1 · Concept overview
Established Extreme heat survivability asks a narrower question than heat adaptation, and a harder one: can a building, the network that feeds it and the body inside it keep a person alive through a multi-day heat event when the mechanical cooling stops. Almost everything the field measures assumes cooling is running. The failure mode that kills is the unconditioned one, and it is the mode for which the built environment carries no requirement, no tested performance figure and, in most jurisdictions, no measurement at all.
Established The physiological limit sits lower than the number in circulation, and it is empirical rather than theoretical. The 35 °C wet-bulb threshold from Sherwood and Huber (2010) is a thermodynamic bound for a resting, unclothed, fully shaded subject in moving air. Direct calorimetry on young healthy subjects at Pennsylvania State University put the critical wet-bulb temperature nearer 30.5 °C in humid conditions, with older subjects lower still. The operative limit for a real population in a real dwelling is several degrees below the figure most policy documents quote, and the gap is where the design margin was supposed to be.
Established Scope boundary. Compound Climate Hazards owns the joint distribution — why hot arrives with dry, and why two rare loads are rarely an independent coincidence — and this brief takes that correlation as given rather than re-deriving it. Wildfire Systems owns smoke, the interface and the deliberate power shutoff, all of which arrive in the same season as heat. Climate-Health Adaptation owns mortality attribution; Infrastructure Resilience owns cascade mechanics and the missing restoration-time distribution; Sustainable Megacities owns urban form; Future Housing Systems owns what a dwelling costs to deliver; Planetary Cooling Concepts owns the global radiative lever. What nothing on the map owns is the coupled object: dwelling, grid and body at the limit, over seventy-two hours, with the compressor off.
Frontier The brief’s claim is that the binding constraint on extreme heat survivability is an unmeasured variable, not a missing material. Radiative-cooling coatings, phase-change plasters and heat pumps all work; none is the constraint. The constraint is that no jurisdiction publishes the distribution of indoor temperature across its housing stock during a heat event, still less during a heat event with the power off, so no code committee can set a performance requirement, no utility can price a reliability obligation and no health department can target a warning. The field has an elegant physiology, an expanding materials literature and no error signal.
Established A note on sourcing. This brief was commissioned in September 2026 from the Institute’s research base. Reading-list entries without links are cited from the bibliographic record rather than re-fetched, and claims are dated no later than early 2026 unless carried by a linked source.
2 · Current scientific position
Established The measured record begins with the observation that lethal heat is an indoor event. The British Columbia Coroners Service review of the late-June 2021 heat dome attributed 619 deaths to it and found the overwhelming majority occurred indoors, in private residences without mechanical cooling, disproportionately among older people living alone. Lytton reached 49.6 °C on 29 June 2021, a Canadian record, and burned the next day. The fatalities were not outdoors, not among labourers, not among the young; they were in bedrooms.
Established Heat-associated death surveillance in the one North American jurisdiction that does it properly shows the same failure with the machine present. Maricopa County, Arizona, publishes an annual heat-associated death report and has recorded totals in the six hundreds in recent years — 645 in 2023 on its own surveillance definition, with a similar order of magnitude in 2024. The composition matters more than the total: among indoor deaths, air conditioning was commonly present and not operating, because it was broken, switched off for cost, or without power. That is a reliability failure, not an equipment-availability failure.
Established The Chicago 1995 investigation established the structure a generation earlier and its protective factor has never been displaced. The case-control study in the New England Journal of Medicine found working air conditioning the dominant protective factor and social isolation the dominant risk. Every well-investigated event since has reproduced the same three predictors: age, isolation, and whether the cooling was running.
Established The largest measured adaptation gain on record belongs to air conditioning, and it is very large. The Barreca and colleagues analysis of United States mortality across the twentieth century found the mortality effect of an extremely hot day falling by more than seventy per cent, concentrated after 1960, with residential diffusion of air conditioning carrying the explanatory weight. No heat-action plan or warning system has a comparable identified effect size, a point Climate-Health Adaptation works through in full. Cooling works. The question is what happens when it is absent, unaffordable, or unpowered.
