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1\documentclass[12pt]{article}2\makeatletter\def\input@path{{../paper/}}\makeatother3\input{../paper/preamble}4\graphicspath{{figures/}{../paper/figures/}}56\title{Online Appendix for\\ ``Faster, Wider, More Fragile? The Evolution of7Intraday Shock Propagation in U.S.\ Equity Markets, 1992--2026''}8\author{}9\date{}1011\begin{document}12\maketitle13\tableofcontents14\clearpage1516\section{Extended data audit}17\label{app:audit}1819\paragraph{Provenance and snapshot.} The data are one-minute OHLCV bars20originally sourced from Finnhub.io and aggregated into 411 monthly files21(January 1992--March 2026). The exact byte-level snapshot is pinned: every22file's SHA-256 checksum was verified at download against the archive's23metadata and re-verified after the full download; the manifest (per-file24checksum, byte size, row count, column schema, timestamp bounds, symbol25count, duplicate count) accompanies the replication package. The archive26carries no explicit licence; the minute data are used for research with27attribution and are not redistributed.2829\paragraph{Calendar and timezone.} Observed trading dates match the official30XNYS calendar exactly over the full sample: zero missing sessions, zero dates31outside the calendar, zero weekend observations. Timestamps are UTC at32bar-start; mapping to Eastern Time was verified empirically on both sides of33every daylight-saving transition (the regular session opens at 13:30 UTC in34summer months and 14:30 UTC in winter months throughout). The regular-hours35share of bars by calendar month is flat (96.75\%--97.09\%), ruling out any36DST mishandling: an offset error would displace roughly 15\% of session rows37in March and November. Early-closing sessions are truncated at the true38exchange close; residual post-close prints (7.3\% of morning volume on392025-12-24 versus 60.4\% on the adjacent full day) are labelled after-hours.4041\paragraph{Integrity.} Across \DataRows{} bars: \DataOHLCViol{} OHLC-impossible42bars (1.3 per $10^8$, concentrated 1993--1995), zero non-positive prices, zero43zero-volume or negative-volume bars, \DataDupKeys{} duplicate ticker-minute44keys (1.3 per million; merged as open=first, high=max, low=min, close=last,45volume=sum). Prices are unadjusted for corporate actions; volumes are in46shares (verified against public daily volumes for benchmark securities).4748\paragraph{Identity and survivorship.} The panel spans \DataTickers{} tickers49forming \DataSpells{} continuous spells (a gap exceeding 30 calendar days50starts a new spell); \DataMultiSpellTickers{} tickers have multiple spells, so51all long-horizon statements operate within spells. Delisted securities are52present throughout (exits run 800--1,600 per year); the single discrete53coverage expansion (2020, over-the-counter names) is absorbed by fixed-rule54lagged universes.5556\paragraph{Corporate actions.} A conservative overnight-ratio screen57(canonical ratios 2 through 8, 10, 20, and 3/2, with their inverses,58$\pm1.5\%$ tolerance, both-day dollar volume $\ge \$50{,}000$, prior close $\ge \$1$)59detects \NSplitEvents{} events (\NSplitFwd{} splits, \NSplitRev{} reverse60splits); event days $\pm1$ trading day are excluded from every return-based61statistic.6263\paragraph{Pilot audit.} Before the full download, three pilot months (June641992, June 2009, December 2025; 58.8~million bars) were audited. Trading-day65counts match the exchange calendar in all three, including the66December~24, 2025 early close; no OHLC-consistency violation, null value,67negative volume, or zero-volume bar occurs; 14 duplicate ticker--minute pairs68(all in inactive over-the-counter names) appear in December 2025. Liquid69securities are densely covered throughout: the four most active tickers in70December 2025 have complete 390-bar regular sessions, and large issuers71already average 277--369 bars per day in June 1992. Volume units were72verified against public daily volumes for benchmark securities.73Figure~\ref{fig:app_pilot_coverage} summarizes raw data volume and per-day74symbol counts, Figure~\ref{fig:app_pilot} the pilot intraday seasonality,75and Table~\ref{tab:pilot_summary} pilot summary statistics for the 50076highest dollar-volume securities in each pilot month.7778\begin{figure}[t]79\centering80\includegraphics[width=\textwidth]{figP1_coverage.pdf}81\caption{\textbf{Dataset coverage.} Panel (a): compressed size of each82monthly source file, 1992--2026 (all 411 files of the pinned snapshot). Panel83(b): number of symbols with at least one bar per trading day in the three84pilot months.}85\label{fig:app_pilot_coverage}86\end{figure}8788\section{Additional descriptive evidence}89\label{app:descriptive}9091Figures~\ref{fig:app_survivorship}--\ref{fig:app_splits} complement the92descriptive results of the main text: universe entry/exit dynamics, dollar93volume concentration, the cross-section of realized volatility, the94stale-price share, and the time series of detected corporate-action events.95Table~\ref{tab:summary_by_decade} reports decade-level summary statistics for96the top-1000 universe.9798\begin{figure}[t]99\centering100\includegraphics[width=\textwidth]{figE2_survivorship.pdf}101\caption{\textbf{Universe dynamics.