Google_maps

Hallucination-resistant answer mode for high-stakes reads. Same routing as ask_pipeworx — picks the right tool from 4,748 across 1234 sources, fills arguments, fetches the data — then EXTRACTS the answer using ONLY what the tool result contains. Returns {answer, evidence (verbatim quote), confidence, source, fetched_at, refusal_reason:null} on success, OR an explicit refusal {answer:null, refusal_reason:"not_in_source"|"no_tool_match"|"tool_error"|"data_truncated"|"llm_error"} when the data doesn't directly answer. Use whenever an answer will be quoted, cited, or acted on, and the agent must not invent facts (financial verdicts, legal claims, medical lookups, public statements). Costs one extra LLM call vs ask_pipeworx — prefer ask_pipeworx for casual lookups.

Research a Polymarket bet by pulling the relevant Pipeworx data for it in one call. Pass a market slug ("will-bitcoin-hit-150k-by-june-30-2026"), a polymarket.com URL, or a question text. The tool resolves the market, classifies the bet, fans out to category-specific data packs in parallel, and returns an evidence packet + simple market-vs-model comparison. Use for "should I bet on X", "what does the data say about Y", or "is there edge in Z". CLASSIFIERS: crypto_price, fed_rate, geopolitical, sports, sports_championship, drug_approval, election_candidate, tech_launch, space_launch, corporate, corporate_earnings, corporate_event, public_figure_speech, weather, other. FAN-OUT EXAMPLES: BTC bet → coingecko + fred + gdelt+gnews; Fed bet → fred (DFEDTARU + EFFR + CPIAUCSL) + kalshi_macro (KXFED implied probs) + recent_fed_actions (federal-register rules, last 365d); Hormuz bet → imf_portwatch + airspace + gdelt; Yankees WS → mlb_stats_standings + parent_event partition + news; hottest-year bet → climate_projection_nyc + gistemp_latest (NASA global anomaly, rank since 1880) + news; NVDA-vs-AAPL → finnhub get_quote + edgar shares-outstanding (derived market cap) + edgar filings + news. RESPONSE SHAPES: result.market carries best_bid/best_ask/spread_pp/liquidity/price_change_1h/1d/1w; result.analysis carries model_probability/edge_pp/kelly_fraction_half when a closed-form model fires PLUS a 24h-move warning ("Market moved X.Xpp in 24h, comparable to model edge — your edge may already be priced in") when relevant; result.evidence is keyed by source. RESOLVER CONTRACT: result.market_match_confidence ∈ {high, medium, low, none}, market_match_score (0-1 token-overlap), market_match_alternatives[] (other candidate markets the resolver considered), and suggestions[] (explicit re-query hints when the match is fuzzy) — ALWAYS inspect these before trusting the analysis block, because medium/low matches can still surface other fields. PARENT_EVENT EXTRACTOR: when the bet is one leg of a partition (Yankees WS, Romania election), result.parent_event{matched_candidate, top_legs_by_price[], partition_size, placeholders_filtered} gives you the peer prices in one place — that's the headline for elections/championships. NEWS FIELDS: news entries carry _fallback_attempted / _fallback_failed_reason / retry_after_sec when GDELT 429s and GNews backfill ran or failed. SAFETY: low-confidence resolutions short-circuit with status:"low_confidence_match" and suppress analysis fields so agents can't accidentally size on phantom matches. Closed/dead markets that ARE still indexed by Polymarket (yes_price≈0, no volume, no liquidity) return status:"market_closed_or_inactive" and skip fan-out. In practice resolved markets are usually de-indexed and instead surface via the low_confidence_match path above — both routes are BLOCKING, just different mechanisms. Wide-spread markets (>10pp) carry tradeability:"illiquid_wide_spread" + an explanatory note. RESOLUTION-RULE RISK: market.cancellation_rule parses the void/postponement settlement out of the resolution text — refund_50_50 (shares settle flat 50¢ on void; EV-material for any entry away from 50¢, with ev_impact quantified), resolves_no_on_cancel, resolves_yes_on_cancel, carries_to_reschedule, or mentioned_unclear. null means the description never mentions cancellation. Check this before sizing sports/esports/event-occurrence bets — audited arb-bot ledgers show flat-50¢ void settlements are a recurring pure-rules loss.

