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igneum/sim/economy/sim.py
igneum-labs c1a44387ee Economy: agent-based mining-versus-proving simulation, six stress scenarios, lever study, analysis and bench entry 
sim/economy/sim.py: 1,000 operators choosing MINE, PROVE, HYBRID or OFF per card class with their own clients; sortition by weight with the 10-s window then open claiming, external jobs with the 90/10 split, backlog rule, difficulty clamps, GBM price. Scenarios a to f, 5 seeds: no backlog, no window miss, hash floor 0.74 of pre-event. Traffic sensitivity finds the shortage oscillation only above the proving fleet's capacity (100 to 300 shards per block); at 100 the sortition window (10 s to 20 s) is the lever that removes it. docs/analysis/economy-2026-10-04.md holds the model, assumptions, results, worst case and the proposal (window = p90 shard time plus a swap, 25 s at today's targets; B_p tied to the live fleet), not applied.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
2026-10-03 23:16:46 +00:00

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#!/usr/bin/env python3
"""Igneum economy simulator: GPU operators choosing between mining and proving.
Agent-based model of N operators (default 1,000) with heterogeneous card fleets and electricity
prices. Every operator runs its own client and maximises its own profit: every ten minutes (own
phase) it compares, per card class, the expected profit of MINING (lottery share of the 80%
emission), PROVING (internal shards from the 20% pool by sortition then open claiming, plus
external jobs in dollars settled in IGN with a burn) and HYBRID (mine, prove only the shards it is
assigned, program swap each way), and switches when the gain beats its own hysteresis. Nothing is
scheduled centrally.
Time is in ticks of TICK seconds (180 s). Everything that happens inside a tick (the 10-s sortition
window, shard times of 6 to 20 s, open-claim races) is resolved with closed-form rates; everything
across ticks (hash, difficulty, backlog, weights, modes, price) is state. Blocks, shards, jobs and
block attribution are sampled; shard allocation across operators is fluid (expected values).
All figures are approximate unless the source says measured (RTX 5090 229 MH/s is measured,
docs/bench-log.md). See docs/analysis/economy-2026-10-04.md for the assumptions table.
Usage
python3 sim.py six scenarios, 5 seeds, markdown to stdout
python3 sim.py --scenarios b --seeds 1 one run
python3 sim.py --levers b --seeds 3 lever study on scenario b
python3 sim.py --set pool=0.3,window=20 override parameters
python3 sim.py --dump b --seeds 1 hourly trajectory CSV for scenario b
"""
import argparse
import math
import sys
import time
import numpy as np
# ---------------------------------------------------------------- parameters (all approximate)
P = dict(
tick=180.0, # s per tick
days=30,
n_ops=1000,
emission=31.688, # IGN per block, pre-halving, ramp complete (spec 2.5)
pool=0.20, # proving pool share of emission (spec 2.5, 5.3)
window=10.0, # sortition exclusive window, s (spec 7.2)
assignees=8, # provers drawn per shard (spec 7.2)
burn=0.10, # external job burn (spec 5.4)
timeout=300.0, # external job claim timeout, s (O-5.6, open; design 6 says 3,600 blocks to expire)
shards_per_block=3.0, # internal demand, shards (3060-20-s units) per block at launch traffic
job_work=10.0, # shard-equivalents of work per external job
ext_usd_day=2000.0, # external demand, dollars per day (customer brief: market low millions/yr)
ext_mult=1.0, # scenario multiplier on the dollar price per job
price0=0.012, # $ per IGN at t=0
vol_day=0.05, # price daily volatility
swap=5.0, # program swap, s each way (hybrid)
aggregation=4.0, # aggregation plus inclusion, s, added to every block proof
waste=0.5, # wasted duplicate attempts per open-claim shard (race losers)
