box

a box is conviction made concrete: amount units of a coin denomination, owned by a neuron, bound to a cyberlink record.

$$\text{box} \;=\; (coin,\; amount) \;\in\; \text{Coin} \times \mathbb{R}_+$$

the pair is the unit. amount alone is a context-free number; a coin alone is a denomination. neither is conviction until paired. the pair is the conviction, and the conviction is the box.

a cyberlink is a link carrying a box, with a valence:

$$(from,\; to,\; coin,\; amount,\; v) \;\longrightarrow\; \text{link}(from,\,to) + \underbrace{(coin,\,amount)}_{\text{box}} + \underbrace{v}_{\text{valence}}$$

(a non-fungible transfer is the special case where the box holds a card with amount = 1 rather than a coin — the same move, a unique token instead of a fungible quantity.)

moving a box

creating a cyberlink is a transaction: the author moves a box from the source from to a new output bound to the cyberlink record. value always moves from one object to another — a box leaves one place and arrives in another, never appears from nothing. this is the whole model: boxes move.

from ──[ box = (token, a) ]──▶ output bound to ℓ

lifecycle

a box bound to a record can itself be spent:

transfer is how a card's transferability works at the protocol level. withdraw is how economic delete works — the assertion is permanent, the position is liquid.

the box is not the assertion

the assertion cannot move or close; the box can be transferred, withdrawn, or spent. the two coexist in one record and are separable.

what a box weighs in the graph

a box's magnitude is the economic force that shapes the tri-kernel fixed point φ*. it feeds the adjacency operator:

$$A_{pq} = \sum_{\substack{\ell \in L \\ \operatorname{src}(\ell)=p,\; \operatorname{tgt}(\ell)=q}} r(\tau(\ell)) \cdot a(\ell)$$

where r: TokenId → ℝ₊ converts denomination to a common scale. higher box value → higher edge weight → more focus through the link → higher cyberank for the target.

with karma and ICBS markets active, the box is one of three factors in effective adjacency:

$$A^{\text{eff}}_{pq} = \sum_\ell a(\ell) \cdot \kappa(\nu(\ell)) \cdot f(m(\ell))$$

a large box with low karma or low market price contributes little — all three must align.

costly signaling

every box makes a cyberlink a costly signal. a neuron with finite will and tokens must choose where to place boxes — directing value to one claim directs it away from all others. this scarcity is what makes the cybergraph accumulate weighted commitments rather than cheap assertions.

yield

a box earns in proportion to how much its target gains focus:

$$R_\ell(T) = \int_0^T w(t) \cdot \Delta\phi^*(to, t)\, dt$$

where w(t) includes the box value a. the first-mover premium applies: the same box placed early (when φ*(to) is low) earns more than placed late. early discovery is maximally rewarded.

the conviction spectrum

authenticated realization

the conceptual box is realized in bbg as a mutator-set record: a commitment in the private polynomial A(x) (the box exists) and a nullifier in N(x) (the box was spent). bbg's BoxMove { nullifier, commitment } is exactly one box leaving (nullifier) and one arriving (commitment). double-spend is N(n) = 0 — structural rejection, no balance check needed. see cyber/bbg box structure for the cryptographic mechanics.

see token for the denomination τ · amount for the magnitude a · cyberlink for the record the box binds to · will for the budget that constrains where boxes go · staking for box placement as a graph act.