Stockatomics - A Constraint Transmission Framework for Mapping Physical Supply Scarcity to Public Equity Exposure

Keywords. critical minerals; supply constraints; physical economy; production exposure; public equities; composite indicators; demand scenarios

Industrial demand reaches a public equity market only after it has passed through a physical production system. A change in the deployment of batteries, transmission equipment or advanced electronics changes the quantity of particular materials that must be mined, converted, qualified and delivered. Additional supply, if it comes, depends on development time, capital, processing capacity, the practicality of substitutes, and the availability of scrap. Those responses do not share a clock. A smelter bottleneck can bind within a year. A new mine, in many jurisdictions, cannot.

The research problem is therefore not solved by naming a growing end market, or by naming a mineral that market uses. An analyst has to establish where adjustment is difficult, at which stage, and which listed companies have a measurable position in the relevant flow. Company sector labels and thematic index membership do not answer that question. They record an association. Association is not output.

Stockatomics is a financial data platform for the physical economy. It connects critical minerals, products, sectors and public companies, and it carries prices, trade flows, supply descriptions and demand context alongside that map. The framework in this paper is the scoring core of that map. Market prices and trade statistics can inform a research note. They are not inputs to the core score calculations documented here.

The organising principle is mineral-first. Minerals are the stable analytical unit, because a copper cathode, a separated rare-earth oxide or a battery-grade lithium chemical is a thing with units, a production stage and a denominator. Sectors and products explain why demand for that thing might change. Companies provide the public-market connection, and only when a production figure can be placed on a compatible basis with world output. Starting from the material makes the chain inspectable. An analyst can ask why demand is assumed to change, how supply could respond, where production or refining sits, and which issuers actually contribute tonnes.

Constraint transmission is the name used here for that sequence of links. Scarcity conditions may show up as availability, price, volume or an investment incentive. Whether a listed company captures an economic benefit is a further question, turning on costs, contracts, asset ownership, financing and the price already in the equity. The core scores stop at physical positioning. They are built to be argued with, not to stand in for a valuation.

Three things follow for the design. The mineral-level objects — responsiveness, demand and concentration — have to remain readable on their own, because they do not move together. The company connection has to be a production share, not a product mention. And a scenario has to say which input moved, so that a later reader can tell a demand revision from a data correction from a change in the method. The paper reports no backtest, no predictive-accuracy estimate and no realised investment result. Those are later projects, with their own designs, and they are not implied by the existence of a score.

The scores answer a positioning question. Given a stated demand scenario and a stated production basis, which listed companies participate in mineral systems whose supply is difficult to expand or replace, and where that participation coincides with concentration? They do not answer whether the mineral is scarce this quarter. A present shortage is a statement about quantities, inventories, utilisation, trade access and timing. Long development lead times can matter in a temporary surplus. A short disruption can produce scarcity in a market whose long-run supply response is relatively flexible. Every reading needs a horizon, and the horizon has to be the same one used for the demand assumption.

They also do not answer whether the equity should reprice. A constrained mineral can raise costs for one company and support revenue for another. A producer with a large physical share can still face fixed-price contracts, operational disruption, dilution, or a project whose capital cost consumes the rent. No monotonic relationship between the core scores and subsequent equity returns is assumed, and none should be inferred from the construction.

Government critical-mineral lists are a different object again. A designation can reflect strategic use, import reliance, allied concentration, environmental damage, or a political process. Graedel et al. (2015) already separate supply risk, vulnerability to supply restriction and environmental implications, precisely because a single label hides the mechanism. A high Stockatomics score is not a substitute for that designation, and a designation is not evidence that a listed issuer has production exposure.

Production-network research supplies the reason to care about transmission, not a template for the scores. Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012) show that the asymmetry of input–output linkages can keep idiosyncratic disturbances from averaging out in the aggregate. Carvalho, Nirei, Saito and Tahbaz-Salehi (2021) document propagation after the Great East Japan Earthquake through actual supplier and customer ties. Both results motivate attention to where a system is connected and where it is concentrated. Neither result validates this framework. Stockatomics does not estimate a production network, does not recover input–output coefficients, and does not model cascade dynamics. The debt to that literature is architectural: dependencies should be written down, and a disturbance at one point should not be treated as if it arrived everywhere at once.