Frontier The coupled heat-plus-blackout case has been modelled and never measured. The Stone and colleagues simulation of a multi-day citywide power failure during a heat wave in Atlanta, Detroit and Phoenix produced the sharpest figures in this literature: in Phoenix, on the order of half the urban population requiring emergency department care and deaths in the high hundreds for a two-day event. Those figures are outputs of a building-energy and exposure model chained to an epidemiological function, and the authors say so. No city has instrumented a real event of this kind, so the model has never been scored against an outcome.
Established The best-documented real instance of the coupled failure has the wrong temperature sign and is still the most useful evidence available. The February 2021 Texas event produced a measured interdependency record: multi-day outage, 322 boil-water notices between 14 and 17 February, air-quality exceedances from restarting flares. Satellite night-lights analysis at census-block-group resolution found minority block groups 1.5 to 3 times more likely to be interrupted, with proximity to critical facilities protective, and a companion analysis found power-line density dominating outage-vulnerability prediction — which is what makes an independent satellite observable possible. The event was a freeze; the topology of the failure is the topology a heat event would produce.
Established Demand-side hardening is a grid-resilience lever with a measured magnitude, which reframes survivability from a network problem into a building-stock problem. Analysis of building-sector retrofits against the same Texas shortfall found envelope and equipment measures capable of materially reducing the peak deficit: the load the grid failed to serve is partly a property of the buildings attached to it. The grid and the housing stock are not two systems with an interface. They are one system with two regulators, one setting load limits and the other setting thermal envelopes, neither accountable for the joint outcome. The interdependency vocabulary comes from Rinaldi and colleagues; the finding that topological metrics are only mildly correlated with physically modelled grid vulnerability warns against ranking neighbourhoods for heat-outage risk off a wiring diagram.
Established Urban form loads the dwelling before the dwelling starts. Three decades of satellite thermal measurement across eleven Southeast Asian capitals found intra-urban warming from land-cover change running partly independent of regional climate trends. The urban heat island is strongest at night, and night is when unconditioned dwellings fail to purge stored heat. A dwelling designed against a rural design temperature is already out of specification in a dense block; Sustainable Megacities carries the form argument.
Established Overheating is regulated in three jurisdictions, unregulated in most of the rest, and the regulated versions are recent. England introduced Approved Document O in 2021, in force 2022, requiring new homes to limit solar gain and provide a means of removing excess heat. France’s RE2020 carries a degree-hour discomfort indicator with a threshold near 350 DH and a cap at 1,250 DH. British Columbia amended its building code after the 2021 heat dome to require one cooled living space in new dwellings. Most of North America has none of this: the model energy codes govern cooling equipment efficiency, not unconditioned thermal performance.
Established Passive survivability exists as a named concept with a metric, and it is a voluntary credit rather than a requirement. The term comes from Alex Wilson’s post-Katrina writing; the operational metric is habitable hours, usually standard-effective-temperature degree-hours accumulated during a simulated multi-day outage, and it appears in the RELi rating system and a LEED pilot credit. It is scored in simulation, not tested, and optional everywhere it exists.
Frontier The infrastructure heat failures outside buildings are individually well understood and collectively unquantified. Oil-filled transformer capacity is a thermal rating, and the loading guides express permissible loading against ambient temperature and accepted insulation ageing, so a heat wave raises load and lowers rated capacity at once. Continuous welded rail buckles above its stress-free installation temperature, which is why operators impose heat speed restrictions; the United Kingdom’s July 2022 event, with 40.3 °C at Coningsby, produced runway and rail damage. Asphalt binders are specified against a drifting pavement design temperature. Each mechanism is textbook. No national system publishes an audited cross-asset inventory of heat-derated capacity — the same shape of gap Infrastructure Resilience identifies for restoration times.
Established Cooling access is distributed far more unequally than cooling demand. Intergovernmental assessments put roughly a tenth of households in the hottest parts of the world in possession of an air conditioner, against near-saturation in the wealthy hot-humid economies, and project cooling as one of the largest drivers of building electricity growth to mid-century. Where wet-bulb exposure is highest the protective factor identified in Chicago in 1995 is mostly absent, and where it is present it is the first thing an arrears disconnection removes.
3 · Frontier questions
Frontier Where exactly is the survivability limit for a real population in a real building? The calorimetry gives critical wet-bulb temperatures for young healthy subjects under controlled activity. Nobody has the equivalent curve for the population that actually dies: people over seventy-five, on medications that impair thermoregulation, in dwellings with elevated mean radiant temperature from hot ceilings and west walls. Air temperature is not the exposure; operative temperature is, and the correction can run several degrees.