hyst_lo=0.05, hyst_hi=0.25,
dwell_ticks=20, # minimum ticks between switches of one (operator, class): 1 h
decide_every=4, # ticks between decisions: 12 min
ema_ticks=20.0, # observation window for realised rates: 1 h
farm_share=0.20, # operator 0 share of total hash
backlog_rule=600.0, # s of oldest age per halving of B_p (design 4.3)
)
# card classes: 5090 (measured hash), 3090, 3060, small (approximate)
CLS = ["5090", "3090", "3060", "small"]
HASH = np.array([229.0, 57.0, 46.0, 25.0]) # MH/s
PMINE = np.array([450.0, 320.0, 170.0, 120.0]) # W while hashing
PPROVE = np.array([500.0, 350.0, 170.0, 0.0]) # W while proving
PIDLE = np.array([60.0, 50.0, 30.0, 0.0]) # W proving-ready, idle
TPROVE = np.array([6.0, 12.0, 20.0, 1e9]) # s per shard (3060 = phase 2 gate target); small cannot prove
CANHYB = np.array([True, True, False, False]) # hybrid needs the dataset and the prover resident: 24 GB cards only
MIX = np.array([0.25, 0.25, 0.30, 0.20]) # fleet mix by card count
CANPROVE = np.array([True, True, True, False])
OFF, MINE, PROVE, HYB = 0, 1, 2, 3
def build_population(rng, p, extra=0):
n = p["n_ops"] + extra
size = np.maximum(1, np.round(rng.lognormal(math.log(5.0), 1.2, n))).astype(int)
cards = np.zeros((n, 4), dtype=float)
for i in range(n):
cards[i] = rng.multinomial(size[i], MIX)
# electricity: farms cheaper; lognormal around $0.10/kWh
z = (np.log(size) - np.log(5.0)) / 1.2
elec = np.exp(rng.normal(math.log(0.10) - 0.25 * z, 0.40, n))
elec = np.clip(elec, 0.02, 0.40)
# operator 0: the farm, all 5090s, sized to farm_share of total hash, cheap power
cards[0] = 0
rest = (cards[1:p["n_ops"]] * HASH).sum()
farm_hash = rest * p["farm_share"] / (1 - p["farm_share"])
cards[0, 0] = max(1, round(farm_hash / HASH[0]))
elec[0] = 0.05
hyst = rng.uniform(p["hyst_lo"], p["hyst_hi"], n)
phase = rng.integers(0, p["decide_every"], n)
return cards, elec, hyst, phase
class Sim:
def __init__(self, scenario, seed, p):
self.p = dict(p)
self.sc = scenario
self.rng = np.random.default_rng(seed)
p = self.p
extra = 0
if scenario == "f":
extra = 200
if scenario == "e":
p["farm_share"] = 0.30
self.cards, self.elec, self.hyst, self.phase = build_population(self.rng, p, extra)
self.n = self.cards.shape[0]
self.n_base = p["n_ops"]
self.active = np.ones(self.n, bool)
if extra:
self.active[self.n_base:] = False
# the incoming pool: 200 operators sized so their hash equals the base hash
base_hash = (self.cards[: self.n_base] * HASH).sum()
pool_hash = (self.cards[self.n_base:] * HASH).sum()
self.cards[self.n_base:] *= base_hash / pool_hash
self.cards[self.n_base:] = np.round(self.cards[self.n_base:])
self.elec[self.n_base:] = np.clip(self.elec[self.n_base:], 0.02, 0.08)
self.mode = np.full((self.n, 4), MINE, dtype=int)
self.mode[self.cards == 0] = OFF
# initial allocation: cards with cheap power start a fifth of their provable cards proving
for i in range(self.n):
for c in range(3):
if self.cards[i, c] > 0 and self.rng.random() < 0.20:
self.mode[i, c] = PROVE
if not self.active.all():
self.mode[~self.active] = OFF
self.fixed_mine = np.zeros(self.n, bool)
self.withhold = np.zeros(self.n, bool)
if scenario == "e":
self.fixed_mine[0] = True
self.withhold[0] = True
self.mode[0] = np.where(self.cards[0] > 0, MINE, OFF)
self.dead = np.zeros(self.n, bool)
# weight: 30-day ring of mined blocks per operator, seeded from hash shares
self.hist = np.zeros((self.n, 30))
h0 = (self.cards * HASH * (self.mode != OFF)).sum(1)
h0[~self.active] = 0
self.hist[:] = (h0 / h0.sum() * 86400.0)[:, None]
self.w = self.hist.sum(1)
self.cards_active = self.cards[self.active].sum()
self.day = 0
self.last_switch = np.full((self.n, 4), -10**9, dtype=int)
self.price = p["price0"]
self.H_est = h0.sum() * 1e6
self.D = self.H_est * 1.0 # expected hashes per block, 1 block/s
