igneum/docs/analysis/class-v6/operator-simulation.md

The profit-maximising operator simulation: do the pricing and capacity rules restore service without an administrator?

8 October 2026, 16:2x to 16:5x UK, branch class-v6-floor-sram, floor lane 3, Igneum 2.0 D4 item 2 (the research lane's word of 17:0x UK; the clock 20:15 UK). First run. Every figure modelled; the script is scratchpad/opsim.py, run on build-4 (build-3 was down from 16:40 UK). The cost rows are the coexistence model's (lane 4's class v5 table, street prices); the proving side carries the fleet lane's measured day on Devnet 3 (8 October 2026, 3,421 claims, 93 paid segments): the 12 GB tier paid 0 of 313 claims (a measured zero for internal proving), steals 4.0 percent of claims, paid to wasted card-seconds 14,800 to 254,000 (5.5 percent, on a day with a floor-link fault until 10:50 UTC). Nothing here is served. The founder is not named.

0. The result in one page

Shock	Launch-shape world (all available cards, assumed proving efficiency 0.5)	Stressed world (1 percent of the cards, the measured 5.5 percent proving efficiency, a 1,000x spike) without a congestion price on internal proving	The same with the resolution's congestion-priced internal proving fee	Reading
A. A proving demand spike (external x10, or x1,000 in the stressed world, lasting)	restored in 0 periods: capacity moves to the external market the same day (263,000 cards in, settling to 44,000), the fee never leaves 1x	NOT restored in 150 periods: 9,900 of 12,300 cards go to the external fee market, internal proving falls from 1,647 to 393 cards, the internal backlog grows without bound (8.9 M shards unproven by day 150) because the pool pays a fixed sum that cannot bid provers back	restored after 35 periods: the internal fee climbs to 2x, pulls 565 cards back, the backlog peaks at 368,000 shards (1.4 days of demand) and clears	the fee market restores EXTERNAL service by itself; INTERNAL proving needs the resolution's congestion-priced fee, or a spike starves it
B. The token price falls to 0.3x	restored in 0 periods: 130,000 cards leave the same day, hash 17.7 to 8.4 TH/s, revenue per MH/s-hour back to 309 to 315 micro-USD within 7 periods	restored in 0 periods	restored in 0 periods	exit at cost is immediate and proportionate; proving capacity stays 4x to 1,600x the demand
C. The six largest proving cohorts leave for good (H100, A100, 5090, 5080, 4090, 3090)	restored in 0 periods: hash 17.7 to 12.0 then 15.2 TH/s as the remaining classes re-enter at the higher rate; internal capacity stays 1,500x the demand	restored in 0 periods: capacity 2.8x to 3.1x the demand on the remaining classes	restored in 0 periods	re-entry at cost fills the gap; the 16 GB tier carries internal proving when the 24 GB and datacentre tiers leave
D1. A specialised entrant in mining (a sunk 1 TH/s SRAM die fleet at 0.06)	restored in 0 periods: 4,000 GPU cards leave, the chip holds 5.6 percent, proving untouched	restored in 0 periods: the chip holds 80 percent of a 1.25 TH/s network, GPU mining falls from 9,177 to 7,671 cards and 1,500 of them move to proving (internal 2,196 to 3,697)	restored in 0 periods	service holds in both worlds; coexistence does not (the coexistence model's finding), but the GPUs that leave mining go to proving, which the chip cannot do
D2. A specialised entrant in proving (a proving ASIC at 2,000 shard-equivalents a day at a tenth of the cost)	restored in 0 periods: the entrant takes the external market at the base fee; nothing else moves	restored in 0 periods	restored in 0 periods	external proving is a commodity market; an entrant lowers the fee and the GPUs leave that market for mining and internal proving

The pass statement, per shock. The pricing and capacity rules (congestion-priced user-funded external proving fees, the fee market, entry and exit at cost) restore service without an administrator in every shock of the launch-shape world, in 0 periods, because idle GPU capacity dwarfs the proving work (16 M shard-equivalents a day of external capacity against 200 of work; 426 M internal against 259,200). In a capacity-limited world the same rules restore B, C, D1 and D2 in 0 periods and FAIL to restore A unless internal proving also carries a congestion-priced, user-funded fee, with which A is restored in 35 periods. The one design finding: the 20 percent pool paid as a fixed sum per block is a subsidy, not a price; when an external fee market outbids it, internal proofs starve, and the resolution's shape (an explicit user-funded proving fee with congestion pricing for internal proving too) is what closes it. No parameter was changed by hand in any run.

