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Commerce · IV.02 · MMXXVI · daylight

La Bourse  /  Volume IV  /  Nº IV.02

Materials and the Return Loop

Volume IV — Production and Regeneration

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THE PLATE

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THE LETTER

You have been told that the economy is seven percent circular. It is the figure everyone quotes, it comes from a serious organisation, and it is arithmetically correct. It is also, on its own, one of the least useful true sentences in modern economics, and this chapter is an argument for replacing it in your head with three other numbers that you can actually act on.

The first is a recovery rate — what fraction of a material comes back when the product it was in stops being a product. The second is a yield — what fraction of what comes back turns into something a buyer will accept. The third is a growth rate, and it is the one that almost nobody puts in the equation, which is why almost everybody's circular-economy plan misses.

Those three numbers combine into a single expression that tells you the maximum share of your material demand that can ever come from your own returns. You can write it on the back of a card. It has two terms. And when you compute it for aluminium, steel, copper, PET and paper using nothing but published recovery rates, it lands within a few points of what those industries are observed to achieve — which is how you know it is describing something real rather than being fitted after the fact.

This is not a chapter about doing better. It is a chapter about knowing where the ceiling is, so that you spend your effort under it rather than against it. Some of what follows is more encouraging than the headline: the returnable fraction of the world's material flow is already about a third recycled, not seven percent. Some of it is less: there are recovery routes that cost more energy than making the material new, and by the end of the Arithmetic you will know which ones and at what threshold.

Bring a calculator. This one rewards it.

— The Editors

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DISCOVERY

What is already working

Start where the loops already close, because several of them do, and they close for reasons you can copy.

Aluminium beverage cans in Brazil. Brazil has recovered close to ninety-eight percent of its aluminium cans for more than fifteen consecutive years — the highest sustained return rate for any consumer packaging material anywhere. There is no deposit law. The mechanism is that the material is worth enough per kilogram, and the collection network dense enough, that recovery is a livelihood for tens of thousands of people. The Associação Brasileira do Alumínio reports the figure annually and the industry's own mass balance corroborates it.

What made it work was not virtue and not regulation. It was value density: a can is almost pure 3004/5182 alloy, it is light, and the metal is worth roughly four times what the same mass of PET is worth. Recovery follows price per kilogram, always, everywhere. Where a loop closes without being forced, look for value density first.

Steel, as an entire industry. Steel has the highest absolute recycling tonnage of any material on earth — on the order of six hundred million tonnes a year returned to furnaces — and an end-of-life recycling rate that the UNEP International Resource Panel places above eighty percent. Electric arc furnace steelmaking is not an environmental programme; it is a mature, profitable, century-old industrial route that happens to run on scrap. The largest circular system in the world was built by metallurgists and scrap dealers, for money, before anyone had a word for it.

Kraft pulp mills, and a fact that surprises people. A virgin kraft mill separates cellulose from lignin and then burns the lignin in a recovery boiler to run itself. A modern one is a net exporter of electricity. This is a two-hundred-year-old technology that already does what industrial ecology asks for: it uses its own residue as its own fuel, and it recovers and reuses its pulping chemicals in a closed loop at better than ninety-five percent. The paper industry did not adopt cascading; it invented it.

Interface and Shaw, in carpet. Shaw's EcoWorx tile, launched in 1999, was designed from the start so the backing could be separated from the face fibre and both returned. The tile carries a printed telephone number and a commitment to collect it. Twenty-five years later it is still running, still at industrial scale, and it is the clearest existing proof that design for return works when the designer also owns the return path. Interface's ReEntry programme is the same lesson from the same industry.

Deposit return, where it exists. Germany's Pfand system returns better than ninety-eight percent of in-scope PET bottles. Norway's returns above ninety percent. These are the highest PET recovery rates in the world and they are achieved with the least sophisticated technology in this chapter: a coin, a machine, and a person walking back to a shop. Nothing in the sorting literature comes close to what a refundable deposit does to a collection rate.

Five cases. Notice what is not on the list: no case here was won by a better separation technology. Every one was won by value density, ownership of the return path, or a financial reason for the holder to hand the material back. That is the appreciative finding of this chapter and it should reorganise your budget: the leverage is in collection and in design, not in sorting.

