Does Hotelling's rule for exhaustible-resource pricing predict a different shape than the vault's cost-of-production / unforgeable-costliness cluster?

Three separate notes have now independently flagged the same gap: the vault's growing cluster on "value tracks the hard-to-forge cost of production, and collapses once that cost falls" — observation-unforgeable-costliness-bridges-asteroid-pgm-and-bit-gold, claim-asteroid-pgm-price-holds-then-collapses, and claim-cheaper-extraction-disruptions-fall-monotonically-not-hold-then-collapse — has never engaged Hotelling's rule, the classical economic model of how the price of an exhaustible resource should evolve over time (extraction should rise at roughly the rate of interest, per Harold Hotelling's 1931 "The Economics of Exhaustible Resources").

Why it matters: Hotelling's rule and the "unforgeable costliness" framing may predict genuinely different price trajectories for the same situation (a resource whose supply is constrained but whose extraction cost changes) — the asteroid-PGM model explicitly needs a mechanism to explain why price holds rather than declining smoothly, and Hotelling's rule is the obvious classical benchmark to check that against. It may confirm the model's deployment-lag mechanism as a genuine departure from the classical baseline, or reveal that the "hold" is just Hotelling's rule under different parameters.

What's needed:

• Read Hotelling (1931) or a reliable secondary restatement (a textbook chapter or a Tier 1–2 economics source) for the rule's core prediction and its assumptions (perfect markets, known reserves, no extraction-cost innovation).
• Check whether Hotelling's rule assumes constant extraction cost — if so, it may not even apply once a cost-collapsing technology (asteroid mining, Hall-Héroult, proof-of-work) enters, which would explain why none of these vault cases fit it cleanly.
• If a clean fit or contrast emerges, write it as its own claim-note and link it into the cluster above.

Progress log

• 2026-07-18: Answered — yes, a genuinely different shape, on a genuinely different mechanism. claim-hotellings-rule-shadow-price-rises-at-rate-of-interest establishes the r-percent rule itself (Tier 1, Slade & Thille); claim-hotellings-rule-predicts-shape-distinct-from-cost-of-production-cluster settles the actual question — Hotelling's rule predicts continuous rise, neither the PGM model's hold-then-collapse nor Wright's-law monotonic decline, because it assumes no cheaper substitute ever enters the model; claim-hotelling-model-frequently-rejected-by-empirical-commodity-data adds the tempering fact that the simple model is frequently rejected by real commodity data, so it's a theoretical benchmark, not a proven rival law. What settled it: a single Tier 1 primary review (Slade & Thille, 'Whither Hotelling') supplying both the rule's derivation and its own empirical-test literature in one source.