the one thing
sigma shows the total balance of a neuron, valued in a token. everything else on this page exists to make that number true and to let the owner decide what "true" means.
the registry
sigma keeps the owner's registry of tokens. a token is any denomination the cybergraph can carry in a cyberlink's box, fungible or not: a coin of tok (TSP-1), a card (TSP-2), a foreign asset the owner chooses to track. an entry is
token the particle that names it
kind coin | card
unit the smallest count, and the scale it is shown in
price a method
balance a method
supply a method
the registry is born with one entry, cx, the default measure; every other entry is the owner's, kept in the book of the neuron: adding a token is a cyberlink from the neuron's name to the token's particle under the sigma dialect, and so is changing a method. two neurons may value the same token by different rules and both are right for their own sum.
the three measurements
every measurement is taken of a token, on a neuron, at a moment, and each token answers through its own method.
| measurement | question | signature |
|---|---|---|
| price | what is one unit of this token worth in that token | price(token, in: token, at: moment) → amount |
| balance | how much of this token does this neuron hold | balance(token, neuron, at: moment) → amount |
| supply | how much of this token exists | supply(token, at: moment) → amount |
a method is a rule that produces the number, and its provenance travels with the number: sigma reports the value and the tier it came from (proof-verified, anchor-verified, unproven, typed by hand), never the value alone. the tiers are those of state.
methods
a token may use any method for any measurement. the standard set ships with sigma; the owner may write others as rune cells.
price
book— the price the neuron's own book records for the token (the last box it moved, or a price link the neuron wrote)market— a quote from a named market or oracle, with the quote's identity and ageformula— a rule over other measurements: a share of a supply, a basket, a bonding curve, a fixed ratio to another tokenhand— a number the owner typed; the honest default for a token nobody quotes
balance
book— the sum of the neuron's boxes in the token, read from the cybergraph (the only balance that is provable)chain— a balance answered by a network the token lives on, through statehand— for what is held off any book
supply
conservation— mints minus burns per tok's conservation law; provable for tok coinschain— the supply a network reportsfixed— a cap or a declared numberhand
turnover is not a measurement. what moved, and when, is the log's business; sigma reads it when a method needs a rate and ignores it otherwise.
the derived quantities
with three measurements every token yields the rest without a fourth method:
- value of a holding:
balance(t, n) × price(t, in: k)for any numeraire k - the sum:
Σ_t balance(t, n) × price(t, in: k)over the registry — the number sigma exists for - share:
balance(t, n) / supply(t)— how much of a token this neuron is - capitalisation:
supply(t) × price(t, in: k) - the price of a token in any other:
price(a, in: b) = price(a, in: k) / price(b, in: k)for any k both are priced in; a token priced only byhandprices everything else through that hand
the numeraire k defaults to cx, the century index: a fixed basket of eight world assets (BTC, ETH, gold, CNY, USD, copper, oil, uranium), measured in itself constant, so a sum in cx keeps its meaning across years and across neurons. cx is a formula token in every registry from birth: its price in any leg is the published fix of the basket, its supply is undefined (it is a unit, not a coin), its balance is a holding of the cx token where one exists. the owner may set any other token as numeraire; the sum in a coin of the neuron's own book is the same computation with a different k.
what sigma is not
- not a wallet: it holds nothing and signs nothing; vault holds and signs, sigma spends by asking it
- not a market: it never quotes, it reads quotes
- not an accountant of flows: turnover, yield and cost basis are derived from the log by whoever needs them
surfaces
one registry, three faces: cy sigma prints the sum and the table in a terminal; the sigma world in cyb paints the same table; a cell may ask any measurement by name. the number on the page is last known and the method runs behind it (live).
open
- the sigma dialect of neural: the exact sentences for "register token", "set method", "price in"
- which methods are provable:
bookandconservationtoday;marketnever;formulawhen the inputs are - the seed: the owner's terminal sigma (positions, nine price sources, a cache) is the first implementation of
marketandhandmethods and is not public