1. The model

Element	Rule	Label
Cohorts	17 card classes x 3 electricity prices (0.06, 0.12, 0.25 per kWh), a third of each class's available count per price; each cohort holds continuous shares of its cards in MINE, INTERNAL PROVE, EXTERNAL PROVE and OFF	modelled
Decision	each period (one day) a cohort moves a quarter of its cards toward the mode with the best profit per card-day, evaluated at the MARGINAL rate (the pool or fee divided by the capacity after its own move), with a 10 percent hysteresis; v1's all-or-nothing cohorts herded and oscillated and were replaced	modelled
Mining revenue	the miner emission (0.77 B IGN in year 1, 80 percent) at IGN 0.10 (assumption), shared by hash; the tip stays whole to the miner (the resolution's shape)	the spec's constant; the price an assumption
Internal proving	3 shards per block (259,200 shard-equivalents a day); the 20 percent pool (0.53 M IGN a day) shared by proving capacity; a backlog accrues when capacity is short; the 12 GB tier earns nothing (measured zero); under the resolution's shape a user-funded congestion fee on top of the pool, rising 25 percent a period while the backlog exceeds a day of demand and falling 10 percent while under half a day, bounded 1x to 100x	measured zero (the fleet lane), modelled rule
External proving	USD 2,000 a day of demand at the base fee (spec 05's launch grid; USD 10 per shard-equivalent), 90 percent to the provers who deliver; the congestion fee rises 25 percent a period while job latency exceeds a day and falls 10 percent while under half a day, bounded 1x to 100x; demand elastic to the fee with exponent 0.5	spec 05; the elasticity and the fee rule modelled
Proving capacity per card	the bench table's shard times (5090 6.3 s, 4090 6.3, 5070 4.8, 3080 7.1, 4070 12.1, 3060 14.4, 3090 14.9, H100 3.0, A100 5.0; the 9070 XT and the Mac cannot prove), times the proving efficiency (0.5 assumed after the fault fix; 0.055 the measured day), times 1 minus the 4 percent steal rate	measured shard times; the efficiency as stated
Costs	power at the card's floor joules (mining) or its proving watts, a wear allowance of 5 percent of the used price a year, 97 percent accepted work	the coexistence model's rows
Shocks	applied at period 0 after a 90-period warm-up; 150 periods observed
Restored	the first period from which ALL of the following hold to the end of the run: external job latency under a day, internal backlog under a day of demand, internal capacity at least the demand, block production at least a fifth of the baseline hash; "NOT restored" otherwise	the test; v2's latching version was replaced
Worlds	launch-shape (all available cards) and stressed (1 percent of the cards, a 1,000x spike, the measured efficiency)

2. The runs

2.1 Launch-shape world (all available cards; proving efficiency 0.5; shock A at x10)

Baseline after warm-up: hash 17.7 TH/s on 408,829 mining cards; 109,221 cards on internal proving (426 M shard-equivalents a day against 259,200 of demand); 3,011 on external proving (16 M against 200 of work); 712,937 off (the cards whose power at their price exceeds the revenue); revenue 496 micro-USD per MH/s-hour; fees at 1x.

Shock	t+0	t+7	t+30	t+149	Restored
A. external x10	263,000 cards move to external proving the same day (external capacity 16 M to 1,197 M)	44,000 settle there; mining back to 17.8 TH/s	unchanged	unchanged	0 periods
B. price x0.3	130,696 cards leave; revenue per MH/s-hour 149 micro-USD	hash 8.4 TH/s; revenue 313	8.4; 315	8.5; 309	0 periods
C. six cohorts leave	hash 12.0 TH/s; revenue 735	15.5 TH/s as 55,870 cards of the other classes enter; 568	15.2; 576	15.2; 576	0 periods
D1. a 1 TH/s SRAM fleet	hash 18.7 TH/s; 4,000 GPU cards leave	17.9 (GPU 16.9)	17.8	17.8	0 periods
D2. a proving ASIC	external capacity +2,000 shard-equivalents; nothing else moves				0 periods

Reading: at launch-shape demand the proving service has 100x to 1,600x spare capacity in the GPUs idle at the price, so no shock in the four can break it; the fee never leaves 1x. Mining re-prices itself within 7 periods of a 70 percent price fall or a 32 percent capacity loss. Both proving efficiencies (0.5 and 0.055) give the same result here.

