The Flywheel — N-Squared Times Log(Compute)

Status: pre-launch. This page describes target design; this document does not establish a deployed service.

Current reading — 2026-09-28

N² × log(C) is a network-value hypothesis, not a demonstrated universal economic scaling law. Its variables, units, normalization and causal evidence require specification. The stated derivatives do not imply that one extra user always adds more value than one extra compute unit; for example, N=1,000,000 and C=1,001 reverses that comparison in the toy formula. [I]

Service pricing and sustainable funding require their own costs, incentives and evidence. The retained subscription and spread proposals below are not adopted prices or proof of non-extraction. See current status.

Historical network-value and pricing hypothesis — not a proven law or commercial terms

The organism's value scales as N^2 x log(compute). This is not a marketing claim. It is a consequence of eta = 0 and the network topology. Understanding why eta > 0 kills the flywheel is understanding why Skyzai must be zero-extraction.

The N-Squared Term

Every user who connects to the organism contributes three things:

1. Observations (Circle): what they see, what they report, what sensors they carry
2. Predictions (ReFu): what they bet on, what confidence they stake
3. Outcomes (Settlement): what actually happened, timestamped and immutable

Each contribution benefits ALL other users. This is Metcalfe's Law applied to intelligence, not connections. N users producing observations means N^2 observation-pairs (every user's observations inform every other user's context). The value of the network scales with the square of participants.

The Log(Compute) Term

Raw network effects hit diminishing returns without intelligence amplification. The log(compute) term captures what AI adds: each doubling of compute applied to the N^2 observation graph produces a linear increase in insight quality. This is the empirical scaling law of large language models (chinchilla scaling) applied to collective intelligence rather than pre-training.

Combined: V(N, C) = N^2 x log(C)

Why eta = 0 Maximizes N

Extraction (eta > 0) is a tax on participation. Every dollar extracted from the network is a dollar that could have attracted or retained a participant.

The critical insight: N is the most sensitive variable. Because value scales with N^2, losing one participant costs more than losing one unit of compute. Specifically:

dV/dN = 2N x log(C)    (linear in N, grows fast)
dV/dC = N^2 / C         (inverse in C, shrinks fast)

At any reasonable scale (N > 100, C > 1000), the marginal value of one additional user vastly exceeds the marginal value of one additional compute unit. Therefore: spend everything on N. Extract nothing.

The Death Spiral of eta > 0

When eta > 0:

1. Each user pays extraction cost per cycle
2. Users with lowest marginal benefit exit first (rational)
3. N decreases by delta-N
4. Network value decreases by (2N x delta-N) x log(C) — quadratic loss
5. Remaining users now face worse value proposition
6. More users exit
7. Goto step 3

This is the MySpace/Facebook/Twitter pattern. Every platform that introduces extraction eventually watches its N^2 term collapse. The flywheel reverses into a death spiral.

The eta = 0 Counter-Pattern

When eta = 0:

1. No extraction cost per cycle
2. The only cost to users is opportunity cost of attention
3. Each new user increases value for all existing users (N^2)
4. Increased value attracts more users
5. N grows
6. Goto step 3

The flywheel accelerates. The constraint is that the organism must fund operations from value creation (fees on services rendered), not value extraction (rent on access).

The Distinction: Fees vs. Extraction

eta = 0 does NOT mean zero fees. It means zero extraction.

• Fee: Payment for a specific service rendered (Circle API call, ReFu bet settlement, OFN transaction processing). The user receives value equal to or greater than the fee.
• Extraction: Payment for access to the network itself, or rent on data the user contributed, or margin on services that cost less to provide. The user receives less value than they pay.

The test: if the user could get the same service without the organism and the organism's fee exceeds the cost of that alternative, it is extraction. If the organism provides value that cannot be obtained elsewhere (N^2 intelligence), the fee is compensation for value created.

Skyzai Revenue Under eta = 0

• Circle: API fees for intelligence queries + The Access subscription ($99/mo for premium analysis)
• ReFu: LMSR spread (the mathematical cost of market-making, not rent)
• OFN: Implementation services (consulting, integration, customization)
• Aureus: Lombard Bridge spread (cost of gold custody and collateralization) — target design (frozen claim until reconciliation complete)

All fees are for value created. None are for access to the network. eta = 0.

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N^2 x log(C). Protect N above all else. Extraction kills N. Therefore: eta = 0.

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