Frontier How much of the indoor-temperature distribution is explained by building attributes at all? Occupant behaviour — window opening, shading operation, whether a person will accept the security risk of an open ground-floor window at night — may dominate the physics in real stock. Evacuation research keeps rediscovering that information-dependent human delay is a first-order term rather than a correction; the heat literature has no equivalent field dataset.
Frontier Does heat-hardening the building stock relieve the grid enough to change reliability planning? The retrofit analysis says the effect on peak deficit is material. Whether it is large enough for a system operator to count as firm capacity is unanswered, and the question is regulatory as much as physical: no North American reliability framework currently credits envelope performance as a resource.
Speculative Can night-time radiative cooling carry a meaningful share of a survivability load? Daytime sub-ambient radiative coolers are demonstrated, with measured cooling powers of tens of watts per square metre under clear skies. Whether that is ever enough to hold a dwelling below a lethal threshold through a humid, cloudy, high-dewpoint night — the exact condition in which people die — is not established, and the honest reading of the physics is that atmospheric water vapour closes the radiative window precisely when it is needed.
4 · Technological bottlenecks
Established The first bottleneck is instrumentation, and it is embarrassingly cheap to fix. A calibrated temperature-and-humidity logger costs tens of dollars. A stratified sample of a few thousand dwellings, logging at fifteen-minute resolution with power-state metadata, would cost less than a kilometre of urban transmission. It does not exist anywhere at the scale required to produce a distribution. The obstacle is not money but that no agency’s mandate covers indoor conditions in private dwellings.
Established The second is that the code compliance path for overheating is simulation, and the simulations are unvalidated against measured indoor temperature. Dynamic thermal models are calibrated for annual energy, which is an integral, and used for peak indoor temperature, which is a tail. Those are not the same estimation problem. Where model-against-measurement comparisons exist for free-running buildings in heat events, reported errors run from one to several degrees — the entire margin between uncomfortable and lethal.
Frontier The third is the cooling-equipment supply chain under a demand shock. A tripling of installed cooling capacity implies compressors, refrigerants under a legally scheduled phase-down, and skilled installation labour, in that order of scarcity. The low-global-warming-potential replacements carry flammability classifications that in turn drive electrical and building code changes. Nobody has published a bottom-up supply model for a survivability-driven rather than comfort-driven deployment.
Established The fourth is electrical, and it is distribution rather than generation. Adding cooling to a dwelling that never had it changes the service load, and in older residential distribution the constraint is often a pole-mounted transformer sized for a load profile from a different climate. Transformer procurement lead times have been long since the early 2020s. This is the least glamorous item on the list and the most likely to set the pace of any mass cooling programme.
5 · Research dependencies
Established This topic depends on climate information at a resolution the climate enterprise does not routinely deliver. Survivability design needs joint distributions of dry-bulb, dew point, wind and night-time minimum over multi-day windows at neighbourhood scale, not annual design temperatures at an airport. The design-condition datasets engineers use are percentile summaries — the right object for equipment sizing and the wrong object for tail exposure.
Established It depends on the compound-hazard result being taken seriously in reliability standards. The correlation structure Compound Climate Hazards documents is the load case; until a reliability standard contains a concurrent heat-and-outage contingency, the engineering demand for this brief’s numbers does not exist.
Established It depends on the restoration-time distribution Infrastructure Resilience identifies as missing. Habitable-hours metrics take outage duration as an input, and every published passive-survivability simulation picks that duration by assumption — commonly seventy-two hours — because the empirical distribution has never been published. The metric is only as good as a number nobody has measured.
Established It depends on an electricity system running on a different clock. Summer peaking, electrified heating pushing some systems back toward winter peaks, data-centre load growth and storage deployment all change the coincident-peak arithmetic. The Physical Stack of AI carries the load-growth side; the interaction with a residential cooling obligation is unmodelled in public.
6 · Required experiments
Frontier The decisive result is a measured indoor-conditions dataset spanning a real multi-day heat event that includes a real power interruption, in a stratified sample of ordinary dwellings. This would change this brief’s assessment more than any other result, because every quantitative claim downstream — the habitable-hours metric, the passive-survivability credit, the modelled blackout casualty figures, the case for envelope retrofit as grid capacity — currently rests on simulation calibrated for a different quantity. The instrument is a calibrated logger, the sample frame is an existing dwelling register, and the output is a distribution rather than a mean. Nobody has funded it at the required scale in any heat-exposed city.