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THE ARITHMETIC

What works, what does not, and where the line sits

First, the headline number, and exactly how it is made.

The Circularity Gap Report computes one metric: cycled materials as a share of total material input to the economy.

        cycled                8.4 Gt
  ---------------------  =  ----------  =  9.05 %      (2015 data, CGR 2018)
   virgin  +  cycled        84.4 + 8.4

That is the whole method. The series since:

Now decompose the fall from 9.1 to 6.9. The numerator fell about seven percent. The denominator rose about twenty-three percent. In log terms, roughly three-quarters of the decline in the world's circularity rate is the world using more material, not the world recycling less. The metric is a ratio, and a ratio can fall while its numerator is doing nothing wrong.

The method's limits, stated plainly, because they are large.

The denominator is all material input. It includes fifteen or so gigatonnes of fossil energy carriers that are burned and cannot be cycled by any technology. It includes around thirty gigatonnes a year of net additions to in-use stock — concrete, steel and brick that went into buildings this year and will not come back for fifty years, and which it would be actively bad to have back sooner. It includes biomass that was eaten.

Take Haas and colleagues' world material flow account for 2005 and do the subtraction:

  processed materials                    62.0 Gt
  less added to in-use stock (37 %)      22.9 Gt
  less dissipated or burned  (44 %)      27.3 Gt
  --------------------------------------------
  physically returnable in-period        11.8 Gt
  recycled                                4.0 Gt

  as a share of input        4.0 / 62.0  =  6.5 %
  as a share of returnable   4.0 / 11.8  = 34.0 %

Both numbers are true. The first is the one that gets quoted; the second is the one an engineer can move. Use the headline figure to describe the scale of material throughput, and never as a score for the recycling industry, because it is not measuring that.

Second, recovery and yield, material by material.

Two distinct fractions, and conflating them is the commonest error in this field. The collection or end-of-life recovery rate ρc is what comes back. The process yield Y is what survives sorting, washing, melting and refining into something saleable. Their product is what actually returns to the market.

One caution before you use anyone's published recycling rate: most quoted rates include new scrap — the off-cuts and trimmings that never left the factory and were never at risk of being lost. New scrap is good housekeeping, not recycling, and counting it inflates every statistic it touches. Copper's oft-quoted thirty-two percent "recycling input rate" becomes about seventeen percent when you count only metal that actually came back from a user.

Third, the formula. This is the chapter.

Material reaching end of life this year was put into service L years ago, when demand was smaller by exactly the compounding factor. So the secondary supply available this year is the recovered fraction of that smaller demand:

                     ρc · Y              ρ
        c   =   ---------------  =  -----------
                    (1 + g)^L        (1 + g)^L

  c   the maximum share of this year's demand that returns can supply
  ρ   recovery rate times process yield
  g   demand growth rate per year
  L   mean product life in years

Run it against the table, and compare with what each industry is actually observed to achieve:

Five materials, five independent data sources, one two-term expression, and four of the five land within a few points. The outlier is PET, and the reason is instructive rather than embarrassing: a large share of collected bottle is cascaded into polyester fibre and never returns to bottles, so the bottle-to- bottle figure is lower than the formula's ceiling. The formula gives the ceiling. Cascading is how you spend it.

The cut. A perfect recycler in a growing economy is still a mine.

Set ρ = 1.00. Every atom returned. No melt loss, no contamination, no export, no landfill. Keep steel's forty-year life:

At two percent growth, a flawless recycling system supplies forty-five percent of demand and fifty-five percent must still come out of the ground. The binding constraint on circularity is not the recovery rate. It is the growth rate, and no amount of sorting technology touches it.