self.q = 0.0 # backlog, shards
self.age = 0.0 # oldest unproven block age, s
self.duty = np.zeros((self.n, 4)) # hybrid proving duty
# observed rates (EMA)
self.R_hash = p["emission"] * (1 - p["pool"]) / self.H_est # IGN per hash per s
self.open_pc = np.zeros(4) # $ per hour per PROVE card by class, open claims
self.asg_pw = 0.0 # $ per hour per unit weight, assigned shards
self.asg_pw_h = 0.0 # same for hybrid responders
self.asg_ext_pw = 0.0 # $ per hour per unit weight, assigned external jobs
self.t_open = p["window"] + TPROVE[0]
self.eligible = CANPROVE.copy()
self.ok60 = 1.0
self.ok20 = 1.0
self.hourly = []
self.hour_acc = []
self.cls_profit = np.zeros(4)
self.cls_cards = np.zeros(4)
self.cls_shards = np.zeros(4)
self.ext_served = 0.0
self.ext_demand = 0.0
self.burned_ign = 0.0
self.switches = 0
# ------------------------------------------------------------ one tick
def step(self, t):
p = self.p
T = p["tick"]
day_f = t * T / 86400.0
rng = self.rng
# scenario events
if self.sc == "d" and day_f >= 10 and not self.dead[0]:
self.dead[0] = True
self.mode[0] = OFF
if self.sc == "f" and day_f >= 10 and not self.active[self.n_base]:
self.active[self.n_base:] = True
self.mode[self.n_base:] = np.where(self.cards[self.n_base:] > 0, MINE, OFF)
self.cards_active = self.cards[self.active].sum()
ext_mult = p["ext_mult"]
if self.sc == "b" and day_f >= 7:
ext_mult = 10.0
if self.sc == "c":
ext_mult = 0.0
# price
dt = T / 86400.0
self.price *= math.exp(p["vol_day"] * math.sqrt(dt) * rng.standard_normal() - 0.5 * p["vol_day"] ** 2 * dt)
if self.sc == "b" and 7 <= day_f < 14:
self.price *= math.exp(math.log(0.30) / (7 * 86400.0 / T))
price = self.price
cards, mode = self.cards, self.mode
is_m = mode == MINE
is_p = mode == PROVE
is_h = mode == HYB
# hash
hcards = cards * HASH * 1e6
h_op = (hcards * (is_m + is_h * (1 - self.duty))).sum(1)
H = h_op.sum()
if H <= 0:
H = 1.0
# difficulty controller (dual-lane response approximated: 120-block estimate, 3%/10% clamps)
lam = T * H / self.D
blocks = rng.poisson(lam)
self.H_est += (H - self.H_est) * min(1.0, blocks / 120.0)
ratio = self.H_est / self.D
ratio = min(max(ratio, 0.90 ** blocks), 1.03 ** blocks)
self.D *= ratio
E = p["emission"]
# mined blocks per operator
mined = rng.multinomial(blocks, h_op / H) if blocks > 0 else np.zeros(self.n, int)
self.hist[:, self.day % 30] += mined
self.w += mined
w = self.w # a dead operator's weight stays in the window until it ages out
W = w.sum()
mine_ign = mined * E * (1 - p["pool"])
pool_ign = blocks * E * p["pool"]
# internal shard demand with the backlog rule
spb = p["shards_per_block"] * 0.5 ** math.floor(self.age / p["backlog_rule"])
shards = rng.poisson(blocks * spb) if blocks > 0 else 0
pool_per_shard = pool_ign / shards if shards > 0 else 0.0
# capacities in shard-equivalents per tick
capP = np.where(is_p, cards * T / TPROVE, 0.0)
capP[:, 3] = 0
capH = np.where(is_h, cards * T / (TPROVE + 2 * p["swap"]), 0.0)
capH[:, 2:] = 0
capP[self.dead | ~self.active] = 0
capH[self.dead | ~self.active] = 0
capP_op = capP.sum(1)
capH_op = capH.sum(1)
resp = ((capP_op + capH_op) >= 1.0) & ~self.withhold & ~self.dead
a = (w * resp).sum() / W if W > 0 else 0.0
p_resp = 1 - (1 - a) ** p["assignees"]
shards_served = np.zeros((self.n, 4))
# external jobs
jobs_usd = p["ext_usd_day"] * ext_mult
job_price = (p["ext_usd_day"] / (p["ext_usd_day"] / 50.0)) * ext_mult # $50 per job baseline
jobs = rng.poisson(p["ext_usd_day"] / 50.0 * T / 86400.0) if jobs_usd > 0 else 0
ext_work = jobs * p["job_work"]
ext_pay_per_shard = job_price / p["job_work"] * (1 - p["burn"])
eligible = (p["job_work"] * TPROVE <= p["timeout"]) & CANPROVE
ext_served = np.zeros((self.n, 4))
ext_asg = [0.0]
ext_open = np.zeros(4)
self.ext_demand += ext_work
internal_first = pool_per_shard * price >= ext_pay_per_shard
def serve_external():
