adaptive hybrid economics
how cyber splits security spend between compute work and active stake without hard-coding arbitrary percentages. parameters self-calibrate from on-chain observables via control-theoretic feedback (P / PD / PID). applies to CYB hybrid mint under tok / plumb
normative home: this page under specs. equations for rewards: rewards. token utility surface: $CYB. historical long essay + minimal implementation notes lived under cybics game
problem
fixed issuance schedules and fixed PoW/PoS splits are bets about the future: security cost, fee volume, capital opportunity cost. the protocol cannot know those a priori. hard-coding them (21M, fixed 50/50, fixed tail emission) freezes ignorance into consensus
objective triad (in tension):
| objective | meaning |
|---|---|
| security | attack cost > attack profit |
| efficiency | do not overpay for security |
| dilution | mint only as much as security requires |
mechanism: sense and adapt — thermostat, not calendar
objects
| symbol | meaning |
|---|---|
| (M) | circulating supply |
| (S \in [0,1]) | active staked fraction (epistemic lock with (v \neq 0); not idle bag) |
| (E(t)) | baseline emission rate from schedule (for cyber: power-law head of CYB M(t), not a free knob) |
| (F) | fees collected in window |
| (\beta \in [0,1)) | fee burn fraction |
| (\alpha \in [0.3, 0.7]) | allocation curve exponent |
| (B) | gross reward budget this window |
allocation curve
Given staking ratio (S):
[ R_{\mathrm{PoS}} = B \cdot S^{\alpha},\qquad R_{\mathrm{PoW}} = B \cdot (1 - S^{\alpha}) ]
(neutral prior (\alpha = 0.5): equal marginal treatment of stake and work. (\alpha < 0.5) favors stake at low participation; (\alpha > 0.5) pulls toward compute)
why power: maps ([0,1]\to[0,1]), one parameter, smooth, no kink that governance can fight over
mapping to cyber mint channels
| share | pays | cyber realization |
|---|---|---|
| (R_{\mathrm{PoW}}) | compute | mining: prove Δφ* division + fold |
| (R_{\mathrm{PoS}}) | active risk | staking with valence ≠ 0; passive lock earns rank only |
see cyber/$CYB utility §mint
gross vs net
[ B = \mathrm{floor}\cdot M + (1-\gamma)(1-\beta)F ]
[ I_{\mathrm{net}} = \mathrm{floor} - \frac{F\beta}{M} ]
when diffusion burn exceeds floor, net inflation is negative: velocity shrinks supply while floor still pays security. gross rewards to workers can still exceed net mint when service fees recycle into (B)
fee path for CYB (cyber/$CYB §revenue):
- tax on diffusion (\tau = 1%) on every transfer — pay, lock, unlock, including staking
- simple split: (\mathrm{burn} = \tfrac12\tau G); (B_V = \tfrac12\tau G) paid to everyone who earns under the same hybrid as emission ((R_{\mathrm{PoW}}), (R_{\mathrm{PoS}})) — not a pro-rata airdrop to idle holders
- (B_{\mathrm{tot}} = B + B_V); velocity is the long-run self-development faucet when (M(t)) thins
- service fees (queries, DA, inference peer leg) may still feed (F) into (B); orthogonal to the diffusion tax
- (\beta) in the budget equations applies to any service-fee burn/pool split; diffusion tax already fixes half burn
security floor
floor is the one emission component not gated by Δφ* — paid only to work providers (PoW compute + active stake), never to idle capital. derived bound (attack economics sketch):
[ \mathrm{floor} \ge c_{\mathrm{sec}} \cdot \frac{\mathrm{TVL}}{M} \cdot r_{\mathrm{atk}} ]
with (c_{\mathrm{sec}}) safety margin and (r_{\mathrm{atk}}) attacker cost of capital per epoch. floor PID-decays toward zero as fees cover security (healthy coverage + healthy security margin)
staking equilibrium (sketch)
per-token active stake yield scales as (B \cdot S^{\alpha-1}/M). capital enters until yield meets opportunity cost (r):
[ S^* = \min!\left(1,\ \Big(\frac{B}{r M}\Big)^{\frac{1}{1-\alpha}}\right) ]
protocol does not target (S^*); it emerges. α moves the equilibrium sensitivity
feedback (PID)
errors from observables only — no price oracle required for the core loop:
| error | definition | drives |
|---|---|---|
| efficiency | (\eta_{\mathrm{PoW}} - \eta_{\mathrm{PoS}}) (security per reward unit) | (\alpha) |
| fee coverage | (F/E(t) - 1) (or (F/\mathrm{floor}-1)) | (\beta), floor |
updates (conceptual; gains as ops parameters):
[ \alpha \leftarrow \mathrm{clamp}\big(\alpha + K_{p\alpha} e_{\eta} + K_{d\alpha}\dot e_{\eta},\ 0.3,\ 0.7\big) ]
[ \beta \leftarrow \mathrm{clamp}\big(\beta + K_{p\beta} e_{F} + K_{d\beta}\dot e_{F},\ 0,\ 0.9\big) ]
derivatives via EMA. start P-only; add D if oscillation; full PID if volatility demands it
not PID-controlled: the long-horizon supply shape M(t) for CYB (power law, field cap) — that is genesis physics. hybrid control only allocates B and recycles fees inside that envelope
what this is not
- not a third consensus finality rule — foculus decides what is final; this decides how the security budget is paid
- not passive staking yield — idle lock does not mint (anti-compounding; see rewards)
- not a second emission schedule for robots — robot cards only redirect creator shares of mints/pays (cyber/$CYB)
cyber placement
| layer | owns |
|---|---|
| tru / rewards | Δφ*, Shapley, karma, mint eligibility |
| foculus | finality, settlement lottery timing |
| this design | α, β, floor dynamics; PoW/PoS split of B |
| tok / plumb | conservation of mint/burn/pay/lock |
sources
consolidated from:
- long form motivation + PID thesis (formerly cybics game adaptive hybrid consensus economics)
- minimal implementation notes (sliding window difficulty, on-proof handler) — formerly cybics game adaptive hybrid economics
implementation detail and simulation notebooks stay optional attachments; normative reward equations remain in rewards
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