Established It needs no new hardware and no new physics, which makes its absence an institutional fact rather than a technical one. The closest analogues are utility indoor-sensor pilots and academic deployments of a few hundred homes, neither stratified to represent a stock nor designed to capture outage state. The design that would settle it is unglamorous: recruit across building age, tenure, floor level, orientation and cooling equipment; log temperature, humidity and a power-state flag; pre-register the analysis; publish the tail.
Frontier The second experiment is a prospective cohort scoring the Stone-type model against an actual event. Somewhere in the next decade a large heat-exposed city will lose power for more than a day during a heat wave. If indoor telemetry and emergency-department presentations are collected in advance under a pre-specified analysis plan, that event scores the model; if not, it produces another retrospective reconstruction with an interval wide enough to accommodate any policy conclusion.
Established The fourth is already running and nobody is reading it: the code natural experiment. England has mandated overheating mitigation in new homes since 2022, France imposes a degree-hour cap, British Columbia requires a cooled room, and most of North America requires nothing. Cohorts of dwellings built either side of each boundary exist and are dated. A difference-in-differences comparison of measured indoor summer conditions across those regulatory boundaries would test whether the regulated version of this problem produces different buildings, and it has not been published — for the same reason as everywhere else here: nobody measures indoor temperature.
7 · Engineering requirements
Established The engineering hierarchy for survivability is the reverse of the hierarchy for comfort. For comfort, equipment efficiency dominates. For survivability with the power off, the order is solar control first, then thermal mass coupled to a night-purge path, then insulation, then equipment. External shading beats internal shading because it stops the gain before it enters. Glazing area is the largest design variable and the most resistant to change, because it is an amenity and a sales feature.
Established Thermal mass only helps if the night can be used, and in a severe heat dome the night is the problem. Mass buffers the diurnal swing and re-radiates after dark; if the night-time minimum stays high, mass converts a peak into a plateau, and the plateau is what kills over three days. Night purge also requires openable, secure, quiet, insect-screened openings — four constraints usually in conflict in dense urban housing, a point Future Housing Systems reaches from the cost side.
Established Cool roofs are the best-evidenced single retrofit and the benefit is asymmetric by climate and by storey. High-albedo roofing measurably lowers roof-surface and ceiling temperatures and reduces cooling load; the effect on the top floor is large and on lower floors small, which matters because the top floor under an uninsulated roof is where indoor extremes are worst. City-scale albedo claims are a weaker literature, and Planetary Cooling Concepts handles the planetary version of the same argument.
Frontier The back-up cooling specification that does not exist would be small. A single heat-pump zone holding one room within survivable limits draws on the order of a few hundred watts to a kilowatt in operation; a battery sized for intermittent duty over seventy-two hours is a single-digit kilowatt-hour device, within reach of existing residential storage and bidirectional vehicle hardware. The engineering is not the obstacle. The absence of a defined essential-cooling load is.
8 · Adjacent technologies
Established The compound-hazard frame is the direct upstream dependency. Compound Climate Hazards supplies the reason heat, drought, generation shortfall and smoke arrive together rather than independently, and its charge that design standards price hazards one at a time is the charge this brief inherits for the heat case specifically.
Established The fire season is the same season. Wildfire Systems owns smoke exposure, the wildland-urban interface and public-safety power shutoffs. The intersection with heat is operationally acute: filtration requires a closed building, night purge requires an open one, and a deliberate de-energisation removes cooling and filtration at once. This brief flags the conflict; that brief owns the smoke side of it.
Established Urban form and housing delivery bound what is achievable. Sustainable Megacities carries the evidence that urban adaptation is constrained by land availability and buried infrastructure rather than by intent, which is why canopy and green-infrastructure targets underdeliver. Future Housing Systems carries the cost decomposition that decides whether a heat-hardened dwelling is buildable at the price the market clears.
Established Two neighbours own the escape routes. Climate Migration Planning owns movement as adaptation, including the interaction this brief cannot resolve: successful in-place hardening may suppress a relocation that would have been the better outcome. Underground Cities owns the most thermally stable built environment available, and the ground is the only free thermal mass at civilisational scale.