"Compare X and Y" / "X vs Y" / "X versus Y" / "which is bigger / better / larger / more profitable" / "rank these companies" / "head to head" — side-by-side comparison of 2–5 companies or drugs in ONE parallel call. ALWAYS PREFER over sequential single-pack lookups when comparing entities. type="company" pulls LATEST 10-K revenue + net income + cash + long-term debt from SEC EDGAR/XBRL (off-calendar fiscal years handled correctly — AAPL Sep, NVDA Jan, etc.). type="drug" pulls FAERS adverse-event counts, FDA approval counts, active trial counts. Results sorted by primary metric so "largest" / "most" / "biggest" reads off the top of the response. Returns paired data + pipeworx:// citation URIs per entity. Replaces 8–15 sequential lookups.

ACCOUNT REQUIRED (free — sign in via GitHub at https://pipeworx.io/signup; depth:"thorough" needs a paid plan). If you are not signed in, use ask_pipeworx instead — it works on every tier. Grounded multi-source research across Pipeworx's 1234 STRUCTURED data sources (SEC filings, FRED/BLS economics, FDA, USPTO patents, markets, science, government records, etc.) in ONE call — this is NOT open-web search. Decomposes your question into focused facets, routes each to the right one of 4,748 tools IN PARALLEL, and returns a findings packet: verbatim evidence + confidence + source + fetched_at + a stable pipeworx:// citation per finding, with explicit gaps[] for facets the data couldn't answer (never invented). Best for broad/multi-part questions over structured data ("compare X and Y's regulatory + financial exposure", "research the filings + market picture for ACME"). For a single lookup use ask_pipeworx (one LLM call, not many). For BREAKING or colloquial CURRENT-NEWS / "what's the world saying about X" topics, prefer ask_pipeworx — it routes to live news APIs and the *-news-feeds packs; deep_research returns mostly empty gaps[] when the topic isn't in the structured catalog. Expect 15-60s.

Find tools by describing the data or task. Use when you need to browse, search, look up, or discover what tools exist for: SEC filings, financials, revenue, profit, FDA drugs, adverse events, FRED economic data, Census demographics, BLS jobs/unemployment/inflation, ATTOM real estate, ClinicalTrials, USPTO patents, weather, news, crypto, stocks. Returns the top-N most relevant tools with names, descriptions, and full input schemas (with curated examples) — each result is ready to call directly, no second schema lookup needed. Call this FIRST when you have many tools available and want to see the option set (not just one answer).

"Tell me about X" / "research Acme" / "brief me on Tesla" / "what does Apple do" / "company profile for Microsoft" / "give me the rundown on NVDA" / "everything you know about $TICKER" — full cross-source profile of a US public company in ONE parallel call. ALWAYS PREFER over chaining single-pack SEC/XBRL/news lookups when the user asks for a holistic view. Fans out across SEC EDGAR, XBRL, USPTO, news, GLEIF and returns: cik + company_name; recent_filings (up to 5 with pipeworx://edgar/company/{cik}/filings/{accession} URIs); fundamentals (LATEST 10-K Revenues + NetIncomeLoss + Cash, sorted period_end DESC); patents (USPTO PatentsView API sunset May 2025 — soft-fails until reactivated); recent news mentions via GDELT→GNews fallback; LEI via GLEIF. Pass ticker "AAPL" or zero-padded CIK "0000320193" — names not supported (use resolve_entity first if you only have a name).

Delete a previously stored memory by key. Use when context is stale, the task is done, or you want to clear sensitive data the agent saved earlier. Pair with remember and recall.

Generate a production-ready llms.txt file for any URL so AI crawlers (ChatGPT, Claude, Perplexity) can index the site cleanly. Fetches the page, extracts title/description/key links, and emits the standard llms.txt markdown format. Output is a single text blob ready to drop at site-root/llms.txt. Useful for: getting a client's site indexed by AI, drafting llms.txt for your own project, or auditing how an AI crawler would see a competitor.

List the caller's active subscriptions. Returns id, type, params, created_at, last_fired_at, fire_count for each. Use this to review what you're monitoring before adding more or to find an id to cancel.

"Google Maps directions from A to B" / "transit / public-transport directions" / "bus / subway / train route" / "best way to get from [X] to [Y]" — turn-by-turn directions via Google Maps. Modes: driving, walking, transit (bus/subway/train), bicycling. Requires Google Maps API key. PREFER over Mapbox/OpenRouteService specifically for public-transit routing — Google has the best transit data.

