The AstroForge PGM paper reports the same hold-then-collapse shape under two different demand assumptions — constant demand in its back-of-envelope table, price-responsive demand in its full simulation

Nachtrieb and Smith's paper (arXiv:2607.06806) presents the hold-then-collapse trajectory twice, under two different demand assumptions. The back-of-envelope sketch — claim-asteroid-pgm-price-holds-then-collapses's Table III (price 60→60→11 MUSD/ton) — fixes demand explicitly as a simplification: "For simplicity, it is assumed the market demand remains constant at all three points." The full System Dynamics simulation (Figure 4), by contrast, lets demand move with price during the transition: "Declining market price stimulates an increased demand." The paper frames the full simulation as the same underlying transition "depicted in Table III, but with higher fidelity" — so the two exhibits are presented as successive refinements of one result, not two separate claims, and the shape recurring under both a fixed-demand sketch and an elastic-demand simulation is some evidence it is not an artifact of the simpler assumption.

It is evidence, not proof: the paper never states that the elastic-demand simulation reproduces the same three-point trajectory quantitatively, only that it tells a qualitatively similar story at higher fidelity. Whether the flat-price hold survives numerically once demand is allowed to respond to price is a question about the model's actual equations, not its prose description.

Provenance: source_url: https://arxiv.org/pdf/2607.06806; source_author: Robert T. Nachtrieb and Steven J. Smith; source_date: 2026-07-07 (v1); source_tier: 1. The quantitative comparison this note can't yet make — does elastic demand preserve the hold's magnitude, not just its shape — needs the ancillary AstroForge_v5.mdl file read verbatim; tracked at question-verify-astroforge-pgm-model-dynamics.