9 · Institutional requirements
Established The institutional defect is jurisdictional, and it can be stated exactly. Building codes govern construction, not operation. Utility regulators govern system reliability, not indoor outcomes. Health departments count deaths afterwards. Nobody owns indoor temperature during an outage, which is why it is not measured, which is why there is no requirement, which is why nobody owns it. The loop closes.
Established Occupational heat regulation is the one branch where an enforceable numerical threshold is actually being contested. The United States Occupational Safety and Health Administration published a proposed rule on heat injury and illness prevention in indoor and outdoor work settings in August 2024, with heat-index initiation and high-heat trigger levels and required rest, water and acclimatisation provisions, and several states already operate their own standards. It shows what a numerical, enforceable heat requirement looks like and what it costs politically to obtain one.
Frontier The final status of that federal rule in 2026 is not something this brief will assert. A notice of proposed rulemaking is not a standard, the hearing record was large and contested, and United States regulatory practice in this period makes prediction unreliable. What would confirm the position either way is the Federal Register: a final rule with numerical trigger temperatures, or a withdrawal notice.
Frontier The institution that would have to be created is a measurement authority, not a regulator. The pattern across this corpus is consistent: fields without a published outcome distribution do not converge, whatever the quality of their modelling. The cheapest institutional intervention available is a standing indoor-conditions monitoring programme with published microdata, run by a statistical agency rather than a code body, because the first requirement is a number nobody can argue with rather than a rule somebody must enforce. Summer disconnection moratoria, which exist in a minority of jurisdictions with varying triggers, are a second natural experiment sitting in administrative files that nobody has evaluated.
10 · Ethical & societal considerations
Established The distribution of heat death is the most reliably replicated finding in the field. Age, isolation, tenure, floor level, pre-existing illness and absence of working cooling predict who dies, across every well-studied event from Chicago 1995 to British Columbia 2021. This is not a gradient a general efficiency programme corrects; it is concentrated in people outside the market for building upgrades because they rent, are poor, or are too old and too alone to seek help.
Established The outage gradient runs the same direction as the exposure gradient. The satellite night-lights evidence from Texas found minority census block groups substantially more likely to lose power, with proximity to critical facilities protective. Stacked on the housing gradient, the households least able to ride out a heat wave are also more likely to be without power during it — a compounding measured on one side and inferred on the other.
Established Adaptation success can suppress a better outcome. The managed-retreat literature treats relocation as a deliberate adaptation choice with its own typology of who initiates it. Hardening a dwelling in a place that will become uninhabitable within the asset’s life spends capital on a delay. Climate Migration Planning owns that trade; the point here is that survivability standards applied without a horizon systematically favour staying.
11 · Civilizational implications
Frontier The civilisational stake is habitability, and the honest version of that claim is narrower than the popular one. Regions do not become uninhabitable when a threshold is crossed; they become dependent on continuous mechanical cooling, a different and more precise statement. A region dependent on continuous cooling has converted a climate problem into a reliability problem, and reliability failures are correlated, political and recoverable in ways climate is not.
Established Labour is the economic channel with the clearest measured signal. International assessments project losses on the order of a couple of per cent of total working hours by 2030, concentrated in agriculture and construction and in South Asia and West Africa. The mechanism is reduced work capacity rather than mortality: measurable, already happening, and largely absent from the survivability framing because it happens to working-age people who do not die.
Handwave The claim that heat will drive population redistribution at continental scale is where this argument works by assertion. Migration responds to income, networks, policy and violence far more legibly than to temperature, the empirical literature on climate-driven movement is contested, and heat-specific attribution is weak. State it as a hypothesis with a named test — destination choice conditional on origin heat exposure, controlling for income and networks — or do not state it.
12 · Timelines
These horizons track when the measurement, the requirement and the physical fleet could plausibly change, not when the climate does.
- 10 yr: Frontier A handful of jurisdictions publish indoor-temperature distributions from stratified monitoring; overheating requirements spread through Northern European and Canadian codes; occupational heat standards with numerical triggers exist in more jurisdictions; the modelled blackout-casualty figures are scored against at least one real event.
- 25 yr: Speculative Habitable hours under outage becomes a compliance metric in some codes rather than a voluntary credit; distribution capacity is planned against survivability rather than comfort peaks; residential back-up cooling acquires a defined essential load in at least one national code.