"Travel time matrix between [N] origins and [M] destinations" / "drive-time grid via Google Maps" / "transit times between addresses" — N×M distance and duration matrix between many points via Google Maps. Modes: driving, walking, bicycling, transit. Use for delivery routing, multi-stop optimization, transit-heavy planning.

"Elevation at [coords] via Google" / "altitude / height above sea level" — elevation in meters for one or more lat/lng pairs via Google Maps Elevation API. Pipe-separated locations for batch queries.

"Geocode [address] via Google Maps" / "Google Maps coordinates of [place]" / "lat lng for [address] using Google" — convert an address to lat/lng + formatted address via Google Maps Platform. Premium-quality geocoding (highest accuracy for US addresses); requires Google Maps API key. Use when Mapbox/MapTiler/OpenStreetMap miss the address.

"Hours / phone / reviews of [business]" / "Google business info for [place]" / "is [restaurant] open" — full details for a Google Place: address, phone, hours, website, ratings, user reviews. Requires a place ID from `maps_place_search`. Use after search to drill into one specific business.

"Find restaurants / hotels / coffee shops / [businesses] near [location]" / "nearby [type] within [radius]" / "places to eat in [area]" — find nearby businesses and points of interest via Google Maps Places. Returns names, addresses, Google ratings, distances. Premium-quality POI data; requires Google Maps API key. Use over Yelp/OSM when you want Google's POI coverage and ratings.

"Reverse geocode [lat,lng] via Google Maps" / "what address is at [coords] in Google" — coordinates → address via Google Maps Platform. Requires Google Maps API key. Use when you need Google's street-address parsing (most accurate for US).

Tell the Pipeworx team something is broken, missing, or needs to exist. Use when a tool returns wrong/stale data (bug), when a tool you wish existed isn't in the catalog (feature/data_gap), or when something worked surprisingly well (praise). Describe the issue in terms of Pipeworx tools/packs — don't paste the end-user's prompt. The team reads digests daily and signal directly affects roadmap. Rate-limited to 5 per identifier per day. Free; doesn't count against your tool-call quota.

What other AI agents are calling on Pipeworx right now. Returns the top tools, top packs, and total call volume over a recent window (24h, 7d, or 30d). Useful for: (1) discovering what data sources are hot for current events, (2) confirming a popular tool is the canonical choice before asking your own question, (3) seeing whether your use case aligns with what most agents need. Self-aggregating signal — derived from CF analytics-engine, no PII, just (pack, tool, count). Cached 5min-1h depending on window.

Find arbitrage opportunities on Polymarket via monotonicity violations + partition-sum checks. Call with NO args for a `trending_scan` of the top ~200 markets by weekly volume; pass `event` for the strongest per-event partition_check, or `topic` for a themed cross-event scan. `event` (recommended for a specific market): pass a Polymarket event slug like "fed-decision-may-2026" or "when-will-bitcoin-hit-150k"; walks child markets, checks date-axis / threshold-axis ordering AND computes the partition_check (sum of YES prices across mutually-exclusive legs — should ≈1; deviations >3pp emit a BUY/SELL EVERY LEG signal). `topic` (for cross-event scanning): pass a seed question like "Strait of Hormuz traffic returns to normal" or "Fed rate decision"; searches related events across the platform, flattens markets, runs the comparator on the union. Cross-event mode catches "...by May 31" vs "...by Jun 30" patterns that single-event misses. SEMANTIC ANCHOR: cross-event pairs require ≥0.30 Jaccard similarity on question tokens (prevents Powell-Fed-Pause being paired with Powell-DOJ-probe); skipped_low_similarity surfaces the rejected pair count. PARTITION FILTER: drops will-person-X / will-manager-Y / will-someone-else- placeholder slugs; partitions with >20% placeholder fraction return null arb signal. Response: opportunities[] (gap_pp, suggested_trade, reasoning, monotonicity violation context), and in event mode partition_check{sum_yes_prices, gap_from_1, placeholders_filtered, suggested_trade}. FILL CHECK: when the partition signal fires, arbitrage.fill_check prices it against live CLOB depth (theoretical_edge_pp_at_book vs realizable_edge_pp at 1000 shares/leg, thin_legs[]) — realizable_edge_pp ≤ 0 means the overround exists only at last-trade, not in the book; do not trade it. For custom sizing use polymarket_fill_risk.