Invert it, and you get a planning number nobody currently uses. The fastest growth at which a target secondary share c is reachable is g* = (ρ/c)^(1/L) − 1:

  steel   to 50 % secondary    (0.816/0.50)^(1/40) − 1  =  1.23 % / yr
  steel   to 70 % secondary    (0.816/0.70)^(1/40) − 1  =  0.38 % / yr
  alum.   to 50 % secondary    (0.651/0.50)^(1/20) − 1  =  1.33 % / yr
  copper  to 40 % secondary    (0.428/0.40)^(1/35) − 1  =  0.19 % / yr

Fourth, the steady-state stock. The same logic integrated rather than differenced. If inflow grows at g and every unit lasts L years, the in-use stock is the last L years of inflow:

        K  =  D · (1 − e^(−gL)) / g            and as g → 0,  K/D → L

Test it against something measured. Pauliuk, Wang and Müller estimated the global in-use iron stock at about twenty-five gigatonnes. World crude steel production in 2008 was 1.33 Gt/yr; mean life forty years.

  at g = 2 %   K/D = 27.53 yr   K = 36.6 Gt   vs 25 Gt measured   +46 %
  at g = 4 %   K/D = 19.95 yr   K = 26.5 Gt   vs 25 Gt measured    +6 %

Four percent is close to the actual compound growth of world steel over the four decades to 2008. Fed the growth rate the era actually ran at, a formula with two inputs lands within six percent of an independently measured global stock. Fed the wrong one, it is out by half. The sensitivity is the finding: a stock is a statement about growth history, and if you do not know the history you do not know the stock.

And the stock is the asset. Thirty-three gigatonnes of in-use steel at twenty megajoules per kilogram is 660 exajoules of embodied energy — about one full year of all human primary energy, standing up in the buildings and machines that already exist.

Fifth, why downcycling happens — and it is not entropy.

The usual explanation is that mixing increases entropy and the second law makes unmixing expensive. Do the arithmetic and that explanation collapses.

Copper in shredded end-of-life vehicle steel runs about 0.35 weight percent — mole fraction 0.003077. The ideal entropy of mixing is ΔS = −R[x ln x + (1−x)ln(1−x)] = 0.1735 J/mol·K. The minimum work to separate it at room temperature is T·ΔS = 51.7 J/mol, and there are 17.9 moles of alloy in a kilogram:

  minimum separation work      926 J/kg steel   =   0.93 kJ/kg
  making that steel from ore                       20,000 kJ/kg
  ------------------------------------------------------------
  the thermodynamic floor is                           0.0046 %

Forty-six ten-thousandths of one percent. Even at a second-law efficiency of one percent, which would be a dismal process, unmixing costs 0.46 percent of what the steel cost to make. Thermodynamics does not forbid this. It barely notices it.

What actually forbids it is structural. Copper substitutes for iron on the lattice; it is in solid solution; there is no interface — no boundary, no surface, no phase — for a separation process to act upon. You cannot float it, magnetise it, sieve it, or eddy-current it, because there is nothing there to grip. Downcycling is not an entropy tax. It is the absence of a process, and that is a much more hopeful diagnosis, because absences can be filled.

So the mechanism of downcycling is an inequality, not a law of physics. For any element that cannot be removed, a blend is the mass-weighted mean of its inputs, so the blend can never be cleaner than its cleanest input. Meeting a tight specification means dilution:

  f = (C_scrap − C_spec) / (C_spec − C_clean)     parts clean iron per part scrap

  automotive deep-drawing sheet, 0.06 % Cu    (0.35−0.06)/(0.06−0.01)  =  5.80
  flat product, general,         0.10 % Cu    (0.35−0.10)/(0.10−0.01)  =  2.78
  structural section,            0.25 % Cu    (0.35−0.25)/(0.25−0.01)  =  0.42
  reinforcing bar,               0.40 % Cu     no dilution needed

To put end-of-life vehicle scrap into car body sheet you must add 5.8 kilograms of clean iron per kilogram of scrap — and clean iron is precisely the thing you were trying not to make. So the scrap goes to rebar, where 0.40 percent is within specification. That sentence is the whole of downcycling, and it is arithmetic, not chemistry. Daehn, Serrenho and Allwood have shown that on current dismantling practice this constraint binds globally by mid-century.

Aluminium has the same structure in a different key. A mixed wrought stream averaging 0.6 percent silicon cannot be lifted to the 7.5 to 9.5 percent that cast A380 requires by any amount of sorting — it can only be alloyed upward, a thirteen-fold gap. So wrought flows to cast, one way, and cast demand is finite and shrinking as engine blocks leave the vehicle fleet.

Sixth — the honest negative. Where recovery costs more than making it new.