2.2 Stressed world (1 percent of the cards; the measured 5.5 percent proving efficiency; shock A at x1,000)

Baseline: hash 0.34 TH/s on 9,177 cards; internal capacity 1.1 M shard-equivalents a day (4.2x the demand) on 2,196 cards; external capacity 47,000 (240x the work) on 87 cards; 878 off; revenue 25,500 micro-USD per MH/s-hour.

Shock	Without a congestion price on internal proving	With the resolution's congestion-priced internal fee
A. external x1,000 (USD 2 M a day)	t+0: external latency 3.2 days, the external fee 1.25x, 2,963 cards move; t+7: external capacity 4.8 M (latency 0), the fee back to 1x, but internal proving has fallen to 393 cards and 197,000 shard-equivalents a day (0.76x the demand), backlog 123,000; t+30: backlog 1.55 M; t+149: backlog 8.9 M. NOT restored in 150 periods	t+7: internal 378 cards, backlog 153,000, the internal fee 1x; t+30: the internal fee 2x, 505 cards back, backlog 286,000; by t+35 the backlog is under a day of demand and stays so; t+149: 565 cards on internal, backlog 0, the fee back to 1x. Restored after 35 periods; worst backlog 368,000 (1.4 days)
B. price x0.3	restored in 0 periods; the mining fleet re-prices (revenue 25,500 to 7,650 micro-USD) and 913 cards move to external proving	restored in 0 periods
C. six cohorts leave	restored in 0 periods: internal capacity 802,000 (3.1x the demand) on the 16 GB tier	restored in 0 periods
D1. a 1 TH/s SRAM fleet	restored in 0 periods: the chip holds 80 percent of 1.25 TH/s; 1,500 GPU cards move from mining to proving (internal 2,196 to 3,697)	restored in 0 periods
D2. a proving ASIC	restored in 0 periods	restored in 0 periods

The same world at the assumed 0.5 efficiency restores A in 0 periods in both variants (internal capacity 10 M against 259,200: the spike cannot pull enough capacity away); at 0.1 percent of the cards and 0.5 efficiency the internal backlog again grows without bound under A without the internal fee (11.5 M by day 150). The failure needs two things at once: a proving fleet near the demand (a small network or the measured efficiency) and a fee market that outbids the fixed pool.

3. What the runs say about the rules

1. The external fee market works as designed. In every run the congestion fee brings capacity to the external market within a day (launch-shape) or seven (stressed) and returns to 1x when the backlog clears; demand elasticity keeps the fee bounded; a cheaper entrant (D2) takes the work at the base fee and the GPUs leave that market for the other two, which is coexistence in the proving market.
2. The fixed internal pool is the one rule that fails under stress. It pays per block whatever the backlog, so it cannot bid provers back from a hotter market; with the resolution's congestion-priced internal fee it can, in 35 periods at a 2x peak fee. The pass line for shock A reads "restored only with the internal congestion fee".
3. Entry and exit at cost handle the price fall, the capacity loss and the mining entrant in 0 periods in both worlds; the GPUs that a mining entrant displaces move to proving, which the SRAM die cannot do, and that is the second income the coexistence model's T3 table prices.
4. The 12 GB tier's measured zero matters for C: when the 24 GB and datacentre cohorts leave, internal proving falls on the 16 GB tier (5080, 5070 Ti, 5060 Ti, 4080, 4060 Ti); the 12 GB cards (5070, 4070, 3060: 525,000 of the 1.1 M cards in the population) contribute nothing to it today.

4. Unverified and owed

• Every row is modelled; the price (IGN 0.10), the external demand (USD 2,000 a day), the elasticity (0.5), the fee rule (25 percent up, 10 percent down, bounded 100x), the hysteresis and the quarter-per-period adjustment are assumptions; the proving efficiency is the fleet lane's one measured day (with a fault) and an assumed post-fix value.
• The available card counts are approximate; the stressed world is a scale factor, not a measured network.
• Block production is read as hash; propagation and the 30-second lock are outside the run. The internal pool is shared by capacity (a sortition-like share), not by shards delivered, which flatters high-capacity classes.
• A second cut: per-card (not per-cohort) agents as in sim/economy/sim.py, the hybrid mode (mine and prove assigned shards), the steal rate as a function of latency, the external bond and timeout (O-5.6), and a run on the measured stage times (inputs 2.4 s, proving 26.8 s median and 365 s at the slowest 1 percent, aggregation 22.8 s, claim to paid 336 s) instead of the bench table's shard times.
• Nothing was run on the Mac; the script ran on build-4.