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Long-term momentum sustains the market.

The Case-Shiller Index, which tracks U.S. residential home prices using a repeat-sales methodology, reflects the actual appreciation of specific properties over time, controlling for quality and characteristics. Since 2012, the index has shown nearly continuous growth, demonstrating resilience even during periods of recession or interest rate hikes. Robert Shiller, in Irrational Exuberance, highlights that such sustained trends often indicate underlying structural support, including persistent demand and limited supply, which can carry the index above 350 despite short-term fluctuations.

Structural housing shortages drive upward pressure.

The U.S. faces a residential housing deficit estimated between 2–6 million units, with vacancy rates at multi-decade lows. Kindleberger, in Manias, Panics, and Crashes, explains that physical supply constraints in active markets can create temporary spikes in asset prices. Applied to the current housing market, these structural shortages make it plausible that the Case-Shiller Index could register 350 in at least one month, satisfying the question’s resolution criteria.

Monetary policy and credit conditions still provide support.

Despite higher recent interest rates, most mortgage holders remain in historically low fixed-rate agreements, and alternative credit channels continue to support demand. Hyman Minsky’s Financial Instability Hypothesis suggests that periods of stability generate confidence, allowing moderate leveraging that sustains asset prices. In practical terms, even a partial slowdown in demand may not prevent the index from temporarily hitting 350.

Historical patterns indicate possible peaks.

According to Reinhart & Rogoff in This Time Is Different, housing markets can record price peaks even when fundamentals are not fully supportive, due to a combination of credit, scarcity, and investor sentiment. This historical pattern reinforces that a temporary exceedance of 350 is possible, particularly given the resolution criteria require only a single-month breach.

Moderate speculative demand contributes.

Investments in residential assets as inflation hedges, alongside institutional investment in REITs and private equity, maintain upward pressure. While not extreme, this speculative component complements structural and momentum factors, increasing the likelihood of the index briefly exceeding 350.

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It is possible that U.S. entities, such as OpenAI (in partnership with Microsoft), Google DeepMind, Anthropic, Meta AI, and xAI (Elon Musk), could train models of 10^27 FLOPs by mid-2027. These companies are already operating near 10^26 FLOPs and possess the largest computational resources available globally.

However, energy limits, costs, and hardware availability remain significant barriers. Understanding the costs of training such large models is crucial because it defines who really has a chance to reach 10^27 FLOPs. This separates the “frontier club” countries/companies (U.S., China, some big techs) from those that will rely on ready-made technologies.

The time vs. number of GPUs graph shows that having many GPUs is not enough — industrial-scale infrastructure is required to train models quickly. In addition, electrical infrastructure is directly impactful: planning power plants, transmission lines, and energy efficiency is essential.

Note: [attachment] for the illustrative table on energy and GPU costs to train a 10^27 FLOPs model by 2027 (Portuguese).

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Use of AI in military contexts (reconnaissance, logistics, and cybersecurity)

• Probability: 70–80%

Armed forces are already using AI in various applications, such as satellite and drone image analysis, detecting cyberattacks, autonomous systems (air, land, or maritime), and logistics/maintenance of equipment.

There is no public evidence that large models (≥10^26 FLOPs) are being used directly in autonomous weapons, but governments closely monitor and fund research in this area.

AI companies, including OpenAI, Anthropic, and Google DeepMind, have publicly positioned themselves against direct military use of their models in weapon systems.

Official references:

U.S.: DoD AI Strategy (2019), AI Executive Orders (2023), Responsible AI Strategy and Implementation Pathway (2022) – [ UNT Digital Library]

European Union: AI Act (2024), AI@EC Communication (European Commission) 

China: Next Generation Artificial Intelligence Development Plan (2017) 

Brazil: Brazilian Artificial Intelligence Strategy (EBIA, 2021)

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