The robot buildout is real, large and already the loudest industrial story in the market. That is precisely the problem. When everyone agrees a wave is coming, the interesting question is no longer whether the machines arrive—they will, by the million. The question is where the money settles once they do. The deployment is a cost-deflation event, not a profit event, and the surplus lands almost nowhere the popular baskets are pointing.
40.1% vs 21.7%
In the same layer, quarter and price war, the single cleanest evidence in the theme shows that cost-curve leadership is a monopoly rather than an attribute. Own the number one; the number two wears a growth multiple over commodity economics.
10 November 2026
Expiry of China’s suspension of its October 2025 rare-earth and technology export package. The market is priced for continuation, so the asymmetry runs to failure. This is binary and tradeable.
20 January 2027
The EU Machinery Regulation becomes applicable into an AI Act notified-body pool that is effectively empty. This is a modest European delivery air-pocket and an engineering tax, not a wall.
The following overview summarizes the strategic building blocks, position directions, and allocated companies for this research theme.
The permitter is also the payer. Clearance, qualification and multi-decade budgets restrict supply and protect the state-facing enablement layer.
Consumables, spares, retrofits and certified service density earn from machines already installed. Uptime is the product.
Only the number one in a commoditising layer keeps margin as prices fall. The number two is structurally exposed to commodity economics.
Operators book labour savings as slow margin improvement, but the market does not pay a higher multiple for it.
Not a value-chain layer but a date-bound trade on the expiry of China’s export suspension on 10 November 2026.
Humanoid suppliers, undifferentiated assembly, the number two in every hardware layer and sub-scale Western sensing. The adverse disclosure evidence is not priced.
Not a value-chain layer but the sentiment basket that mixes semiconductors with robotics and therefore carries AI-capex beta.
By the mid-2030s, robot capability is cheap, abundant and Chinese-priced. What is scarce is the right to operate and the ability to keep machines running. Two stacks come to coexist.
Machine work is bought as metered capacity—per pick, per flight or per hour. Uptime is therefore the product, and certified field-service density plus spares become the annuity. It is not electrons and not multi-megawatt depots: kilowatt-class machines never create a grid-interconnect industry, whatever the trucking-and-robotaxi analogy suggests.
Three years of humanoid enthusiasm have produced abundant vanity metrics—runtime hours, parts handled, totes moved, robots produced per hour and teleoperation job postings—and zero disclosure of the three numbers that would settle the argument: the teleoperation ratio, fleet uptime and cost per productive hour. By anyone. In any jurisdiction.
Companies publish flattering numerators and withhold the denominators that would not flatter. Sustained selective disclosure of throughput while suppressing the efficiency denominator is not neutral absence; it is adverse evidence.
The corollary is that the humanoid-adjacent supply chain—reducers, actuator-narrative companies, magnet stories and undifferentiated assemblers—trades on 2030–35 dream revenue against end-markets too small to move earnings this cycle. It is the largest single mispricing here.
If open-weight vision-language-action models plus cheap Chinese hardware collapse integration, commissioning and safety-case cost toward zero, permission stops being scarce. The safety case becomes a per-release software artefact, underwriters price a model rather than a bespoke installation, and the integration, service and certification tollbooths evaporate. Value migrates to the frontier lab and edge silicon. This is the counter-case that invalidates the structure rather than merely delaying it. The tell is integration hours per deployed unit falling across successive cohorts at the same customer with flat field headcount, or any safety case approved at model level rather than installation level.
Immateriality does not de-rate on logic; it de-rates on revenue arrival, funding stress or forced disclosure. Narrative momentum, passive flow and analyst anchoring to addressable-market slides can sustain dream multiples for years. A structurally correct call can therefore be practically painful, which is why the humanoid-adjacent leg belongs in option-like or paired form and not as a naked short.
