2 days; the unit over which decay accrues