Mineral criticality research is closer in subject and easier to confuse with the present exercise. Graedel et al. (2015) place 62 metals in a three-axis criticality space. Supply risk in that study is driven in part by geopolitical concentration of primary production, weak substitutes and political instability. The metals of most concern are often by-products, used in small quantities for specialised applications, with no effective substitute. That description is useful here as a warning. A mineral-level score compresses asset-level and host-commodity economics, and a by-product flag is not a model of the host metal. The narrower question in this paper is how difficulty in expanding or replacing mineral supply interacts with a downstream demand scenario and with listed-company production. Environmental implications are outside the core scores.

Official commodity sources fix the units in which an exposure claim is allowed to be made. The International Energy Agency’s Global Critical Minerals Outlook 2026 describes mineral systems in terms of mining, refining, demand and diversification (IEA, 2026). The U.S. Geological Survey’s Mineral Commodity Summaries 2026 provides commodity-specific production, reserve and market information, and is explicit that world mine production, reserves and resources are not interchangeable (USGS, 2026). Those publications do not feed the scores automatically. They illustrate the discipline the scores require: the material form, the stage and the year have to be named before a share is computed.

On the construction of composites, the OECD and Joint Research Centre handbook remains the relevant standard (OECD/European Union/EC-JRC, 2008). A composite is an argument about what belongs in the index, how inputs are normalised, and how sensitive the ranking is to those choices. Numerical precision does not retire uncertainty in the evidence. Equal weights, used below for SES, are a declared choice made in the absence of a validated weighting model, not a finding that each mechanism contributes a fifth of economic constraint.

The Supply Elasticity Score, SES, expresses how difficult it is for the mineral system to respond to a change in demand. Higher values mean greater constraint and lower responsiveness. The scale is 0–100. The name is retained because it is the label used on the platform. It should not be read as an elasticity. SES is not an estimate of the percentage change in quantity supplied caused by a percentage change in price, and it is not identified from a supply curve.

Five dimensions define the profile: time to add meaningful supply, capital intensity, processing bottlenecks, substitution difficulty and recycling difficulty. Scoring direction is fixed. One hundred means the constraint is extreme; zero means the adjustment route is comparatively open. In the present specification the dimensions are equally weighted:

Equal weights are a methodological commitment, not an empirical result. There is not yet a body of outcome evidence that would justify putting more weight on lead time than on processing, or on substitution than on recycling. Asymmetric weights would look more precise than the supporting information. They can be introduced in a later version if sensitivity analysis and outcome studies show that a particular dimension dominates realised supply response. Until then, the component profile is part of the output, not a private input to a weighted sum.

Capital intensity is written K here, not C. Concentration, introduced below, is written Γ. The two objects are different, and a shared symbol would make the company formulas unreadable. Nothing in the economics depends on the letter.

The profile is informative when the summary is not. Two minerals can share an SES because one is constrained by development lead times and the other by processing, or because one cannot be substituted and the other cannot be recycled. Their response to a price spike, a policy subsidy or a technical change will differ. Publishing only the average would erase the distinction the score is supposed to preserve. Section 10 constructs a pair with identical SES values and opposite profiles for that reason.

Component scores are not measurements in the sense that a production tonne is a measurement. They are structured judgements: a reviewer applies the rubric to a cited body of evidence and records the score. Disagreement between reviewers is evidence about the rubric, not a nuisance to be averaged away in silence. The evaluation agenda in Section 12 treats inter-reviewer agreement as a primary test.

Processing bottlenecks and concentration can describe overlapping features of the same chain. A rare-earth separation circuit can be both hard to replicate and geographically concentrated. Keeping the concepts in separate terms makes the overlap visible. It can also amplify a shared underlying condition when SES and Γ later meet in a company score. Sensitivity analysis has to remove one of the overlapping terms before a small difference between two company scores is treated as independent information.

Supply concentration describes how activity is distributed across the relevant production or refining system. It is not the same object as responsiveness. Responsiveness asks how the system can adjust. Concentration asks where activity sits, or who controls it. A concentrated market can be elastic if capacity is idle and expandable. A fragmented market can be inelastic if every producer faces the same decade-long development path.