Chinese cost-curve winners carry political risk that can override a 40% gross margin entirely. Procurement bars, indirect-procurement extensions, connected-hardware rules and index actions can make the deflation-winner leg effectively untradeable for Western capital regardless of the fundamentals. The honest bear case on that leg is regulatory, not economic.
| Rank | Layer | Rationale for margin capture |
|---|---|---|
| 1 | State-as-Customer Enablement | The permitter is also the payer. Clearance and qualification limit supply against multi-decade, budget-backed demand in anti-jam navigation, tactical inertial systems, electronic warfare, hardened datalinks, seekers, energetics, counter-drone systems and command-and-control. Undersea autonomy is the least crowded and longest-dated slice. |
| 2 | Installed-Base Consumption | Consumables, interceptors, spares, retrofits and certified service density recur by construction because metered machine work is priced on failure rates and repair time. This annuity keeps earning when robot hardware gross margin goes to zero. |
| 3 | The Single Cost-Curve Owner | The number one in each commoditising sensing or actuation layer earns respectable margin on collapsing prices because it sets them. This is predominantly Chinese and therefore as much an access trade as a fundamentals trade. The number two is a value trap. |
| 4 | Orchestration and Integration | Robots-as-a-service and system integration have a moat in contract duration and enterprise-software entanglement rather than margin structure. The business is real but project-shaped. |
| 5 | Certification and Testing | Certification is a genuine but small toll, not a profit pool. The delivery air-pocket around the EU Machinery Regulation shows why it should not be valued as a software business. |
| 6 | Deployers at Scale | Scale operators book labour arbitrage as bargained, uncapitalised margin drift. The surplus is real, but the market does not reward it with a higher multiple. |
Structurally poor capture sits in chassis, motors, generic edge compute, bearings, sub-scale Western sensing, precision reducers with a real moat attached to an immaterial market, undifferentiated humanoid assembly and standalone perception software that open-weight models are commoditising. Western component and standards franchises are an under-appreciated risk when a China-defined standard takes the ex-Western installed base and truncates the terminal market. Robot inference is 10–100W edge silicon, decoupled from data-centre depreciation cycles. Training and simulation demand is already inside the AI-capex trade, so robotics does not provide a second bite at compute.
For the robot-revolution research topic, the discussion among several models selected the following stocks as the more interesting positions. The ratings attached to each company come from Leeway’s general equity analysis and are independent of the robot-revolution topic.
The Business-Rating scores the quality of the business model, independent of the share price. The Market-Fit-Rating tests eighteen fundamental figures for how well the company currently fits the market; a negative reading implies expected negative performance. The Cycle-Rating places the valuation in the stock’s own history: a higher figure means the shares are historically cheaper. The Leeway-Score combines the three in equal parts. How the ratings are calculated
From 18 August 2026 to 4 September 2026: Portfolio+3.4%ACWI+1.1%
The permitter is also the payer. Clearance, qualification and multi-decade budgets restrict supply and protect the state-facing enablement layer.
Role in thesis: Licence-scarce enablement across PNT, sonar and synthetic-aperture mine detection, electronic warfare and secure datalinks—the state-as-customer layer at a less-narrated multiple than the Nordic and German primes.
Valuation context: Its franchises sit precisely where the regime says rent is durable: contested spectrum, contested seabed, GPS-denied navigation, sovereign cryptography and datalinks. Supply is limited by clearance and qualification, while demand is budget-backed for decades.
Invalidation risk: Conglomerate dilution from civil avionics and digital identity, French state influence, lumpy naval order timing and a ceasefire-driven peace-headline de-rating that hits fundamentals-immune multiples.
Role in thesis: The purest listed expression of two of the least crowded scarcities: fibre-optic-gyro inertial navigation for GPS-denied PNT and undersea or USV autonomy.
Valuation context: Exail owns genuinely hard physics on twenty- to forty-year naval budget lines that land and air robotics screens never pick up. Anti-jam PNT and seabed-infrastructure protection are standing budget lines in the regime, not cyclical procurement.
Invalidation risk: Small cap, illiquid and family-controlled; already re-rated on the naval cycle. Slippage in a single large programme moves the whole P&L, and European naval contract timing is notoriously lumpy.
Role in thesis: Undersea autonomy through HUGIN-class AUVs, remote weapon stations, missiles and maritime C2—the longest-dated licence-scarce slice plus consumables.
Valuation context: Kongsberg combines the undersea leg of the regime with effectors and installed-base consumption. Seabed-infrastructure protection after the cable incidents is a structural, not episodic, demand driver.
Invalidation risk: Already heavily re-rated. The market prices it as a defence compounder, so the regime is broadly in the price. This is a fundamentals-right, price-generous holding, best sized as core rather than as the alpha leg.