# jobs are assigned by the same sortition as shards (design 6), claimed with a bond, so the
# assignee keeps the job: the assigned part goes by weight, the rest is open and the fastest
# eligible proving card claims it; what nobody can take before the deadline expires.
nonlocal ext_work
if ext_work <= 0:
return
capE_P = capP * eligible
capE_H = capH * eligible
capE_op = capE_P.sum(1) + capE_H.sum(1)
respE = (capE_op >= 1.0) & ~self.withhold & ~self.dead
aE = (w * respE).sum() / W if W > 0 else 0.0
pE = 1 - (1 - aE) ** p["assignees"]
s_asg = ext_work * pE
over = 0.0
wrE = w * respE
WrE = wrE.sum()
if s_asg > 0 and WrE > 0:
x = s_asg * wrE / WrE
got = np.minimum(x, capE_op)
over = s_asg - got.sum()
capE = capE_P + capE_H
frac = capE / np.maximum(capE.sum(1, keepdims=True), 1e-9)
alloc = got[:, None] * frac
ext_served[:] += alloc
ext_asg[0] += got.sum()
usedP = alloc * (capE_P / np.maximum(capE, 1e-9))
capP[:] -= usedP
capH[:] -= alloc - usedP
else:
over = s_asg
open_w = ext_work - s_asg + over
for lat, cap, c in self.open_order(capP, capH):
if not eligible[c] or open_w <= 0:
continue
tot = cap[:, c].sum()
if tot <= 0:
continue
take = min(open_w, tot / (1 + p["waste"]))
alloc = cap[:, c] * (take / tot)
ext_served[:, c] += alloc
ext_open[c] += take
cap[:, c] -= alloc * (1 + p["waste"])
open_w -= take
ext_work = open_w
if not internal_first:
serve_external()
# assignee race: class mix of responders
wr = w * resp
Wr = wr.sum()
if Wr > 0:
capPH = capP + capH
share = capPH / np.maximum(capPH.sum(1, keepdims=True), 1e-9)
mixP = (wr[:, None] * (capP / np.maximum(capPH.sum(1, keepdims=True), 1e-9))).sum(0) / Wr
mixH = (wr[:, None] * (capH / np.maximum(capPH.sum(1, keepdims=True), 1e-9))).sum(0) / Wr
else:
mixP = np.zeros(4)
mixH = np.zeros(4)
t_open = p["window"] + np.inf
for lat, cap, c in self.open_order(capP, capH):
if cap[:, c].sum() > 0:
t_open = p["window"] + lat
break
LA_P = TPROVE
LA_H = TPROVE + p["swap"]
winP = (LA_P <= t_open) * mixP
winH = (LA_H <= t_open) * mixH
p_win = winP[:3].sum() + winH[:3].sum() # given p_resp
s_asg = shards * p_resp * p_win
# allocate assigned shards by weight, cap by capacity
if s_asg > 0 and Wr > 0:
x = s_asg * wr / Wr
capPH_op = capP.sum(1) + capH.sum(1)
got = np.minimum(x, capPH_op)
overflow = s_asg - got.sum()
# split within operator across classes by capacity
capPH = capP + capH
frac = capPH / np.maximum(capPH.sum(1, keepdims=True), 1e-9)
alloc = got[:, None] * frac
shards_served += alloc
usedP = alloc * (capP / np.maximum(capPH, 1e-9))
usedH = alloc - usedP
capP -= usedP
capH -= usedH
else:
overflow = s_asg
open_new = shards - s_asg + overflow
q_prev = self.q
open_total = open_new + q_prev
served_open = 0.0
open_by_cls = np.zeros(4)
open_lat = np.zeros(4)
for lat, cap, c in self.open_order(capP, capH):
tot = cap[:, c].sum()
if tot <= 0 or open_total - served_open <= 0:
continue
take = min(open_total - served_open, tot / (1 + p["waste"]))
alloc = cap[:, c] * (take / tot)
shards_served[:, c] += alloc
open_by_cls[c] += take
open_lat[c] += take * lat
cap[:, c] -= alloc * (1 + p["waste"])
served_open += take
self.q = max(0.0, open_total - served_open)
if internal_first:
serve_external()
self.ext_served += ext_served.sum()
# backlog age and proof latency
arr_rate = max(shards / T, 1e-9)
if self.q <= 0:
self.age = 0.0
elif served_open >= q_prev:
# the old queue drained this tick; what is left arrived this tick
self.age = min(T, self.q / arr_rate) + p["window"] + TPROVE[2]
else:
self.age += T
wait = q_prev / max(served_open / T, 1e-9) if q_prev > 0 else 0.0
thr60 = 60.0 - p["aggregation"]
thr20 = 20.0 - p["aggregation"]
p_q = min(1.0, max(0.0, (open_new - max(0.0, served_open - q_prev)) / max(shards, 1e-9))) if shards > 0 else 0.0