Recovery loses when the energy per kilogram of usable output exceeds primary production. Since yield converts input to output, that happens below a threshold yield Y* = E_secondary / E_primary:

Megajoules per kilogram. Four of ten routes lose, and here is where each line sits.

Steel from shredder fines crosses at 32 percent yield. Mixed fines and mixed construction arisings run twenty-five to thirty-five percent usable. This route is on the line, and which side it falls depends on the sorting plant.

PET by chemical depolymerisation crosses at 66 percent monomer yield. Coloured, multilayer and thermoform streams routinely sit below that. This is the sharpest finding in the chapter and it is the one a board should hear before it signs a chemical recycling contract: the technology works, and at the contamination levels of a real mixed stream it can cost more energy than making virgin PET from oil.

Paper crosses at 60 percent yield on total energy — reached by mixed grades with high ash and plastic content. And on purchased fossil energy the threshold is 120 percent, which is above one: recycled paper buys more fossil energy than virgin kraft at every yield, because a kraft mill burns its own lignin and sells the surplus power while a deinking mill buys everything from the grid. Recycled paper still wins on fibre, land and water. It does not automatically win on purchased energy, and saying so is what makes the rest of the case believable.

Aluminium never crosses. Melt loss would have to exceed ninety-four percent before remelting lost to electrolysis. Aluminium's failure mode is alloy quality, not energy, and that is a different problem with different tools.

Copper's threshold is a grade, not a yield. Primary copper from a 0.5 percent sulphide ore costs about 45 MJ per kilogram of metal — which is only 0.225 MJ per kilogram of rock, because flotation is cheap per tonne. A mixed metallic residue must be smelted at around 3 MJ per kilogram of feed. So:

  x*  =  E_feed / E_primary  =  3.0 / 45.0  =  6.67 % copper

A scrap stream smelted at that intensity must assay above 6.67 percent copper to beat an ore assaying 0.5 percent. Automotive shredder residue assays one to two percent. It is three to seven times below the line, which is why it is landfilled by people who are not being careless. Halve the feed processing energy and the threshold halves with it — that is the lever, and it is a pre-concentration lever, not a smelting one.

The rule to carry: a waste stream is an ore, and it competes at its grade.

Seventh, Cradle to Cradle, assessed on evidence.

McDonough and Braungart's framing — two cycles, technical and biological, with materials designed to stay in one of them — has held up unevenly, and the unevenness is the useful part.

The technical cycle scores. EcoWorx, Interface's ReEntry, Desso's take-back, aluminium closed-loop programmes at automotive stampers: these are real, industrial, and decades old. The chemical-inventory discipline the framework imposes — a banned list, a positive assessment of every input — has measurably changed formulations across furniture, textiles and flooring. That is a genuine contribution and it came from this framework.

The biological cycle mostly does not, and the reason is not chemistry. A certified compostable package in a country where about twelve percent of households have food-waste collection is, for the other eighty-eight percent, ordinary landfill with a certificate. Most industrial composters reject compostable packaging outright because they cannot distinguish it from conventional plastic at the tipping face. Geyer, Jambeck and Law's mass balance of all plastics ever made is the scale check: of 8,300 Mt produced to 2015, 747 Mt recycled, 996 Mt incinerated, and 6,557 Mt still in landfill or the environment. The chemistry was never the binding constraint. The collection was.

And the framework's real weakness, as Bjørn and Hauschild argued, is that it is relative rather than absolute: it says make materials that can cycle, and it does not say how much throughput the system can carry. Read it with the formula above in hand and that gap closes, because the formula prices growth.

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DREAM

What becomes ordinary

In the firm that has done this, the bill of materials carries a column that is not there today: the assay. Beside every input is what that material will be worth when it comes back, and what it will assay at, and which specification it will then be able to meet. The column is filled in at design time by the person who chooses the fastener, because the choice of fastener is what decides whether the assembly can be separated in nine seconds or not at all.

Purchasing knows the grade of everything leaving the site, not the tonnage. A skip is not "mixed metal"; it is a stream with an assay, a moisture content and a price, and it is sold under a specification the way any other product is. Where the assay is too low to be worth recovering, the firm knows the number and knows what would move it — usually a separation at the point of arising, done once, by the person who made it, for free, instead of ten times downstream by a shredder, expensively.