Role in thesis: Installed-base consumption plus licence-scarce sensing through countermeasures, energetics and electronic warfare or counter-UAS systems.
Valuation context: Consumables and countermeasures recur by construction and are price-set by qualification and national licensing, not competition. Chemring carries far less narrative premium than the pure counter-UAS plays.
Invalidation risk: UK single-customer and export-licence dependence, capacity-expansion execution risk and directed energy as the late-window structural threat to countermeasure and interceptor economics.
Role in thesis: Anti-jam GNSS, resilient timing and tactical inertial navigation—the PNT scarcity, owned inside a cash machine.
Valuation context: GPS-denied operation as standing doctrine makes inertial and anti-jam timing a multi-decade demand line with an assured-PNT qualification moat. Buying it inside Safran means paying an aerospace multiple rather than a defence-tech narrative multiple.
Invalidation risk: The civil aftermarket dominates the equity story, so the PNT thesis is heavily diluted and will not drive the share price on its own. It is a low-variance way to own the layer, not a high-torque one.
Role in thesis: Counter-UAS radar, electronic warfare and force-protection electronics—the enablement layer that captures value as airframes commoditise.
Valuation context: Short-range air-defence radar and electronic warfare sit in the fastest-growing, most qualification-gated part of US autonomy and counter-UAS budget lines. Leonardo DRS profits from drone proliferation regardless of which airframe wins.
Invalidation risk: US budget-cycle and continuing-resolution timing risk, parent-company overhang and a valuation that already reflects much of the counter-UAS story. A Ukraine freeze would compress sentiment.
Role in thesis: The third-way integrator: the mechanism by which Western-prime pricing power is diluted in the allied mid-market, and a direct electronic-warfare, PNT and counter-UAS play.
Valuation context: High domestic content and an export machine target the price-sensitive middle of allied demand. Aselsan captures the enablement layers that hold rent at a valuation reflecting Turkish macro rather than the franchise.
Invalidation risk: Lira depreciation, opaque related-party and state-directed pricing, governance and sanctions or geopolitical tail risk, plus restricted foreign-investor access.
Role in thesis: Third-way defence electronics: C2, electronic warfare, radar and sensors on India’s indigenisation lists; permission-scarce demand with a captive domestic monopsony.
Valuation context: Indigenisation lists are literal permission scarcity: a legally protected supplier position against a decades-long budget ramp. Bharat is the least-correlated licence-scarce defence exposure to Western AI-capex sentiment.
Invalidation risk: A rich multiple after a long re-rating, state-set pricing and margin caps, lumpy order intake, and heavy retail or domestic-flow ownership that makes the stock vulnerable to Indian market risk-off.
Role in thesis: Third-way industrial base at scale, with additional undersea and naval exposure through the group.
Valuation context: Korea has become the default supplier of affordable, fast-delivery allied systems. The group’s ocean and shipbuilding arm sits on the undersea and MRO annuity that the regime ranks highly. It structurally caps Western-prime pricing power while capturing volume.
Invalidation risk: Extremely re-rated, cyclical order lumpiness, capital-intensive capacity expansion, Korean governance and holding-structure discounts, and high peace-headline sensitivity.
Role in thesis: Licence-scarce sensing in thermal, infrared, marine and subsea instruments—the Western sensing franchises that survive Chinese deflation because export control, not performance, is the moat.
Valuation context: Infrared, thermal and subsea instrumentation are export-controlled, qualification-gated and embedded in defence and marine platforms. Teledyne is also the natural consolidator of distressed sub-scale Western sensing.
Invalidation risk: A diversified conglomerate, so the theme is diluted; industrial and test end-markets are cyclical; commercial thermal is exposed to Chinese price entry at the low end.
Consumables, spares, retrofits and certified service density earn from machines already installed. Uptime is the product.
Role in thesis: The permission-and-uptime toll through machinery safety sensing, functional safety and hazard detection.
Valuation context: The EU Machinery Regulation pushes vendors toward deterministic, certified safety envelopes. This is a recurring, regulation-mandated bill-of-materials tailwind regardless of which robot wins.
Invalidation risk: A premium quality multiple already; robotics and machinery safety are a minority of a highly diversified group; and the serial-acquisition model needs continued cheap bolt-ons.
Role in thesis: A non-obvious Japanese small cap in safety components—a direct uptime and permission toll on every deployed machine.