Where a reliable set of market shares exists, the preferred concentration factor is a normalised Herfindahl–Hirschman index at a named stage:

The current implementation does not yet compute that index for every mineral. It uses a structured concentration rubric, scored against named evidence, and that rubric should not be described as a calculated HHI. Assessments have to state whether concentration refers to countries, firms, mining or refining. Geographic dependence does not establish firm-level market power. Refining concentration can be the economically relevant object when mined supply is diverse and conversion is not, which is a familiar pattern in several battery and speciality metals.

Γ enters the company formulas below as a 0–100 factor. Switching a mineral from the rubric to a calculated HHI is a methodology change if it moves scores, and it should be versioned as one. It is not a silent data refresh.

Raw sums are not on a common scale. MES raw multiplies a share by two 0–100 factors; CMCS raw multiplies a share by three. A company with exposure to several minerals accumulates contributions. The published scores apply a fixed affine map and then bound the result:

Fixed bounds are a design choice with a specific purpose. A moving cross-sectional normalisation would make every existing score depend on who else had been added to the universe. That is an undesirable property in a research database: an analyst comparing two vintages could not tell a change in the physical evidence from a change in the peer set. The cost of fixed bounds is saturation. Several exposures can share an upper score despite different raw contributions. Component values and raw contributions should be retained, and saturation should be reported rather than interpreted as equality of economic position.

A score is not a percentile rank, not a probability, and not a unit of economic value. A value twice as high does not imply twice the rent or twice the expected return. Comparability across companies still depends on consistent definitions, data vintages and the same calibration. Any change to the constants, the weights or the demand identity is a methodology version, with an explicit rule for historical comparison. The numerical endpoints of the current calibration are implementation parameters. This paper discloses the aggregation identities so that the transmission logic can be inspected; it does not publish the affine constants or the component-rubric thresholds.

Financial interpretation starts where the score stops. The mapping to public equity ends at the issuer’s physical positioning. The subsequent questions are whether that positioning is material, whether it is commercially accessible to the listed entity, and whether it is already in the valuation. Those questions are not optional extras. They are the reason a high CMCS is a research prompt rather than a conclusion.

The following case is constructed. Mineral M, mineral Q and mineral N are not descriptions of particular commodities, and Companies A, B and C are not descriptions of particular issuers. The arithmetic uses the identities in Sections 5 to 8. Where a demand-pressure value is required inside MES and CMCS, it is stated as a scenario input, not estimated from a calibrated transform. The point of the case is to show which objects move, and which do not.

This paper specifies the tests. It does not report completed validation. The order matters. A return study run on economically incompatible inputs would be a precise answer to the wrong question.

The first test is data validity. Mineral units and production stages have to be reconciled. Issuer mappings have to be verified. Derived quantities, including back-calculated shares and apportioned rare-earth denominators, have to be flagged and, where possible, replaced. Coverage has to be measured. A score can be calculated consistently from inputs that do not refer to the same thing. Computational consistency is the initial test, not the interesting one.

The second test is the reliability of the judgement-based assessments. Independent reviewers should apply the SES and concentration rubrics to the same evidence pack, with disagreement reported and then reconciled. If reviewers cannot reproduce a processing-bottleneck score from the cited sources, the score is a private note, whatever its number of decimal places. Sensitivity analysis should vary plausible component scores, drop one overlapping term at a time, swap rubric concentration for an HHI where shares exist, and recompute company scores under incomplete coverage. The reportable objects are rank changes, score changes and the incidence of saturation. Conclusions that survive those perturbations are different in kind from conclusions that depend on a single component.

The third test is coherence with the declared identities, of the sort Section 10 illustrates. Raising a sector growth rate, with physical inputs held fixed, should move DM and the demand-sensitive company terms and should leave SES and SLS alone. Adding an unrelated issuer should leave existing scores alone under fixed calibration. Setting a production figure to missing should remove that contribution and should not silently insert a zero that still occupies the denominator. These are tests of the implementation. Passing them is not evidence of economic predictive power.

Empirical work on the supply side can then ask whether the constraint profiles relate to observed supply responses, commissioning delays or production changes during documented shocks. That work needs dated inputs, a stated horizon and a comparison group. It has to separate structural responsiveness from outcomes driven by inventories, export restrictions, demand destruction or a failure at a single asset. A mineral with a high T that in fact delivers new tonnes on a short horizon is a finding about the rubric, or about the episode, and either finding is useful.