Design reviews ask two questions that are currently asked nowhere: what does this become, and who will be holding it. Not as an environmental screen. As a revenue question, because the firm has a secondary materials line in the accounts with a gross margin on it, and the people in that review are measured on it.

The industry association publishes mean product life by category, because everyone now needs L to do their own arithmetic, and nobody can compute their own. Trade statistics report recovery separately from new scrap, so the numbers stop flattering themselves. A national materials account exists and is updated annually, the way the energy account is, and it reports the returnable fraction alongside the headline share so that the two numbers stop being confused.

And the language has changed in one specific way: nobody says recyclable. People say returns at this rate, at this grade, into this specification, which is four facts instead of one adjective, and which can be put in a contract.

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DESIGN

The structure that gets there

The unit of design is the return loop, and a loop has four components. Name them and you can build one; leave one out and you have a good intention.

1. A stream with an assay. Not "waste". A defined stream, sampled, assayed, with a written specification: composition, tolerance, moisture, contamination limits, and the test method. Everything downstream is priced off this document. If you do only one thing from this chapter, produce this document for your three largest arisings.

2. A holder with a reason to return it. Value density, a deposit, a take-back obligation, a service contract that never transferred ownership, or a gate fee that exceeds the cost of handing it back. Brazil's cans and Germany's bottles are the same mechanism in two currencies. The question is never "will they recycle it"; it is "what does the holder get".

3. A specification it can actually meet. This is where the blending inequality does its work. Decide, at design time, which specification your returns are aimed at, and then choose the alloy, the polymer and the fastener so that they hit it without dilution. A single-alloy assembly is worth more at end-of-life than a lighter multi-alloy one, and that trade is now computable.

4. An off-take that exists before the plant does. A signed contract for the output, at a formula price linked to the primary index, with an assay-based rejection clause. A recovery plant without an off-take is a warehouse.

The governance. Ostrom's design principles apply here almost without translation, because a materials loop is a common-pool problem: clear boundaries on who is in the scheme, rules matched to local conditions, those affected participating in setting them, monitoring by people accountable to the participants, graduated sanctions, and cheap conflict resolution. Deposit schemes that work have all six. Voluntary take-back pledges that fail typically have none — most obviously no monitoring, which is why their reported rates and their measured rates diverge.

The sequence, and it matters.

Collection before sorting. The leverage in every case in Discovery was at collection. A ten-point improvement in ρc is worth more than any realistic improvement in Y, and it is usually cheaper.

Separation at the point of arising before separation downstream. One separation done once by the person holding the part beats ten downstream. This is why dismantling beats shredding for copper, and it is the only route Daehn and colleagues found that relieves the copper constraint on steel.

Specification before technology. Decide which spec you are aiming at, then buy the machine. Buying the machine first is how a firm ends up with a sorter producing a grade nobody has agreed to buy.

And measure ρc, Y, g and L for your own material, in your own accounts, before you accept anyone's industry average. The formula is only as good as its four inputs, and three of them are in your ERP system already.

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DESTINY

How it holds when nobody is pushing

A return loop sustains itself when the material is worth more inside it than outside it, and it decays the moment that stops being true. So the honest failure modes are all price and all specification.

It fails when the primary price falls. Secondary material competes with virgin at a discount; when virgin collapses, the discount has nowhere to go. The protection is a formula price in the off-take contract with a floor — the same instrument a mining company uses, for the same reason.

It fails when the specification tightens under it. A stream sold into rebar is safe until the rebar specification moves. Loops die quietly this way, and the early warning is a rejection rate creeping up before anyone renegotiates.

It fails when the cast sink disappears. Aluminium's wrought-to-cast cascade depends on there being cast demand. Modaresi and Müller showed the fleet transition removes it. A one-way cascade with a shrinking sink has a date on it, and you can compute the date.

It fails when new scrap is counted as recycling and the reported number stops tracking the physical one. Nobody notices for years, because every report is green. Separate the two lines in your own accounts on the first day and you are immune to this.