# the assignee branch only counts where it wins; losers were served open
pa = p_resp
p_assigned_won = pa * p_win
okA60 = pa * (((LA_P <= t_open) & (LA_P <= thr60)) * mixP)[:3].sum() + pa * (((LA_H <= t_open) & (LA_H <= thr60)) * mixH)[:3].sum()
okA20 = pa * (((LA_P <= t_open) & (LA_P <= thr20)) * mixP)[:3].sum() + pa * (((LA_H <= t_open) & (LA_H <= thr20)) * mixH)[:3].sum()
if open_by_cls[:3].sum() > 0:
# open-served shards: latency = window + wait + class time, class by share served
l_open = p["window"] + wait + open_lat[:3] / np.maximum(open_by_cls[:3], 1e-9)
sh = open_by_cls[:3] / open_by_cls[:3].sum()
okO60 = (sh * (l_open <= thr60)).sum()
okO20 = (sh * (l_open <= thr20)).sum()
else:
okO60 = okO20 = 0.0
p_open_served = max(0.0, 1 - p_assigned_won - p_q)
ps60 = min(1.0, okA60 + p_open_served * okO60)
ps20 = min(1.0, okA20 + p_open_served * okO20)
lam_s = max(spb, 1e-9)
def block_ok(ps):
return (math.exp(-lam_s * (1 - ps)) - math.exp(-lam_s)) / (1 - math.exp(-lam_s))
self.ok60 = block_ok(ps60)
self.ok20 = block_ok(ps20)
# income and power
prove_ign = shards_served * pool_per_shard
ext_usd = ext_served * ext_pay_per_shard
self.burned_ign += ext_served.sum() * (job_price / p["job_work"]) * p["burn"] / max(price, 1e-9)
busyP = np.where(is_p, np.minimum(1.0, (shards_served + ext_served) * TPROVE / np.maximum(cards * T, 1e-9)), 0.0)
busyP[:, 3] = 0
dutyH = np.where(is_h, np.minimum(1.0, (shards_served + ext_served) * (TPROVE + 2 * p["swap"]) / np.maximum(cards * T, 1e-9)), 0.0)
dutyH[:, 3] = 0
self.duty = dutyH
kwh = cards * T / 3600.0 / 1000.0
power_w = is_m * PMINE + is_p * (busyP * PPROVE + (1 - busyP) * PIDLE) + is_h * ((1 - dutyH) * PMINE + dutyH * PPROVE)
cost = kwh * power_w * self.elec[:, None]
# mining income per class within operator by hash share
hsh = hcards * (is_m + is_h * (1 - self.duty))
hfrac = hsh / np.maximum(hsh.sum(1, keepdims=True), 1e-9)
mine_usd = (mine_ign * price)[:, None] * hfrac
inc = mine_usd + prove_ign * price + ext_usd
profit = inc - cost
# observed rates
al = 1.0 / p["ema_ticks"]
self.R_hash += ((blocks * E * (1 - p["pool"]) / H / T) - self.R_hash) * al
nPH_cls = (np.where(is_p | is_h, cards, 0.0)).sum(0)
open_inc = open_by_cls * pool_per_shard * price + ext_open * ext_pay_per_shard # $ by class from open claims
open_pc = np.where(nPH_cls > 0, open_inc / np.maximum(nPH_cls, 1e-9), 0.0) * 3600.0 / T
self.open_pc += (open_pc - self.open_pc) * al
asg_usd = (s_asg - overflow) * pool_per_shard * price
asg_pw = asg_usd / max(Wr, 1e-9) * 3600.0 / T
self.asg_pw += (asg_pw - self.asg_pw) * al
asg_ext_pw = ext_asg[0] * ext_pay_per_shard / max(W, 1e-9) * 3600.0 / T
self.asg_ext_pw += (asg_ext_pw - self.asg_ext_pw) * al
self.t_open = t_open
self.eligible = eligible
# decisions
self.decide(t, price, w, Wr, p_resp, p_win, t_open)
# accumulate hourly
ca = max(self.cards_active, 1)
n_p = (cards * is_p).sum()
n_h = (cards * is_h).sum()
n_m = (cards * is_m).sum()
self.hour_acc.append((
H / 1e6, (hcards * (mode != OFF)).sum() / 1e6, n_p / ca,
n_h / ca, 1 - (n_p + n_h + n_m) / ca,
blocks / T, self.D, self.q, self.age, self.ok60, self.ok20, price,
ext_served.sum(), ext_work, shards,
))
self.cls_profit += profit.sum(0)
self.cls_cards += (cards * self.active[:, None]).sum(0)
self.cls_shards += shards_served.sum(0)
if len(self.hour_acc) * T >= 3600:
arr = np.array(self.hour_acc)
self.hourly.append(arr.mean(0).tolist() + [arr[:, 8].max(), arr[:, 0].min()])
self.hour_acc = []
if (t + 1) * T % 86400 == 0:
self.day += 1
self.w -= self.hist[:, self.day % 30]
self.hist[:, self.day % 30] = 0
def open_order(self, capP, capH):
"""Open-claim service order: the fastest responder wins the race. PROVE cards at their shard
time, HYBRID cards at shard time plus one program swap."""
