soft3/mudra/specs/neuron-measures.md

neuron measures

every scalar the protocol attaches to a neuron, in one place. a neuron is a particle (its identity is a Hemera hash, and hashes are particles), so it carries every per-particle measure plus the per-neuron ones. this page names them, says what each measures, and points at the repo that owns the computation.

the measures

measure scope what it is type transferable owner
identity neuron Hemera hash of the neuron secret; the address, itself a particle $\mathbb{F}_p^4$ no mudra
cyberank particle collective focus that lands on a node; the node's $\phi^*$ coordinate $[0,1]$ no tru
karma neuron accumulated Bayesian Truth Serum score; epistemic track record $\mathbb{R}$ no tru
focus balance neuron spendable energy; consumed per cyberlink (the costly signal) $\mathbb{R}_+$ yes tok
stake neuron $CYB locked across the neuron's conviction boxes | $\mathbb{R}_+$ locked tok
signals neuron ordered history of committed signals list cybergraph
conviction cyberlink $CYB committed to one edge (the amount $a$) | $\mathbb{R}_+$ locked tok
valence cyberlink the BTS meta-prediction $v \in \{-1, 0, +1\}$ ternary cybergraph
syntropy share neuron net information the neuron added: $\sum \Delta J$ over its signals $\mathbb{R}$ no tru

two reputations, not one

a neuron carries two distinct reputational scalars, and they answer different questions:

  • cyberank — reputation as attention. because the neuron's identity is a particle, the tri-kernel assigns it a $\phi^*$ coordinate like any node: how much collective focus flows to the neuron itself.
  • karma — reputation as track record. the accumulated Bayesian Truth Serum score: how often the neuron's cyberlinks carried genuine private signal the crowd had not yet priced in.

cyberank can be earned by being linked-to. karma can only be earned by being right before the crowd, and cannot be bought — it is the one measure that capital cannot purchase.

the composite

three of these combine into the weight a neuron's cyberlink carries in the tri-kernel effective adjacency:

$$A^{\text{eff}}_{pq} = \sum_\ell \underbrace{\text{stake}(\ell)}_{\text{capital}} \times \underbrace{\text{karma}(\nu(\ell))}_{\text{track record}} \times \underbrace{f(\text{ICBS price}(\ell))}_{\text{market belief}}$$

capital and market belief are buyable; karma is not. this is what keeps the value function honest before Shapley attribution splits it.

the risk dial

valence is a per-cyberlink choice of risk exposure, not a fixed tax:

  • $v = 0$ — passive stake. the conviction still weights the edge in $A^{\text{eff}}$, so it affects the rank, but it earns no staking reward. structure for free, yield for none.
  • $v = \pm 1$ — active epistemic bet. the conviction is wagered through the BTS zero-sum and earns from it: right pays, wrong pays the right.

a neuron picks its exposure link by link. passive capital shapes the graph but extracts no rent — reward flows only to non-zero valence. this is what keeps wealth from compounding by sitting still: idle stake cannot earn, only correct risk can.

reward, in terms of these

the impulse reward a neuron mints is its Shapley share of the joint focus shift, computed on the karma-weighted effective graph and bounded by the real global $\Delta\phi^*$:

$$\text{mint}(\nu) = \text{Shapley}_\nu(v), \qquad v(S) = \Delta\phi^*\big(\text{effective graph} + S\big)$$

karma enters through the value function $v$ (so copies and noise carry near-zero marginal); Shapley splits the result fairly and conserves by its efficiency axiom. because $v(S)$ is weighted by stake, splitting one neuron into many Sybils with the same total stake yields the same total share — stake-weighting makes the attribution split-proof. identity is cheap; stake and karma are not. see cyber/rewards for the full specification.

see also

Graph