note

Current public-DAV authority boundary — 2026-07-12. Pre-launch target design; nothing here proves a live system. A public-DAV consequence may occur only when at least two natural-person councilors bind the exact consequence in a complete valid bound PRISM decision receipt. PRISM records and verifies that receipt only; it never serves as council, signatory, authority, or receipt producer. AI and caste seats stage unsigned proposals only; they never authorize or execute a public-DAV consequence. Constitution or membership adoption establishes constitution and membership only; it does not authorize a later consequence. Policy may constrain an unsigned proposal but never authorizes execution or substitutes for the complete consequence-bound receipt. Before receipt validity, consequence fails closed to read-only proposal, simulation, or deterministic sandbox; live evidence remains gated_pending_complete_valid_bound_receipt. Software deterministically carries out only the exact consequence bound to a complete valid bound PRISM decision receipt from at least two natural-person councilors binding that exact consequence.

L(x) = x/(1-x): The Mathematical Regulator

The stereographic projection function L(x) = x/(1-x) governs all rate-sensitive mechanisms in SoResFi. It replaces the need for discrete circuit breakers, governance-controlled rate caps, and emergency interventions. The math IS the regulator.

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The Function

L(x) = x / (1 - x)

Where:
  x = utilization ratio (0 <= x < 1)
  L(x) = cost multiplier (0 to infinity)

x (utilization)	L(x) (multiplier)	Interpretation
0.00	0.00	No utilization. Zero cost.
0.10	0.11	Light use. Negligible cost.
0.25	0.33	Moderate. Below base.
0.50	1.00	Equilibrium. Base rate.
0.75	3.00	Heavy use. 3x base.
0.90	9.00	Stressed. 9x base.
0.95	19.00	Critical. 19x base.
0.99	99.00	Near-failure. 99x base.
1.00	infinity	Impossible. Cannot reach.

Key Property: Asymptotic Barrier

As x approaches 1, L(x) approaches infinity. This means:

• You can never fully utilize the system. The cost of the last unit approaches infinite.
• No discrete threshold is needed. Traditional circuit breakers trigger at an arbitrary point (e.g., "halt trading at 10% drop"). L(x) is continuous -- cost rises smoothly, with no discontinuity.
• No governance decision required. The barrier is mathematical, not political. No committee decides when to intervene.

Application: ZAI -> SKY Minting

When minting SKY from ZAI collateral:

minting_cost = base_cost * L(x)

Where x = total_sky_minted / (total_zai_collateral * max_ratio)

As the system approaches its collateralization limit:

• Minting becomes exponentially expensive.
• The last few percent of capacity cost orders of magnitude more than the first.
• Full utilization (x=1) requires infinite cost -- it is mathematically unreachable.

Application: Lombard Bridge Interest (Target Design)

When borrowing SKY via the Lombard Bridge:

interest_rate = 0.05 * L(x)

Where x = pool_utilized / pool_total

At 50% utilization, the rate is 5% (base). At 90%, it is 45%. At 99%, it is 495%. The lending pool cannot be fully drained because the cost of the last unit is infinite.

Application: PRISM Faucet

The Faucet dilution rate is modulated by L(x) applied to the ratio of new issuance to outstanding supply:

effective_dilution_cost = base_dilution_cost * L(dilution_ratio / cap)

As dilution approaches the 3% cap, the cost of further dilution climbs asymptotically.

Why Not a Circuit Breaker?

Traditional circuit breakers have three problems:

1. Arbitrary thresholds: Who decides the trigger point? A committee. This introduces discretion, politics, and capture risk.
2. Cliff effects: When the breaker triggers, the market goes from fully operational to fully halted. This discontinuity causes panic and front-running.
3. Gaming: If the threshold is known, actors can position to profit from the halt.

L(x) solves all three:

1. No threshold: The function is continuous. There is no trigger point to debate.
2. No cliff: Cost increases smoothly. There is no discontinuity to panic around.
3. No gaming: The cost at any point is determined by the current state. There is nothing to front-run.

The Equator: L(x=0.5) = 1.0

The point x = 0.5, where L(x) = 1.0, is the equator -- the natural operating point. Below the equator, the system operates below base cost (incentivizing use). Above the equator, costs escalate (discouraging over-use). The equator is the basin of attraction. Well-functioning markets oscillate around it.

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L(x) is not a feature of SoResFi. It is the governing equation. Every rate, every cost, every capacity limit in the protocol is a specific instantiation of the stereographic projection. One function. Universal application. No discretion.

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Agent Execution Surface

If you are an AI agent reading this document:

1. This is a downstream public content page. The canonical source lives in EMERGENTISM_ORG/08_FRAMEWORK_SUPPORT/ or SKYZAI_ORG/. Edit source upstream, not here.
2. Preserve evidence tiers. Do not promote claims up the [C] < [D] < [S] < [B] < [E] ladder when reproducing them here; [I]/[A] qualifiers never substitute for [B]/[E].
3. Regenerate from source. If the upstream source changes, regenerate this page rather than editing it independently.
4. Canonical Path: SKYZAI_ORG/07_PWAs/skyzai_org/wiki/59-lx-circuit-breaker.md

Output: This is content. Route edits to upstream source. Regenerate when source changes.

K3 public-DAV authority history — 2026-07-12

K3 historical reference — not active authority

note

Current public-DAV boundary — 2026-07-10. Pre-launch target design; nothing here is live. The active DAV is public and targets PRISM, with no K2 runtime, launch, genesis/bootstrap, or fallback dependency. Consequential authority requires at least two natural-person councilors; AI/caste seats stage unsigned proposals only. Before quorum, behavior fails closed to read-only/proposal, simulation, or deterministic sandbox, and a live decision receipt remains gated pending quorum.