machine

value·price·light·updated

Model

Every table and figure on this page is computed from the fixed parameters. None of it is a measurement and none of it needs the coin to exist. It is what the machine will do at any given volume, read off the formulas.

PARAMETERS

SYMBOL	MEANING	VALUE
P_i	pitch of coil i, USD of curve volume per full turn	250, 400, 650, 1000, 1600, 2500, 4000, 6500, 10000, 16000, 25000, 40000 for i = 1 to 12
A_i	asset of coil i	BTC, ZEC, XMR, ETH, SOL, NEAR for i = 1 to 6, repeating for i = 7 to 12
f	packet fraction, share of a coil's balance sold per vend	1/24
σ0	base spread the machine charges on every quote	0.30%
δ	spread step added per markup notch	0.05%
k	kick, degrees a coil loses when a sell exceeds its last vend	30
N	stale age, vends after which a tray packet burns	6
D_c	confirmation depth per source chain, in that chain's own units	bitcoin 6 blocks, zcash 10 blocks, monero 10 blocks, ethereum 32 slots, solana 32 slots, near 1 block

Δθ_i = 360 · sP_i(1.1)

The degrees coil i advances on a curve trade of size s dollars.

turns_i(V) = VP_i(1.2)

The cumulative turns of coil i after cumulative curve volume V.

vends_i(V) = ⌊VP_i⌋(1.3)

The vends coil i has fired after volume V, ignoring kicks.

packet_i = f · B_i(2.1)

The shelf asset sold on a vend of coil i, where B_i is the coil's balance at that moment.

B_i(n) = B_i(0) · (1 − f)^n(2.3)

The balance after n vends with no refills.

σ_i = σ0 + n_i · δ(3.1)

The spread on coil i after n_i sold outs.

θ_i′ = max(0, θ_i − k)(4.1)

A coil's rotation after a kick.

age(p) = vends since p entered the tray, stale ⇔ age(p) ≥ N(5.1)

A packet becomes stale after six later vends.

TURNS PER TRADE

TRADE SIZE	C1	C3	C6	C9	C12
$10	0.0400	0.0154	0.0040	0.0010	0.0003
$50	0.2000	0.0769	0.0200	0.0050	0.0013
$100	0.4000	0.1538	0.0400	0.0100	0.0025
$500	2.0000	0.7692	0.2000	0.0500	0.0125
$1,000	4.0000	1.5385	0.4000	0.1000	0.0250
$5,000	20.0000	7.6923	2.0000	0.5000	0.1250
$10,000	40.0000	15.3846	4.0000	1.0000	0.2500
$50,000	200.0000	76.9231	20.0000	5.0000	1.2500

VENDS PER VOLUME

VOLUME	C1	C3	C6	C9	C12	ALL COILS
$1,000	4	1	0	0	0	8
$10,000	40	15	4	1	0	104
$100,000	400	153	40	10	2	1067
$1,000,000	4000	1538	400	100	25	10693

fig. 1 · Total vends from all twelve coils against cumulative curve volume. The line is a staircase at small volumes and nearly straight above ten thousand dollars because the tight coils dominate.

PACKET SIZE

COIL BALANCE	PACKET	AFTER 6 VENDS	AFTER 24 VENDS
0.1	0.004167	0.077464	0.036008
0.5	0.020833	0.38732	0.18004
1	0.041667	0.774639	0.360079
5	0.208333	3.873197	1.800397
10	0.416667	7.746394	3.600794

SPREAD INCOME

FILL SIZE	NOTCH 0	NOTCH 2	NOTCH 4	NOTCH 8
$100	$0.30	$0.40	$0.50	$0.70
$1,000	$3.00	$4.00	$5.00	$7.00
$10,000	$30.00	$40.00	$50.00	$70.00
$100,000	$300.00	$400.00	$500.00	$700.00

fig. 2 · One coil at every thirty degree step. A kick moves the pointer one step left; a trade moves it right by size over pitch.

KICKS

ROTATION BEFORE	AFTER ONE KICK	AFTER TWO
0	0	0
15	0	0
30	0	0
90	60	30
180	150	120
359	329	299

Reading the model

The machine does not predict. These tables say what a given amount of trading does to the coils, which is arithmetic, and nothing about what price that trading happens at, which is not. A coin can trade a million dollars at a falling price and the machine will vend exactly as many times as the table says.

The packet fraction is small on purpose. One twenty fourth per vend means a coil that fires often sells often and small, and a coil that fires rarely still has most of its balance when it does. No single vend is large relative to the shelf.

The spread schedule is the only thing that remembers history. A coil that has sold out four times charges a tenth more than one that never has. That is the whole of the machine's pricing memory.