p = self.p
order = [(TPROVE[c], capP, c) for c in range(3)] + [(TPROVE[c] + p["swap"], capH, c) for c in range(2)]
order.sort(key=lambda x: x[0])
return order
# ------------------------------------------------------------ decisions
def decide(self, t, price, w, Wr, p_resp, p_win, t_open):
p = self.p
due = ((t + self.phase) % p["decide_every"] == 0) & self.active & ~self.dead & ~self.fixed_mine
if not due.any():
return
idx = np.nonzero(due)[0]
cards = self.cards[idx]
elec = self.elec[idx][:, None]
n_pcards = (self.cards[idx] * ((self.mode[idx] == PROVE) | (self.mode[idx] == HYB))).sum(1, keepdims=True)
# $ per card-hour by class
v_mine = HASH * 1e6 * self.R_hash * price * 3600.0 - PMINE * elec / 1000.0
per_w = w[idx][:, None] / np.maximum(n_pcards + (n_pcards == 0) * cards, 1e-9)
asg_int = self.asg_pw * per_w # assigned internal shards, $ per card-hour at this operator's weight
asg_ext = self.asg_ext_pw * per_w * self.eligible
# a prover with no weight gets only open claims; one with weight gets assigned work shared over its proving cards
v_prove = self.open_pc + asg_ext + asg_int * (TPROVE <= t_open) - PIDLE * elec / 1000.0 - 0.3 * (PPROVE - PIDLE) * elec / 1000.0
v_hyb = v_mine * (1 - np.minimum(0.5, self.duty[idx])) + 0.9 * (asg_ext + asg_int * ((TPROVE + p["swap"]) <= t_open))
v_prove[:, 3] = -1e9
v_hyb[:, 2:] = -1e9
v_off = np.zeros_like(v_mine)
V = np.stack([v_off, v_mine, v_prove, v_hyb], 0) # (4 modes, ops, classes)
cur = self.mode[idx]
v_cur = np.take_along_axis(V, cur[None], 0)[0]
best = V.argmax(0)
v_best = V.max(0)
hy = self.hyst[idx][:, None]
gain = v_best - v_cur
ok = (gain > hy * np.abs(v_cur) + 1e-4) & (cards > 0) & ((t - self.last_switch[idx]) >= p["dwell_ticks"])
ok &= best != cur
if ok.any():
newmode = np.where(ok, best, cur)
self.mode[idx] = newmode
ls = self.last_switch[idx]
ls[ok] = t
self.last_switch[idx] = ls
self.switches += int(ok.sum())
def run(self):
nt = int(self.p["days"] * 86400 / self.p["tick"])
for t in range(nt):
self.step(t)
return np.array(self.hourly)
COLS = ["hash_MHs", "hash_pot", "frac_prove", "frac_hyb", "frac_off", "bps", "D", "q", "age", "ok60", "ok20",
"price", "ext_served", "ext_lost", "shards", "age_max", "hash_min"]
def metrics(hourly, sim):
h = hourly
d = {}
hrs = h.shape[0]
nd = hrs // 24
def day_mean(col, d0, d1):
d0, d1 = min(d0, nd - 1), min(d1, nd)
return h[d0 * 24:d1 * 24, COLS.index(col)].mean()
def day_max(col, dd):
dd = min(dd, nd)
return h[(dd - 1) * 24:dd * 24, COLS.index(col)].max()
pre_hash = day_mean("hash_MHs", 1, 7) if nd >= 7 else h[:, COLS.index("hash_MHs")].mean()
d["hash_pre"] = pre_hash
d["hash_min_ratio"] = h[24:, COLS.index("hash_min")].min() / pre_hash if nd >= 2 else 1.0
d["hash_d30_ratio"] = day_mean("hash_MHs", 29, 30) / pre_hash
# hours below 50% of pre-event hash
d["hours_hash_lt50"] = int((h[24:, COLS.index("hash_MHs")] < 0.5 * pre_hash).sum())
d["mining_hash_share"] = (h[:, COLS.index("hash_MHs")] / np.maximum(h[:, COLS.index("hash_pot")], 1e-9)).mean()
for dd in (1, 7, 10, 15, 20, 30):
d[f"prove_d{dd}"] = day_mean("frac_prove", dd - 1, dd)
d[f"hyb_d{dd}"] = day_mean("frac_hyb", dd - 1, dd)
d[f"off_d{dd}"] = day_mean("frac_off", dd - 1, dd)
d["age_max"] = h[:, COLS.index("age_max")].max()
d["q_max"] = h[:, COLS.index("q")].max()
d["age_d10"] = day_max("age_max", 10)
d["age_d20"] = day_max("age_max", 20)
d["age_d30"] = day_max("age_max", 30)
daily_age = h[:, COLS.index("age_max")].reshape(-1, 24).max(1)
x = np.arange(10)
slope = np.polyfit(x, daily_age[-10:], 1)[0] if nd >= 10 else 0.0
d["backlog_growing"] = bool(slope > 0 and daily_age[-1] > 60)
d["backlog_600"] = bool(d["age_max"] > 600)
d["ok60_mean"] = h[:, COLS.index("ok60")].mean()
d["ok60_min_day"] = h[:, COLS.index("ok60")].reshape(-1, 24).mean(1).min()
d["ok20_mean"] = h[:, COLS.index("ok20")].mean()
d["bps_mean"] = h[:, COLS.index("bps")].mean()
d["bps_max"] = h[:, COLS.index("bps")].max()
d["bps_min"] = h[:, COLS.index("bps")].min()
d["D_end_over_start"] = h[-1, COLS.index("D")] / h[min(24, hrs - 1), COLS.index("D")]
d["price_end"] = h[-1, COLS.index("price")]
es, el = h[:, COLS.index("ext_served")].sum(), h[:, COLS.index("ext_lost")].sum()
d["ext_delivered"] = es / (es + el) if es + el > 0 else float("nan")
# oscillation: zero crossings of the proving fraction around its 24-h mean, per day, last 10 days
fp = h[:, COLS.index("frac_prove")]
ma = np.convolve(fp, np.ones(24) / 24, mode="same")
dev = (fp - ma)[-240:]
d["osc_cross_per_day"] = float((np.diff(np.sign(dev)) != 0).sum() / 10.0)
d["osc_amp_pts"] = float((np.percentile(fp[-240:], 90) - np.percentile(fp[-240:], 10)) * 100)
d["osc_std_pts"] = float(fp[-240:].std() * 100)
days = sim.p["days"]