Edge persistence and decay telemetry built from daily polymarket_edges snapshots. Answers "how long has this edge existed and is it shrinking?" — a fresh wide edge and a 3-week-old wide edge are different trades (the latter is wide for a reason nobody is willing to take). Args: days (lookback, default 14, max 30), window (snapshot family, default "1wk"). RESPONSE: tracked[] = every opportunity in the LATEST snapshot with its full edge_pp_net time-series across prior snapshots, first_seen, trend (new | widening | stable | decaying) and decay_pp_per_day (both computed on |edge_pp_net| — the value itself is signed by trade direction, negative = SELL YES); expired[] = opportunities that appeared in earlier snapshots but are GONE from the latest (closed, resolved, or arbed away) with their lifespan_days — the median lifespan is your competition clock; snapshot_dates[] = which days actually have data (snapshots are written when polymarket_edges runs on a cache-miss, so gaps mean nobody scanned that day). LIMITS: history depth is bounded by the 60-day snapshot TTL and starts from when snapshotting was enabled; decay numbers come from daily closes of edge_pp_net (net of default slippage), not intraday.

Scan top Polymarket markets and return opportunities where Pipeworx data disagrees with market price. Built for "what should I bet on today" — agents discover opportunities without paging hundreds of markets. FIVE MODEL FAMILIES grouped into three response segments under by_segment: (1) MODEL_DRIVEN — crypto_price (lognormal barrier from 90d FRED log-returns) and news_momentum (GDELT 7d/21d article-volume ratio, soft signal w/ halved Kelly). (2) STRUCTURAL_ARBITRAGE — partition_overround on mutually-exclusive events; per-leg favorite-longshot bias correction with per-sport α (tennis 1.02, soccer 1.10, MMA 1.15, default 1.0); placeholder-slug filter drops will-person-X / will-team-Y / will-manager-Z / will-someone-else- backstops; partitions with >20% placeholder fraction skipped entirely. (3) CONCENTRATED_LONGSHOT — basket trade when one leg ≥75% AND ≥2 longshots ≤8% AND portfolio return ≥25:1; rare-by-design (gates relaxed Run 8 from prior 85%/5%/50:1). EVERY OPPORTUNITY carries edge_pp_net (after slippage), kelly_fraction + kelly_fraction_half (capped at 0.25), market.liquidity, market.spread_pp, market.volume, plus a 24h-move warning ("Market moved X.Xpp in 24h") when the recent move alone exceeds the edge — your edge may already be in the price. TRADEABLE-EDGE KNOBS: min_liquidity / max_spread_pp drop opportunities where edge isn't realizable; min_partition_leg_kelly filters partitions by best per-leg Kelly. RESPONSE TOP-LEVEL: by_segment{model_driven,structural_arbitrage,concentrated_longshot}, fed_candidates/fed_note (Fed bets surface here, excluded from ranking — 1m-T vs EFFR signal is unreliable at meeting-month horizons without paid OIS/SOFR-futures data), and _diagnostics{concentrated_longshot:{...funnel counters},category_counts,filter_skips} so callers can see WHY a segment is empty (top-N stale, all candidates failed gates, knob dropped them). Cached 1h at the KV level keyed on all knobs.

Realizable-vs-theoretical edge check against live CLOB order-book depth. REQUIRES one of `market` (single-market mode) or `event` (basket/partition mode). SINGLE-MARKET: pass a market slug/URL + side (buy_yes|sell_yes|buy_no|sell_no, default buy_yes) + size_usd (default 1000 — max spend on buys, target proceeds on sells); walks the ladder and returns top_of_book, vwap_fill_price, slippage_pp, shares_filled, max_fillable_usd, and a verdict (clean|degraded|cannot_fill). BASKET: pass an event slug/URL + side (sell_yes = capture overround by selling every leg, buy_yes = capture underround; default auto from partition sum) + size_usd interpreted as settlement notional S (shares per leg; each share pays $1); returns theoretical_sum vs realizable_sum (top-of-book vs VWAP across all legs), capture_ratio, profit_usd at executed size, per-leg fill detail, thin_legs[], max_clean_notional_usd, and forced_directional_risk naming the legs most likely to strand you unhedged. USE THIS before acting on any polymarket_arbitrage SELL/BUY-EVERY-LEG signal or any polymarket_edges trade above ~$500 — theoretical overround on thin books is not capturable, and partial basket fills convert an arb into an unhedged directional position (the dominant loss mode in real arb-bot P&L).

