SignalRank
Behavioral Trust Scoring · Math Specification
SignalRank is the user-visible trust score computed from five components: signal strength, coherence persistence, proof output, ProofNet trust, and mesh centrality. It represents behavioral trust — measured by process quality, not content quality.
1. Signal Features & Signal Vector
Each node $u$ is represented as a vector in $d$-dimensional signal space, derived from $n$ behavioral features observed at time $t$.
$$\vec{s}_u(t) = W \vec{x}_u(t) \in \mathbb{R}^d$$
$\vec{x}_u(t) \in \mathbb{R}^n$ — behavioral feature vector (clarity, originality, timing, proof output)
$W \in \mathbb{R}^{d \times n}$ — projection matrix mapping features to signal space
Scalar Signal Strength
$$S_u(t) = \vec{w}^\top \vec{x}_u(t)$$
2. Proof Score (Artifacts)
Artifacts generate proof. Each artifact $a$ has a quality score, witness weight, and recency factor that decays over time.
$$p(a) = q(a) \cdot w(a) \cdot e^{-\delta(t - t_a)}$$
$q(a) \in [0,1]$ — quality score of the proof artifact
$w(a) \geq 0$ — witness/credential weight
$\delta$ — recency decay rate
$t_a$ — timestamp of the artifact
Node Proof Total
$$P_u(t) = \sum_{a \in A_u(t)} p(a)$$
Redacted Proof Adjustment Core
When a proof is redacted (Right-to-Erasure or governance action), its contribution is zeroed via a redaction indicator.
$$p'(a) = p(a) \cdot (1 - R(a,t))$$
$R(a,t) = 1$ if a valid redaction proof for $a$ exists at time $t$; $0$ otherwise.
Redacted proof total: $P'_u(t) = \sum p'(a)$
3. Coherence Persistence
Signal must persist over time. Coherence is the rolling average of signal strength over window $W$.
$$C_u(t) = \frac{1}{W} \int_{t-W}^{t} S_u(\tau) \, d\tau$$
4. Stability (Signal vs Spiral)
Divergence detection prevents gaming. Stable signal requires bounded acceleration.
Velocity & Acceleration
$$V_u(t) = \left\| \frac{d\vec{s}_u}{dt} \right\|, \quad D_u(t) = \left\| \frac{d^2\vec{s}_u}{dt^2} \right\|$$
Spiral Risk Score
$$\Psi_u(t) = \alpha_V V_u(t) + \alpha_D D_u(t)$$
Stable-signal constraint: $\Psi_u(t) \leq \epsilon$. If exceeded, the node enters review.
5. SignalRank (Final Score) Core
The user-visible score blends five components:
$$R_u(t) = \alpha S_u(t) + \beta C_u(t) + \gamma P_u(t) + \delta T_u(t) + \zeta M_u(t)$$
$S_u$ — signal strength ·
$C_u$ — coherence persistence ·
$P_u$ — proof output
$T_u$ — ProofNet trust (see
ProofNet Math)
$M_u$ — mesh centrality (see
ProofMesh Math)
$\alpha, \beta, \gamma, \delta, \zeta$ — protocol weights
Normalization to 0–100
$$\hat{R}_u = 100 \cdot \frac{R_u - \min(R)}{\max(R) - \min(R)}$$
SignalRank Temporal Decay Core
SignalRank itself decays over time independent of signal vector decay, preventing stale scores from persisting.
$$R_u(t + \Delta t) = (1 - \phi \Delta t) \cdot R_u(t) + \Delta R_u(t)$$
$\phi$ — SignalRank decay rate
$\Delta R_u(t)$ — new rank contributions from proof, trust, and mesh activity in the current window
Adaptive Weights V2
In production, the protocol weights $\alpha, \beta, \gamma, \delta, \zeta$ should adapt based on system conditions and governance decisions.
$$\vec{\theta}(t+1) = \vec{\theta}(t) + \eta_\theta \nabla_\theta \mathcal{L}(\vec{\theta}, \text{system state})$$
$\vec{\theta} = (\alpha, \beta, \gamma, \delta, \zeta)$ — weight vector
$\mathcal{L}$ — loss function measuring system health (Sybil resistance, rank distribution fairness, spiral frequency)
$\eta_\theta$ — learning rate, bounded by governance constraints
Weight changes require governance proposal + quorum approval (see
Governance Math).
6. Practical Defaults
$d = 12$ dimensions · $\alpha = 0.20, \beta = 0.25, \gamma = 0.20, \delta = 0.20, \zeta = 0.15$ · $\delta_\text{recency} = 0.001$ per hour · $\phi = 0.0005$ per hour · $\epsilon = 2.0$ (spiral threshold)