Any study of equity returns is a separate design. It would need point-in-time company universes, a treatment of delistings and corporate actions, controls for commodity and market exposures, and an out-of-sample period. A trading claim would also have to survive transaction costs. The test should separate information already embedded in prices from subsequent developments. Until that evidence exists, the framework supports exposure research and scenario analysis. It is not an asserted source of excess returns.

The framework is most useful when an analyst already has a material demand thesis and needs a public-company supply position that can be checked. The workflow is deliberately narrow: identify the material, read the adjustment profile rather than only the average, examine the demand allocation, and assess the issuer’s eligible production share. Decomposition is what makes a company signal available for scrutiny. A hero number without the mineral contributions is a branding choice, not a method.

Sector growth does not uniquely determine mineral demand, particularly when technology changes material intensity. The lithium example is the obvious one, but it is not special: anode chemistry, motor design and grid topology do the same work for graphite, rare earths and copper. Supply responsiveness also varies by asset, region and stage, while a mineral-level SES compresses those differences into five numbers. Global concentration may say nothing about a particular buyer’s access to qualified supply. By-product dependence can limit output for reasons that belong to the host commodity. A descriptive flag does not model that relationship, and the capital-intensity component should not be asked to do so in disguise.

The company mapping favours entities with comparable production disclosures. Economically important processors, recyclers and development projects can fall outside the quantitative scores. Comparisons will tilt toward better-disclosed producers. Partial scores cannot be treated as complete company assessments. Aggregation across minerals, and correlation among constraint components, can also move a ranking for reasons that are arithmetic rather than geological. The overlap between processing bottlenecks and concentration, already noted, is the clearest case.

Readers of this preprint can inspect the aggregation identities, the demand allocation rule and the proposed tests. They cannot reproduce a live score from the paper alone. Component rubrics, affine calibration constants and the versioned input database remain implementation objects. That boundary should stay explicit in any claim about transparency. Disclosing the product structure of CMCS is a real disclosure. It is not the same thing as releasing the scoring sheets.

Extensions that would earn a place in a later version are specific. Better material-intensity evidence would allow the product identity in Section 6.2 to replace the sector proxy, provided double-counting is closed. Stage-specific concentration would allow mining and refining to stop sharing a single Γ. Equity-attributable production, recorded separately from operated output, would stop joint ventures from inflating shares. A downstream cost-exposure model would give Company C a score of its own, instead of a disclaimer. Each of those requires units, an overlap check and a versioned change. A plausible story is not a reason to insert a term into the sum.

The Stockatomics Constraint Transmission Framework writes down the path from downstream activity to mineral constraints and on to listed-company production. Growth outlook is not supply responsiveness. Concentration is not firm-level control. A production share is not a revenue share. Physical positioning is not an equity return. The indicators exist so that those distinctions survive contact with a thematic research question.

The current method uses an equal-weighted supply profile, a sector-share demand proxy, a concentration factor, and company production exposure. MES, SLS and CMCS are normalised sums of stated products of those objects. Products and catalysts explain and challenge the assumptions. They do not enter the sums. Detailed financial consequences remain outside the core scores on purpose.

The contribution is a research architecture whose usefulness depends on compatible units, visible coverage and scenario analysis that names the input it changed. Empirical evaluation of supply outcomes, and any later evaluation of investment performance, are still to be done. Until they are done, a high score is a claim about physical positioning under a stated scenario. It is not a claim about what the equity will do.

The identities in Sections 5 to 9 are the scoring specification associated with this preprint. Equal SES weights, the sector-share demand proxy, the separation of catalysts from the core sums, and fixed rather than cross-sectional normalisation are part of that specification. Changes to weights, to the demand identity, or to the calibration constants require a documented revision. The objective is ordinary and strict: two pages in the database should not be implementing two methods.

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• Stockatomics. (2026). A financial data platform for the physical economy, connecting critical minerals, products, sectors and public companies. https://www.stockatomics.com
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Stockatomics develops the platform and the methodology described in this paper. The author is affiliated with Stockatomics. This preprint is not peer reviewed. The worked scenario uses constructed figures and reports no observed company outcome. No empirical investment-performance validation is reported. Aggregation identities are disclosed so that the transmission logic can be examined. Component-rubric thresholds, affine calibration constants and the underlying database are not released with this paper. The method is intended to support research into physical-economy exposure. It is not a recommendation concerning any security.