Cross-venue spread between Kalshi and Polymarket for the same resolving question. The two venues sometimes price the same outcome 2-25pp apart because their participant pools differ — when the bet shapes are equivalent that delta is a real signal, when they aren't the tool says so. TWO MODES: (1) `topic` — 10 pre-mapped macro shortcuts ("fed", "btc", "cpi", "gdp", "sp500", "recession", "next_pope", "next_uk_pm", "next_israel_pm", "2028_president") auto-fetch the matching event on each venue. (2) explicit `kalshi_event_ticker` + `polymarket_event_slug` for custom pairings. RESPONSE: each venue's leg-by-leg prices (raw probability 0-1) plus matched spread[].top_spreads_pp (Kalshi − Polymarket) where the same outcome shows up on both sides. SAFETY FIELDS: compatibility_warning fires in two cases — (a) matched_pairs:0 with skipped_cross_type>0 means the venues frame the topic with non-equivalent bet shapes (e.g. Kalshi range_bucket point-in-time vs Polymarket cumulative_threshold touch-anywhere — no arb exists), (b) matched_pairs:0 with skipped_cross_type:0 and both venues >5 legs means the token-overlap matcher found nothing in common — events likely semantically unrelated despite the topic keyword. temporal_alignment{polymarket_month,kalshi_month,aligned} tells you whether the two events resolve in the same calendar period; aligned:false means spreads are mathematically meaningless across the temporal gap. skipped_cross_type / skipped_cross_subtype counters expose how many leg-pair comparisons were dropped (cross-type = metric_type mismatch like MoM vs YoY; cross-subtype = inequality mismatch like cum_ge vs cum_le). Real cross-venue spreads are rarer than the macro-shortcut list suggests — most pre-mapped topics return compatibility_warning today; pre-mapped ≠ tradeable.

Retrieve a value previously saved via remember, or list all saved keys (omit the key argument). Use to look up context the agent stored earlier — the user's target ticker, an address, prior research notes — without re-deriving it from scratch. Scoped to your identifier (anonymous IP, BYO key hash, or account ID). Pair with remember to save, forget to delete.

Pull fired events from your subscription feed. Returns the most recent alerts the evaluator has written to your persisted feed — each carries source, citation_uri (pipeworx:// when available), and the raw event payload. Filter by type (e.g. "sec_8k") and/or since (ISO timestamp). Set mark_read:true to flag returned events read so the next call only shows newer ones. Polls work fine; the same feed is also at GET registry.pipeworx.io/alerts.json for scripts and dashboards.

"What's new with X" / "latest on Y" / "what happened to Z this week / month / quarter" / "updates on Acme" / "news on Tesla recently" / "what's happening with Apple" — change feed for a company in the last N days/weeks/months in ONE parallel call. Fans out to SEC EDGAR (filings since `since`), GDELT→GNews fallback (news mentions in window — GDELT preferred, GNews when rate-limited or 5xx), USPTO (patents granted; PatentsView API sunset May 2025 so this soft-fails until reactivated). `since` accepts ISO date ("2026-04-01") or relative shorthand ("7d", "30d", "3m", "1y"). Returns structured changes[] grouped by source + total_changes count + pipeworx:// citation URIs. Use entity_profile instead when you want the static profile (filings + fundamentals + LEI + patents) regardless of window.

Save data the agent will need to reuse later — across this conversation or across sessions. Use when you discover something worth carrying forward (a resolved ticker, a target address, a user preference, a research subject) so you don't have to look it up again. Stored as a key-value pair scoped by your identifier. Authenticated users get persistent memory; anonymous sessions retain memory for 24 hours. Pair with recall to retrieve later, forget to delete.