} (a) Active symbols per year; (b) entries102and exits. The shaded band marks the 2020 source-coverage expansion.}103\label{fig:app_survivorship}104\end{figure}105106\begin{figure}[t]107\centering108\includegraphics[width=\textwidth]{figE4_concentration.pdf}109\caption{\textbf{Concentration of trading.} (a) Share of aggregate dollar110volume of the top 1\% and 5\% of symbols; (b) Herfindahl index of dollar111volume.}112\label{fig:app_concentration}113\end{figure}114115\begin{figure}[t]116\centering117\includegraphics[width=.6\textwidth]{figE6_rv.pdf}118\caption{\textbf{Cross-section of realized volatility.} Median, interquartile119range, and 95th percentile of daily 5-minute realized volatility, lagged120top-1000 universe.}121\label{fig:app_rv}122\end{figure}123124\begin{figure}[t]125\centering126\includegraphics[width=.6\textwidth]{figE7_staleness.pdf}127\caption{\textbf{Stale-price share.} Percentage of one-minute returns exactly128zero, lagged top-1000 universe (\ZeroRetNinetySix\% in 1996,129\ZeroRetTwentyFour\% in 2024).}130\label{fig:app_staleness}131\end{figure}132133\begin{figure}[t]134\centering135\includegraphics[width=.6\textwidth]{figE9_splits.pdf}136\caption{\textbf{Detected corporate-action events per year.} Forward splits137(up) and reverse splits (down) from the overnight-ratio screen.}138\label{fig:app_splits}139\end{figure}140141\input{tables/table2_summary_by_decade}142143\clearpage144\section{Additional propagation results}145\label{app:propagation}146147Figure~\ref{fig:app_evolution} shows the year-by-year evolution of abnormal148market-wide breadth at $h=5$ and $h=30$ with 95\% day-block bootstrap bands:149the market-wide difference-in-differences is within two standard errors of150zero in essentially every year, not merely on average. The design diagnostics151(pre-event levels, co-arrival classes, pre-level-stratified estimates,152alternative clustering, signed responses) and the decomposition of the153network differential by decade are reported in the main text.154155\begin{figure}[t]156\centering157\includegraphics[width=.62\textwidth]{figF2_evolution.pdf}158\caption{\textbf{Evolution of abnormal market-wide propagation.}159$\Delta\Delta$ breadth by year at $h=5$ and $h=30$ minutes, with 95\%160day-block bootstrap intervals.}161\label{fig:app_evolution}162\end{figure}163164\begin{figure}[t]165\centering166\includegraphics[width=\textwidth]{figP2_seasonality.pdf}167\caption{\textbf{Pilot-sample intraday seasonality} (June 1992, June 2009,168December 2025; top-500 by within-month dollar volume).}169\label{fig:app_pilot}170\end{figure}171172\input{tables/tabP1_pilot_summary}173174\clearpage175\section{Computational details and reproducibility}176\label{app:compute}177178The pipeline is deterministic end-to-end. All parameters live in versioned179configuration files; the global seed (20260713) governs placebo draws and180bootstrap resampling; every table and figure is generated by a numbered181script from machine-readable intermediate results, and every numerical claim182in the manuscript resolves to a macro generated from those results---no183number is typed by hand. The full run comprises: download and checksum184verification (411 files); per-month integrity audit and daily metadata185construction; clean-panel construction (duplicate resolution, session186labelling with true exchange closes, integrity and corporate-action flags);187universe construction with strictly lagged screens; descriptive aggregation;188shock detection and outcome measurement (\NEventsReal{} events,189\NEventsPlacebo{} placebos); network and co-jump measurement; and estimation.190Every stage operates month-by-month on partitioned columnar files with four191parallel workers on an Apple-silicon workstation; wall-clock times for each192stage are recorded in the run logs of the replication package. The193revision diagnostics (pre-event levels, co-arrival classes, stratified194estimators, alternative clustering) are recomputed from the stored195event-level files in a few minutes without access to the raw minute panel.196197\section{Analyses not executed}198\label{app:notdone}199200The following checks are referred to in the main text as not executed, so201that no claim rests on them: source thresholds $|z|\ge4$ and $|z|\ge5$;202receiver threshold $|z|>3$; the top-1000 and top-3000 shock universes;203neighbor sets estimated on 5- or 30-minute residual correlations or with a204transaction-time covariance estimator; the pre-event ($t-5$) network205contrast; permuted-network placebos preserving industry and liquidity206composition; propagation measured inside scheduled-announcement windows; a207Hawkes-type model of the co-jump minute series; and a reconciliation of208bar volumes against consolidated-tape volumes to establish the venue scope209of the source. Each requires re-running the detection stage on the raw210minute panel or external data.211212\end{document}213