Homebrew formula install velocity (monthly)

Monthly install-velocity ranking of Homebrew formulae in the developer/data-tool ecosystem. The public keyless formulae.brew.sh analytics API supplies per-formula install-on-request counts (direct user installs, not dependency pulls) for the trailing 30d, 90d and 365d windows; the official formula.json supplies the metadata (description, license, homepage, version, oldnames/aliases, deprecated/disabled flags). Transform: (1) entity resolution — analytics names resolve onto canonical homebrew/core formula names via oldnames and aliases (third-party-tap installs such as hashicorp/tap/terraform are out of scope and dropped with a logged count); (2) quality gates — deprecated/disabled formulae dropped, description required, 30d on-request installs >= 1000, versioned formulae (names containing '@', e.g. python@3.13) excluded as out of scope; (3) a curated 16-category taxonomy by a deterministic ordered rule set over formula name + description (machine-learning, database, data-format, data-tool, visualization, cloud-devops, build-tools, programming-language, terminal, version-control, editor, compression, security, network, media, cli-utilities; formulae matching none are dropped as out of scope); (4) scoring — velocity_score = min-max-normalized log10(1 + installs_30d), growth_score = min-max-normalized growth of installs_30d versus the annualized 365d baseline (clipped to -100%/+1000%; new entrants pinned to the cap and flagged), trend_score = their 50/50 composite (0-100), trend_rank orders by trend_score descending (ties: installs_30d desc, then formula name), plus a pure-popularity velocity_rank, momentum_vs_quarter (30d vs the 90d mean month), and a breakout flag (>= 200% above baseline or new entrant). Every row carries the exact source API URLs behind its values. fetched_at is the analytics window end date (UTC day granularity), so re-ingesting the same window is a no-op. Primary key: (month, formula_name). Cadence: monthly. Nullability: license_id and homepage_url may be empty when upstream supplies none; scores and ranks are never null. Caveats: on-request installs still include some automated traffic (dotfile bootstraps); the taxonomy is a first-match heuristic, not an authoritative classification; license ids are maintainer-supplied and informational only. Sample use: order by trend_rank for the month's fastest-rising dev tools, or filter category = 'database'.