d["profit_card_day"] = sim.cls_profit / np.maximum(sim.cls_cards / (days * 86400 / sim.p["tick"]), 1e-9) / days
d["shard_share"] = sim.cls_shards / max(sim.cls_shards.sum(), 1e-9)
d["switches"] = sim.switches
d["miner_shortage"] = bool(d["hours_hash_lt50"] >= 1)
d["window_miss"] = bool(d["ok60_min_day"] < 0.90)
d["oscillation"] = bool(d["osc_amp_pts"] > 10 and d["osc_cross_per_day"] >= 1)
return d
SCEN = {
"a": "baseline",
"b": "external pays 10x from day 7, coin price falls 70% over days 7 to 14",
"c": "no external demand",
"d": "the 20% operator disappears at day 10",
"e": "a 30% operator never fulfils its assignments",
"f": "a pool with hash equal to the network's arrives at day 10 (2x hash)",
}
def fmt(v, nd=2):
if isinstance(v, (bool, np.bool_)):
return "yes" if v else "no"
if isinstance(v, (int, np.integer)):
return f"{v:,}"
if isinstance(v, float):
if abs(v) >= 1000:
return f"{v:,.0f}"
return f"{v:.{nd}f}"
return str(v)
def agg(ms, key):
vals = np.array([m[key] for m in ms], dtype=float)
return vals.mean(), vals.min(), vals.max()
def run_scenarios(scen, seeds, p, quiet=False):
out = {}
for s in scen:
ms = []
for seed in seeds:
t0 = time.time()
sim = Sim(s, seed, p)
h = sim.run()
ms.append(metrics(h, sim))
if not quiet:
print(f"<!-- scenario {s} seed {seed}: {time.time() - t0:.1f} s -->", file=sys.stderr)
out[s] = ms
return out
def table_scenarios(out):
keys = [
("mining_hash_share", "hash mining share (mean)"),
("prove_d1", "cards proving, day 1"), ("prove_d10", "cards proving, day 10"), ("prove_d20", "cards proving, day 20"), ("prove_d30", "cards proving, day 30"),
("hyb_d30", "cards hybrid, day 30"), ("off_d30", "cards off, day 30"),
("hash_min_ratio", "hash min / pre-event"), ("hash_d30_ratio", "hash day 30 / pre-event"), ("hours_hash_lt50", "hours hash under 50%"),
("q_max", "backlog max, shards"), ("age_max", "oldest unproven age max, s"),
("age_d10", "age max day 10, s"), ("age_d20", "age max day 20, s"), ("age_d30", "age max day 30, s"),
("ok60_mean", "blocks proven within 60 s"), ("ok60_min_day", "worst day within 60 s"), ("ok20_mean", "blocks proven within 20 s"),
("bps_mean", "blocks/s mean"), ("bps_max", "blocks/s hourly max"), ("bps_min", "blocks/s hourly min"), ("D_end_over_start", "difficulty end / start"),
("ext_delivered", "external jobs delivered"), ("price_end", "price at day 30, $"),
("osc_cross_per_day", "proving-share crossings per day"), ("osc_amp_pts", "proving-share 10-90 pct range, points"),
("switches", "mode switches (operator x class)"),
]
scen = list(out)
lines = ["| Metric | " + " | ".join(f"{s} | {s} min | {s} max" for s in scen) + " |",
"|---|" + "---|" * (3 * len(scen))]
for k, label in keys:
row = [label]
for s in scen:
m, lo, hi = agg(out[s], k)
nd = 4 if k == "price_end" else 2
row += [fmt(float(m), nd), fmt(float(lo), nd), fmt(float(hi), nd)]
lines.append("| " + " | ".join(row) + " |")
print("\n".join(lines))
print()
print("| Flag | " + " | ".join(scen) + " |")
print("|---|" + "---|" * len(scen))
for k, label in [("miner_shortage", "miner shortage (hash under 50% of pre-event for 1 h or more)"),
("backlog_600", "backlog over 600 s (design's backlog-rule trigger)"),
("backlog_growing", "growing backlog (positive 10-day trend and over 60 s at day 30)"),
("window_miss", "window miss (a day under 90% of blocks within 60 s)"),
("oscillation", "oscillation (proving-share 10-90 range over 10 points in the last 10 days)")]:
row = [label]
for s in scen:
n = sum(1 for m in out[s] if m[k])
row.append(f"{n}/{len(out[s])}")
print("| " + " | ".join(row) + " |")
print()
print("Operator profit by card class, $ per card-day (mean over seeds, all modes including off):")
print()
print("| Scenario | " + " | ".join(CLS) + " | shard share " + " | shard share ".join(CLS[:3]) + " |")
print("|---|" + "---|" * 7)
for s in scen:
pr = np.mean([m["profit_card_day"] for m in out[s]], 0)
sh = np.mean([m["shard_share"] for m in out[s]], 0)
print(f"| {s} | " + " | ".join(f"{v:.3f}" for v in pr) + " | " + " | ".join(f"{v:.2f}" for v in sh[:3]) + " |")
print()
def lever_study(scenario, seeds, p, with_sens=True, sens_only=False):
levers = {
"pool": [0.10, 0.20, 0.30, 0.40],
"window": [5.0, 10.0, 20.0, 30.0],
"burn": [0.0, 0.10, 0.25, 0.50],
"timeout": [60.0, 120.0, 300.0, 600.0],
"shards_per_block": [3.0, 30.0, 100.0, 300.0],
"ema_ticks": [7.0, 20.0, 60.0, 480.0],
}
if sens_only:
levers = {k: v for k, v in levers.items() if k in ("shards_per_block", "ema_ticks")}
elif not with_sens:
levers = {k: v for k, v in levers.items() if k not in ("shards_per_block", "ema_ticks")}
print(f"Lever study on scenario {scenario} ({SCEN[scenario]}), seeds {list(seeds)}, traffic {p['shards_per_block']:.0f} shards per block. One parameter at a time, the rest at the design values.")
