The geometry of
market memory.

Rolling empirical return distributions are located between low- and high-volatility Wasserstein prototypes. The resulting recovery times and cumulative excess memory are compared with an ordered, variance-targeted Markov-switching GJR-GARCH model across the S&P 500, FTSE 100, Nikkei 225, and Hang Seng.

Raw persistence is strongly scale-related. The S&P 500 COVID episode supplies the strongest evidence of a positive distribution-lagging recovery gap. Strictly real-time evaluation, however, finds no stable incremental forecasting gain after multi-horizon volatility history is observed.

A strictly prior-information Wasserstein score compares current return distributions with recursively updated calm and stress barycenters. Detection thresholds are calibrated before 2007 and then frozen.

Across seven episodes and four markets, raw DRP detects 21 of 28 market–event cases, compared with 15 for 22-day realized volatility. The paired advantage does not survive Holm correction. Controlled variance-matched shape shifts show why distribution-sensitive monitoring can remain useful even without universal forecasting gains.

Frozen distributional-regime thresholds softly route observations between calm and stress empirical Value-at-Risk and Expected Shortfall experts. Evaluation compares realized-volatility, EWMA, and frozen-GARCH scale filters using joint VaR–ES loss and calibration diagnostics.

Broad directional gains under realized-volatility scaling weaken under alternative filters. Rolling estimation reverses some S&P 500 gains, while dynamic-quantile failures persist. The prespecified criterion for universal forecast content is not met.

A frozen external-validation design evaluates eight equity markets across three scale filters, three tail probabilities, and four memory rules. The primary comparison is the FZ0 loss difference between Soft-DRP and matched filtered historical simulation.

No configuration passes the universal portability gate. Five European cells pass conditional gates under the prespecified hierarchical model, but the positive result does not survive conservative wider-heterogeneity stress tests. Absolute calibration remains weak. The defensible conclusion is a boundary on portability.

The study asks whether outcome-blind geometric drift anticipates deterioration in static-coordinate tail forecasts and can guide recalibration. A separate locked eight-market panel tests geometric aging and triggered-versus-static FZ0 loss.

In the recorded formal run, the geometric-aging slope is not statistically resolved and triggered recalibration improves none of the eight markets. The dynamic-quantile guardrail passes, but cannot override the failed primary gates. The result supports a diagnostic boundary rather than a universal recalibration claim.

Based on the formal result summary dated 31 August 2026. Manuscript development is ongoing.