"What's the ticker for…" / "find the CIK for…" / "what's the RxCUI for…" / "look up the ID for…" / "what is X's official identifier" — resolve a user-spoken NAME to the canonical/official identifier other tools require as input. Use FIRST whenever you have a name but need an ID. SUPPORTED TYPES: "company" (returns ticker + 10-digit CIK + company_name from SEC EDGAR + pipeworx://edgar/company/{cik} citation URI; accepts ticker, CIK, or company name as input — auto-disambiguated), "drug" (returns RxCUI + ingredient + brand from RxNorm + pipeworx://rxnorm/{rxcui} citation; accepts brand or generic name). Each call cascades through several lookup endpoints internally — using resolve_entity replaces 2-3 manual lookups.

Compare AI visibility across multiple entities side-by-side. Probes each entity (your brand + N competitors) with ai_visibility_check, ranks by score, surfaces which is most/least recognized. Useful for competitive AI-marketing audits: "does Claude know about us as well as our competitors?". Returns ranked list with score, confidence, signal density per entity.

Composite "should I add this npm package to my project" check in ONE call — fans out across deps.dev (license + advisories + version history) and bundlephobia (gzipped/minified bundle size, dependency count, ESM/tree-shake support). Use whenever an agent asks "is X safe / popular / small" or "what does adding lodash cost me". Returns a summary block (is_latest, license, published_at, advisory_count, bundle_kb_min, bundle_kb_gz, dependency_count, has_esm, tree_shakeable), per-advisory detail, links, and a list of recent alternative versions. NPM ecosystem only in v1; PyPI / Maven / Cargo / Go fall under deps.dev:version directly. Partial failures degrade gracefully — bundlephobia's first measurement on a new version can take 5-30s; sources_failed will list it if it times out, the rest still returns.

Semantic search INSIDE a fetched record. Pass the text you already pulled (e.g. a SEC 10-K body, an article, a long tool result) plus a natural-language query; get back the top-N passages with character offsets and similarity scores. Use when the record is too big to cram into the prompt — search_within saves context, returns only the passages that matter, and every passage carries an offset so the agent can verify a verbatim quote. Pairs with ask_pipeworx_grounded: fetch with the gateway, ground over the relevant passages instead of the whole document. BGE-base-en embeddings + cosine over 500-char overlapping windows; cap is 200K chars (longer inputs are truncated and flagged).

Create a proactive monitoring subscription to a live-data event stream. Returns the new subscription id. Requires a Pipeworx OAuth account (anonymous + BYO cannot persist subscriptions). Supported types: "sec_8k" (8-K filings matching ticker + item codes — e.g. items:["5.02"] = officer change), "polymarket_edge" (Polymarket↔Kalshi cross-venue mispricings — params:{topic:"fed"}), "fred_series" (new FRED observations — params:{series_id:"UNRATE"}). Delivery channels: feed (always on — pull via recent_alerts or GET registry.pipeworx.io/alerts.json), and optionally email (set delivery:{email:"you@x.com"}) or sms (delivery:{sms:"+15551234567"} — phone must be verified at /account first; 10/day cap).

What can I ask Pipeworx? / what is Pipeworx good for? / what can you do? / give me ideas / show me examples / getting started / what data do you have? — the onboarding entry point for an agent that just connected and wants to know what is worth asking. Returns category-bucketed example questions (company financials, drugs & clinical trials, economics, real estate, prediction markets, weather, government & patents, science & academia, news) — each with the exact tool + argument shape that answers it, drawn from the live catalog of thousands of tools. Call with no arguments for the full spread, or pass `topic` (e.g. "finance", "pharma", "betting") to focus. Use this FIRST when you do not yet know what Pipeworx can do for you, or to learn how to call the meta-tools (ask_pipeworx, entity_profile, compare_entities, etc.).

Cancel a subscription by id. Ownership is enforced — you can only cancel your own subscriptions. The row is deactivated (not deleted) so its historical events stay available via recent_alerts.

"Is it true that…" / "fact check" / "verify the claim that…" / "did X really…" / "was Y actually…" / "confirm or refute" / "true or false" — natural-language claim verification against authoritative sources. Use whenever the agent needs to check whether something a user said is factually correct. v1 supports company-financial claims (revenue, net income, cash position for public US companies) via SEC EDGAR + XBRL. Returns a verdict (confirmed / approximately_correct / refuted / inconclusive / unsupported), extracted structured form, actual value with pipeworx:// citation, and percent delta. Replaces 4–6 sequential calls (NL parsing → entity resolution → data lookup → numeric comparison).