- 50 yr: Speculative Maximum indoor temperature has the legal standing minimum indoor temperature has today in cold countries, at least in the wealthy hot-humid economies, with the litigation and insurance consequences that implies.
- 100 / 250+ yr: Handwave Claims about habitability at this range depend on emissions paths, on whether any radiative intervention is ever exercised, and on building stocks that do not exist. Anyone giving a date here is describing a scenario, not a forecast.
13 · Technology tree & dependencies
- Depends on Three results on this map. From Compound Climate Hazards: the joint distribution of heat with generation shortfall and drought, without which the load case for survivability design cannot be written. From Infrastructure Resilience: the published restoration-time distribution, the input every habitable-hours calculation currently assumes. From Climate-Health Adaptation: the identified adaptation effect sizes, and the discipline it applies to uncontrolled before-and-after evaluations.
- Requires (not on this map) Six things nobody on this map produces. A measured indoor-temperature distribution during heat-wave outages, because every figure downstream is a simulation calibrated against a different quantity. An overheating performance limit in North American residential codes, because without one the unconditioned failure mode has no owner. An enforceable occupational heat standard with numerical triggers, because the working-age half of the exposure is governed by nothing else. Distribution transformer capacity rated for coincident summer peaks, because the pole-mounted transformer, not generation, sets the pace of electrified cooling. A cooling affordability instrument that survives arrears disconnection, because a protective device switched off for cost is not protective. And low-global-warming-potential refrigerant and compressor supply for a tripled cooling fleet, because the phase-down schedule and the deployment schedule have never been reconciled in public.
- Enables A defensible survivability specification for the dwelling, which is the missing input to Future Housing Systems on the cost side and to Sustainable Megacities on the form side; a firm-capacity claim for envelope retrofit inside reliability planning; and a warning system that knows which buildings, not which postcodes, are failing.
- Adjacent Wildfire Systems owns the smoke that arrives in the same week and the shutoff that removes the cooling; Underground Cities owns the thermally stable alternative; Planetary Cooling Concepts owns the global lever; Climate Migration Planning owns the exit.
14 · Common misconceptions & speculative claims
Established “A wet-bulb temperature of 35 °C is the threshold at which humans die.” It is the thermodynamic ceiling for an idealised resting, unclothed, fully shaded subject in moving air, and real people fail well below it. Using 35 °C as a planning threshold understates exposure and implies that anything below it is safe. Almost every recorded heat death in temperate countries occurred far below it.
Established “Heat kills people outdoors.” In the well-investigated temperate events it kills them indoors, in their own homes, at night, usually alone. Outdoor occupational heat illness is a separate problem with its own regulatory track; conflating the two sends resources to cooling centres while the deaths occur in bedrooms nobody visits.
Established “Air conditioning is maladaptive because it makes the problem worse.” The measured adaptation gain from residential air conditioning is the largest identified effect in the literature, over seventy per cent of the historical mortality effect of extreme heat days in the United States. The emissions and waste-heat objections are real and belong in the efficiency standard, the refrigerant schedule and the grid plan. They are not a reason to withhold the one intervention with a demonstrated effect size.
Frontier “Passive buildings do not need cooling.” Passive design lowers the load and lengthens time to failure; it does not remove the failure mode. A superinsulated, airtight building with poor solar control and no night purge can overheat faster than a leaky one, which is why thermal-resilience studies report the alignment between efficiency and outage survivability as usual but not automatic. Passive measures buy hours; how many is exactly the unmeasured quantity.
Frontier “Radiative cooling materials solve this.” Daytime sub-ambient radiative coolers are a genuine physics result with measured cooling powers in the tens of watts per square metre under clear dry skies. Their output collapses with atmospheric water vapour and cloud, which is the condition of a lethal humid night. As a roof-surface and cooling-load measure they are useful and increasingly deployed; as a survivability technology for the humid tropics they are, on current evidence, oversold.
Handwave “Heat will render whole regions uninhabitable by a stated year.” This is the step where the argument works by assertion. The physical claim — that certain regions will require continuous mechanical cooling for survival during parts of the year — is defensible and nearly established for a few places. The jump to depopulation adds assumptions about capital, reliability, governance and migration that are neither measured nor stated. Demand the assumptions.