Valuation context: Every certified robot cell needs qualified safety components with long design-in cycles. This is content per robot that grows with unit volume, priced as a sleepy Japanese industrial rather than as robotics.
Invalidation risk: Small, illiquid and yen-exposed, with cyclical factory-capex exposure. Chinese safety-component substitution is a long-term risk, while low narrative torque means it will not re-rate quickly.
Role in thesis: The uptime annuity in intralogistics: a large, contracted lifecycle-service and spares base attached to an installed fleet.
Valuation context: Kardex demonstrates the regime’s real orchestration economics: metered machine work is decided by MTBF and time to repair, so durable earnings are in service contracts and spares density. ROIC is high and capital intensity is low.
Invalidation risk: European warehouse-capex-cycle sensitivity, exposure to a possible first-half-2027 European conformity air pocket, a high-quality multiple already and Swiss-franc strength.
Role in thesis: A global material-handling integrator with a growing aftermarket and retrofit annuity.
Valuation context: Daifuku converts commoditising hardware into local project and service margin across Asia and the US. Its after-sales and retrofit mix is exactly the recurring layer the regime rewards.
Invalidation risk: Project-economics volatility, exposure to semiconductor and e-commerce capex cycles, and Chinese integrator price competition in Asia.
Role in thesis: The certification toll: conformity assessment, functional-safety audit and marine or industrial inspection as robots become regulated products.
Valuation context: The EU Machinery Regulation and AI Act conformity obligations add regulated, recurring and price-inelastic assessment volume against constrained assessor headcount.
Invalidation risk: Robotics is a rounding error in a large, diversified TIC group. TIC pricing is competitive and cyclical; this is a low-beta carry position, not an alpha leg.
Only the number one in a commoditising layer keeps margin as prices fall. The number two is structurally exposed to commodity economics.
Role in thesis: The one cost-curve owner in long-range lidar—the purest expression of owning the number-one deflation winner rather than the layer.
Valuation context: Hesai printed a 40.1% gross margin in the second quarter of 2026 while cutting ASPs, while its nearest peer printed 21.7%. This is direct evidence that price-setting scale converts deflation into margin for exactly one player.
Invalidation risk: The 1260H extension into indirect procurement from 30 June 2027, US connected-vehicle rules that structurally close the US auto socket, and ADR or VIE risk mean realised return is driven by Washington headlines rather than mathematics.
Role in thesis: The paired short and funding leg: the structurally impaired number two in the same layer.
Valuation context: A 21.7% gross margin against Hesai’s 40.1% in the same quarter and price war is the cleanest demonstration that winner-take-one is the terminal structure. RoboSense carries the winner’s geopolitical discount without its price-setting power.
Invalidation risk: Borrow cost and squeeze risk in a Hong Kong small or mid cap; humanoid-platform announcements can produce violent short-term rallies. Express it as a relative-value pair, not a naked short.
Role in thesis: Chinese AMR cost-curve leader plus RaaS and orchestration—the layer where deflation and duration meet.
Valuation context: Geek+ is the global unit-share leader in warehouse AMRs, with a genuine international revenue base and recurring service or subscription mix. It expresses the claim that Chinese hardware price levels plus local service margin take the ex-perimeter installed base.
Invalidation risk: Recent IPO with a thin trading history, historically thin-to-negative margins, rising Western security scrutiny of Chinese warehouse robots, and price competition among more than 100 domestic entrants.
Operators book labour savings as slow margin improvement, but the market does not pay a higher multiple for it.
Role in thesis: The deployer capturing labour arbitrage, owned at a price that does not ask to be paid for it.
Valuation context: If automation’s surplus lands in deployers’ operating margin rather than suppliers’ multiples, the cheapest way to own it is a vertically integrated operator that is already automating and valued as a low-multiple retailer with net cash.
Invalidation risk: The thesis itself says deployer surplus earns no multiple. Chinese consumption, competitive-subsidy wars and policy risk dominate the share price, while employment-stability doctrine explicitly caps labour-displacing automation.
Not a value-chain layer but a date-bound trade on the expiry of China’s export suspension on 10 November 2026.
Role in thesis: An event-trade option on the 10 November 2026 rare-earth suspension expiry.
