Tension Index

Phase I: Normalized Divergence

The Normalized Divergence measures how fast research is accelerating relative to capital over a 3-month rolling window, compressed into the −100 to +100 range.

For each month, the algorithm computes the simple return (percentage change from first to last value) of both the research series and the capital series over a trailing 3-month rolling window. The divergence is the difference between the two returns: positive when research is accelerating faster, negative when capital is. This raw divergence is then compressed through a hyperbolic tangent function (tanh) with sensitivity parameter λ = 1.5, which maps any divergence smoothly into the −100 to +100 range without hard cutoffs.

Phase II: Quality Filter

The Quality Filter reduces the Tension Index signal when public interest is volatile, to prevent hype from distorting the metric.

The signal is modulated by a quality factor based on Google Trends volatility. We compute the coefficient of variation (standard deviation / mean) of the public interest series over the last 6 months. If this ratio exceeds 1.5 — meaning the standard deviation is 150% of the mean, indicating speculative hype — the signal is fully suppressed. Below that threshold, the signal is proportionally reduced. This filter ensures that the Tension Index reflects genuine research-capital dynamics rather than media-driven noise.

Phase III: Magnitude Factor

The Magnitude Factor amplifies the signal when current research activity is significantly above its 2015–2023 historical baseline, and attenuates it (to 40%) when below.

The signal is further weighted by how the current research volume compares to the 2015–2023 historical baseline. The z-score of current average publications against the baseline mean and standard deviation is compressed through a logistic sigmoid into the range 0.4–1.0. A sector with research activity well above its historical norm amplifies the signal; one below it attenuates it to 40%, but never zeroes it out.

Synthesis

The final Tension Index for each month is the product of the three components: Normalized Divergence × Quality Filter × Magnitude Factor, rounded to the nearest integer. The result is a series of integers in [−100, +100] that decomposes cleanly: DN measures direction and intensity, QF discounts hype noise, MF weights historical relevance.

How to Read It

• TX > 0: Research is accelerating faster than capital — a potential opportunity window where the market has not yet priced in scientific progress.
• TX < 0: Capital is accelerating faster than research — a potential bubble risk where investment outpaces the underlying science.
• TX ≈ 0: Equilibrium between the two dynamics, or the signal is attenuated by high volatility or low historical magnitude.

Limitations

The algorithm is sensitive to outliers at the edges of the rolling window. The quality filter assumes public interest is independent of the research and capital processes. The volatility threshold (1.5) is a fixed empirical constant. Each sector is treated independently, so systemic market conditions are not captured. Historical baselines are updated quarterly and may lag structural shifts.