print()
print("Rows pool, window, burn, timeout are protocol levers; shards_per_block (chain traffic) and ema_ticks (operators' observation window, ticks of 180 s) are model sensitivities.")
print()
print("| Lever | Value | hash min / pre | hash d30 / pre | hours hash under 50% | age max s | within 60 s (mean) | worst day within 60 s | cards proving d30 | cards off d30 | external delivered | 3060 shard share | balance score |")
print("|---|---|---|---|---|---|---|---|---|---|---|---|---|")
rows = []
for lever, vals in levers.items():
for v in vals:
pp = dict(p)
pp[lever] = v
out = run_scenarios([scenario], seeds, pp, quiet=True)[scenario]
m = {k: agg(out, k)[0] for k in ["hash_min_ratio", "hash_d30_ratio", "hours_hash_lt50", "age_max", "ok60_mean", "ok60_min_day", "prove_d30", "off_d30", "ext_delivered"]}
sh = np.mean([x["shard_share"] for x in out], 0)[2]
# balance score: mean of (hash d30 ratio capped at 1), worst-day proof share, 1 - age_max/600 capped
score = (min(1.0, m["hash_d30_ratio"]) + m["ok60_min_day"] + max(0.0, 1 - m["age_max"] / 600.0)) / 3.0
star = " (design)" if abs(v - P[lever]) < 1e-9 and lever in ("pool", "window", "burn", "timeout") else (" (default)" if abs(v - P[lever]) < 1e-9 else "")
print(f"| {lever} | {v}{star} | {m['hash_min_ratio']:.2f} | {m['hash_d30_ratio']:.2f} | {m['hours_hash_lt50']:.0f} | {m['age_max']:.0f} | {m['ok60_mean']:.3f} | {m['ok60_min_day']:.3f} | {m['prove_d30']:.3f} | {m['off_d30']:.3f} | {m['ext_delivered']:.2f} | {sh:.2f} | {score:.3f} |")
rows.append((lever, v, score))
sys.stdout.flush()
print()
return rows
def main():
ap = argparse.ArgumentParser()
ap.add_argument("--scenarios", default="a,b,c,d,e,f")
ap.add_argument("--seeds", type=int, default=5)
ap.add_argument("--seed0", type=int, default=1)
ap.add_argument("--levers", default=None, help="scenario letter for the lever study")
ap.add_argument("--sens", action="store_true", help="with --levers: only the two sensitivities (traffic, observation window)")
ap.add_argument("--nosens", action="store_true", help="with --levers: protocol levers only")
ap.add_argument("--set", default="", help="k=v,k=v parameter overrides")
ap.add_argument("--dump", default=None, help="scenario letter: print the hourly CSV for the first seed")
ap.add_argument("--days", type=int, default=None)
args = ap.parse_args()
p = dict(P)
for kv in filter(None, args.set.split(",")):
k, v = kv.split("=")
p[k] = float(v)
if args.days:
p["days"] = args.days
seeds = range(args.seed0, args.seed0 + args.seeds)
if args.dump:
sim = Sim(args.dump, args.seed0, p)
h = sim.run()
print("hour," + ",".join(COLS))
for i, row in enumerate(h):
print(f"{i}," + ",".join(f"{v:.6g}" for v in row))
m = metrics(h, sim)
for k, v in m.items():
print(f"# {k}: {v}", file=sys.stderr)
return
if args.levers:
lever_study(args.levers, seeds, p, with_sens=not args.nosens, sens_only=args.sens)
return
scen = args.scenarios.split(",")
print(f"# Igneum economy simulation, {p['n_ops']} operators, {p['days']} days, seeds {list(seeds)}, tick {p['tick']:.0f} s")
print()
print("Parameters: " + ", ".join(f"{k}={v}" for k, v in p.items()))
print()
for s in scen:
print(f"- {s}: {SCEN[s]}")
print()
t0 = time.time()
out = run_scenarios(scen, seeds, p)
table_scenarios(out)
print(f"<!-- total {time.time() - t0:.0f} s -->")
if __name__ == "__main__":
main()
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