Valuation context: Lynas is the only meaningful ex-China separator with heavy rare-earth capability. Re-imposition of the broader October 2025 export package would create a scarcity shock in which it is the primary listed beneficiary. The market is priced for continuation, so payoff is asymmetric to failure.
Invalidation risk: A chokepoint is not a profit pool: Western policy responses convert this into regulated-utility economics. Commodity-price and operating risk remain; exit on the event rather than marrying it.
Role in thesis: The second, less crowded leg of the same event trade: ex-China sintered NdFeB magnet capacity.
Valuation context: If controls re-impose, European magnet buyers have very few qualified non-Chinese sources. Neo is a smaller, more levered expression than the miners and does not carry a humanoid premium.
Invalidation risk: Small cap, illiquid and exposed to ramp execution risk. Humanoid magnet demand is quantitatively trivial, so the equity depends on electric-vehicle and industrial demand plus policy, not robots.
Humanoid suppliers, undifferentiated assembly, the number two in every hardware layer and sub-scale Western sensing. The adverse disclosure evidence is not priced.
Role in thesis: The archetype of a real moat attached to an immaterial end-market, carrying a humanoid overlay.
Valuation context: Harmonic Drive has a genuine technical moat in strain-wave reducers, but humanoid volumes cannot move EPS this cycle while Chinese challengers compress prices in its core factory-automation market. Convergence toward 8–14x EBIT capital-goods economics is the mechanical consequence.
Invalidation risk: Negative narrative carry: Optimus and Figure headlines can squeeze the stock violently, while order recovery in factory automation can rally it on cyclicality alone.
Role in thesis: The listed humanoid pure play that actually discloses, and whose disclosures do not support the narrative multiple.
Valuation context: Heavy reliance on government-linked and demonstration orders, weak cash conversion and structural losses collide with a dream valuation. UBTech is the forced-disclosure mechanism through which immateriality de-rates.
Invalidation risk: Extreme volatility and squeeze risk on Chinese policy and order announcements, Hong Kong borrow constraints, and a genuine industrial-order inflection or state-backed rescue re-rating as real tails.
Role in thesis: The actuator and humanoid narrative premium bolted onto an HVAC-components franchise.
Valuation context: A high-quality core business is now valued substantially on a humanoid actuator option whose revenue is trivial and whose eventual pricing will be set by a Chinese price war. This overlay compresses 40–70% while the unit story stays intact.
Invalidation risk: Difficult access for foreign investors, state-supported narrative persistence and a genuinely good underlying HVAC business that limits downside. This is better as an avoid than as an active short.
Not a value-chain layer but the sentiment basket that mixes semiconductors with robotics and therefore carries AI-capex beta.
Role in thesis: A hedge instrument for the AI-capex correlation trap—the vehicle that expresses the sector’s beta rather than its fundamentals.
Valuation context: Passive robotics baskets bundle semiconductor and AI-capex stocks with actual robotics. They carry AI-capex sentiment beta above one despite near-zero fundamental linkage to robot demand. Puts or a short here can fund the longs through a hyperscaler-digestion drawdown.
Invalidation risk: This is a hedge, not a view: in a bull path it removes most of the upside. Constituent overlap with semiconductors means it may be short exactly the AI stocks that rally.
