6. Topological Scarcity, Delivered Capacity, and the Corridor

Jason St George

doi:10.5281/zenodo.18902696

6. Topological Scarcity, Delivered Capacity, and the Corridor

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Jason St George. "6. Topological Scarcity, Delivered Capacity, and the Corridor" in AfterFiat: The Load-Bearing Thesis. Version v2.0. /v/2.0/brief/read/topological-scarcity-delivered-capacity-and-the-corridor/

Topological Scarcity, Delivered Capacity, and the Corridor

Topological Scarcity Lemma

A nominal stock of resources, capital, or capacity does not secure a monetary service. The relevant quantity is the stress-deliverable flow through the narrowest non-substitutable edge connecting input to holder utility.

Aggregate abundance and local scarcity can coexist. Crude is not diesel when refining is the minimum cut. Savings are not duration absorption when no balance sheet can own the residual risk. Installed accelerators are not verified service when power, cooling, firmware, network access, verification, or settlement fails. The transformation path, location, actor, and required horizon determine the usable service.

This is a mechanism-level synthesis. Physical-conversion and marginal-buyer examples help identify the topology; they are not treated here as facts about a particular geopolitical outcome or as tactical forecasts.

Delivered Verified Capacity

For canonical workload $W$ , interval $t$ , and disruption scenario $s$ , define a directed graph $G_{W,t,s}$ from available energy and fuel to usable settled service. Every edge has surviving capacity $c_e(W,t,s)$ in a workload-specific service unit. Then

\mathrm{DVC}(W,t,s)= \operatorname{MaxFlow}\!\left(G_{W,t,s},c(W,t,s)\right).

The corresponding minimum cut identifies the active bottleneck. The unit is not a generic FLOP. It is a settled, independently verifiable unit of the promised workload at the promised tier.

DVC must incorporate:

scenario specificity: drought, fuel shock, transformer loss, chip embargo, network partition, depeg, and coordinated policy create different graphs;
substitution latency: an alternative counts only if it enters before the service obligation expires; and
common-cause groups: nominally separate facilities may share a firmware signer, transformer vendor, cable, gas market, identity layer, cooling basin, legal safe harbor, stablecoin, or market maker.

Sovereign Optionality asks how many independently substitutable paths exist. DVC asks how much usable service reaches the sink after a scenario binds. A system can score well on one and poorly on the other. Both should be reported, along with the active minimum cut and dependency groups.

Receipts are evidence for edge capacities; they are not capacity. Work Credit and capacity-voucher issuance must be bounded by a conservative stress result,

Q^{\mathrm{issue}}_{W,t} \leq \min_{s\in\mathcal{S}_{\mathrm{constitutional}}} \{\mathrm{DVC}(W,t,s)\}\,h_{W,t}, \qquad 0<h_{W,t}<1,

with a published prudential haircut $h_{W,t}$ . Nameplate power, installed hardware, gross proof throughput, and benign averages are inadmissible substitutes.

The Pressure–Capacity Corridor

Let $A_{\mathrm{full\mbox{-}stack}}(R)$ be complete-path availability under regime pressure and let $H(R)$ be the holder’s practical ability to self-custody, transact, prove, and exit. Potential monetary service is bounded by

\Pi_{\mathrm{monetary}}(R)\propto \Delta(R)\times A_{\mathrm{full\mbox{-}stack}}(R)\times H(R).

The likely shape is an inverted U, not a crisis escalator. Under low pressure, institutional substitutes work and differential value is thin. Under moderate pressure, substitutes weaken while the open stack and holder remain operational. Under extreme pressure, power, networks, hardware, liquidity, custody, or exit can fail. More crisis does not imply more premium.

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