| When | What happens | Why it matters |
|---|---|---|
| 10 November 2026 | China’s suspension of the October 2025 rare-earth and technology export package expires. | The market is priced for continuation. Re-imposition inflates Western bills of material; the asymmetry is to failure. This is a trade, not a franchise. |
| 20 January 2027 | The EU Machinery Regulation becomes applicable. | Safety components with self-evolving machine-learning behaviour have no simple self-assessment route. Expect a first-half-2027 European delivery air-pocket and an architectural retreat to deterministic safety envelopes. |
| 30 June 2027 | US procurement bars extend from direct to indirect and product-based procurement. | This is where real revenue exposure sits for Chinese sensing champions and their Western tier-one customers, not in the current headline listing. |
| A Chinese humanoid IPO prospectus | A Chinese humanoid IPO prospectus publishes unit volumes, prices and gross margins. | This is the most probable forced-disclosure event: dream slides become audited unit economics and the adjacent supply-chain premium de-rates. |
| AI-capex digestion | A hyperscaler guidance cut or credit event digests AI capex. | Robotics equities carry AI-capex sentiment beta above one despite near-zero fundamental linkage. This is the entry, not the thesis. |
| Path | Weight | What happens |
|---|---|---|
| Base Case (50%) — Grinding bifurcation and attribution repricing | 50% | Units grow, prices fall and the number one per layer holds margin while number twos bleed. Defence autonomy converts steadily, with counter-drone, electronic warfare, navigation and undersea growing fastest. Civil deployment and European conformity slip quarters. Humanoid revenue stays trivially small with at least one high-profile timeline slip and still no disclosed teleoperation ratio. The market slowly separates materiality from mapping: immaterial humanoid-adjacent companies de-rate while licence-scarce enablement, uptime annuities and Chinese cost-curve leaders outperform. The theme stays intact, the vehicles rotate and dispersion is extreme. The return is in attribution, not direction. |
| Bear Case (28%) — Beta event first, fundamentals second | 28% | An AI-capex de-rating hits the whole physical-AI basket hardest because its revenue is furthest out. Compounding risks include rare-earth re-imposition, indirect-procurement extension and connected-hardware rules that make the Chinese leg untradeable, plus a geopolitical thaw that loosens the sovereignty premium. Forced humanoid disclosure reveals heavy teleoperation dependence, but the compression arrives inside a general sell-off. Paired trades work while an outright long portfolio still loses money in absolute terms. |
| Bull Case (22%) — Policy and disclosure break favourably | 22% | Rare-earth risk fades without a shock, civil-aviation rules finalise with insurers actually writing cover, defence-autonomy lines lift disproportionately and at least one audited deployment shows cost per productive hour beating regional labour. Breadth widens from crowded leaders into second-tier suppliers. This is the consensus-confirming path: it pays beta more than variant insight, and even here humanoid-adjacent compression only pauses unless integration cost per unit visibly falls. |
The assessment is produced in several steps. Independent model families answer the same question separately and then attack the results. What you read here has survived several rounds.
Any analysis can be wrong. That is why the falsification criteria and the counter-position sit on the same page as the thesis, not in the small print.
The numbers shown against individual companies do not come from this process. The Business-Rating scores business-model quality, the Market-Fit-Rating eighteen fundamental figures against the current market, the Cycle-Rating the valuation against the stock’s own history. They are documented under the Leeway scores.
The physical claim is correct: autonomous machines are going into series production. The surplus goes to buyers and to businesses where the state pays or somebody has to keep the machine running. For most component and humanoid suppliers, costs fall; profits do not rise.
In the second quarter of 2026 Hesai reported a 40.1 percent gross margin and RoboSense 21.7 percent, same segment, same price war. Only the leader sets the price and keeps the margin. The runner-up carries the same geopolitical discount without the power to set prices.
They will deliver the machines. Neighbouring suppliers are priced on revenue for 2030 to 2035, against end markets too small to move earnings per share in this cycle, and against a Chinese comparison that limits the reachable share outside the West. The re-rating comes when revenue and audited figures arrive, likely 2027 to 2029, not with the next demonstration.
10 November 2026 for the rare-earth package, 20 January 2027 for the EU Machinery Regulation, 30 June 2027 for indirect US procurement of Chinese sensors. Add a Chinese humanoid prospectus and the first audited commercial economics. Political dates and disclosure reprice the stocks; technology demonstrations do not.
In two places: state-backed suppliers with scarce licences, especially undersea systems, anti-jam navigation and electronic warfare; and the installed base of consumables, spare parts and certified field service. Certification is only a small fee. Operators book the surplus without the market paying a higher earnings multiple for it.
Passive funds mix semiconductors with physical robotics. They move more with AI spending by the large data-centre operators than robot demand can explain. The most probable large price move in the next two years comes from that corner, not from robotics itself. It would not refute this reading; it would be a possible entry into the more durable businesses.
The Business-Rating scores the quality of the business model, the Market-Fit-Rating the fundamental position against the current market, the Cycle-Rating the valuation against the stock’s own history. Try the linked robotics and defence companies for fourteen days, or read first how the ratings are built.
The data is recalculated on a weekly basis and depends on the current market value of the company and the balance sheet figures of the annual financial statements. The market value changes continuously with price changes, the balance sheets are created annually and change the valuation massively. The time of the annual financial statements and the metrics used can be viewed under "Metrics". Further information on how the analyses work can be found as tooltips directly on the analyses as well as in our explanations.
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