And it fails when growth outruns it, which is the formula again: a loop at constant ρ in a system growing at three percent loses ground every year while performing perfectly. The counter is not to grow less. It is to lengthen L — because L is in the exponent, and doubling product life moves the ceiling more than any recovery-rate programme yet built.

What makes it hold: the assay document, the off-take contract, and one line in the management accounts. Anything with a monthly number and a named owner survives a change of sponsor. Anything reviewed by exception does not.

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DELIGHT

What it feels like

There is a particular satisfaction in holding a piece of shredded metal up to the window and knowing, before the lab confirms it, roughly what it will assay at. It is the satisfaction of a baker who knows the dough by the feel of it. The material stops being a category and becomes a thing with properties, and once that happens you cannot go back to calling it waste — the word simply stops fitting what is in your hand.

And there is a second pleasure, slower. You start seeing the stock. Every building you pass is several hundred tonnes of steel that somebody will one day have to decide about. The bridge is a copper mine with a lower grade problem than most copper mines. The city is not a consumer of materials; it is a very large, very slow-moving deposit that is still being filled, and you happen to know the formula for how much is in it.

That is not a burden to carry. It is the opposite. It is the feeling of having been handed the inventory of a business you did not know you owned.

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OPERATIONALIZE THIS

At the level of finance

The instrument: a materials return facility, financed on the assay.

You are proposing a small capital asset — sortation, a baler, covered storage, a weighbridge, and an assay routine — repaid out of the spread between the virgin material you stop buying and the secondary material you start making, plus the disposal cost you stop paying.

The economics, worked on one grade.

  tonnes of a single grade returned per year        1,800 t
  virgin purchase price displaced                   2,450 $/t
  secondary material cost delivered                 2,150 $/t
  avoided disposal / gate fee                          95 $/t
  ----------------------------------------------------------
  margin per tonne                                    395 $/t
  gross annual benefit  1,800 × 395                711,000 $/yr
  less operating cost                              310,000 $/yr
  less verification and assay                       40,000 $/yr
  ----------------------------------------------------------
  net                                              361,000 $/yr
  facility size                                  1,600,000 $
  return on facility                                  22.6 %   vs WACC 9.0 %
  simple payback                                      4.43 years

The number that decides it is not the commodity price. It is the yield.

  yield 100 %   1,800 t   net 361,000   22.6 %   clears
  yield  90 %   1,620 t   net 289,900   18.1 %   clears
  yield  80 %   1,440 t   net 218,800   13.7 %   clears
  yield  70 %   1,260 t   net 147,700    9.2 %   clears
  yield  65 %   1,170 t   net 112,150    7.0 %   fails
  yield  60 %   1,080 t   net  76,600    4.8 %   fails

  breakeven  Y = (0.09 × 1,600,000 + 310,000 + 40,000) / (1,800 × 395) = 0.695

Sixty-nine and a half percent. Establish that number before you sign anything, because every commercial term in the transaction hangs off it.

The balance sheet treatment. The facility is plant and depreciates normally. The interesting entry is the stream: once a material has a signed specification and an off-take contract, it stops being a disposal liability and becomes inventory. That reclassification is a real balance-sheet event, it is audited against the assay and the contract, and it is frequently larger than the facility itself. Have the conversation with your auditors early; it is a conversation about whether an asset exists, and they have it every year.

The counterparty. Best is an off-taker who already buys the primary material, because they can price the discount instantly and they have the assay capability. Second best is a specialist merchant. A formula price linked to the published primary index, with an assay-based rejection clause and a floor, is the standard structure and it is bankable.

The covenant that matters. Not tonnage. Grade. Write the assay specification into the contract with a defined sampling protocol and a named test method, and make rejection assay-based rather than discretionary. A tonnage covenant rewards volume and punishes nobody for contamination, which is exactly backwards.

The first ninety days.

The one number on the front page:

     tonnes × (virgin price − secondary cost + gate fee) × yield − opex
     ----------------------------------------------------------------   >  WACC
                        facility + verification

If that holds at your measured yield rather than the vendor's quoted yield, this is not an environmental proposal. It is a working-capital improvement with a capital asset attached, and it should be presented as one.

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APPRECIATIVE QUESTIONS

Twelve, for a room

Discovery — what is already working

1. Which material leaves this site in the cleanest condition it will ever be in again — and who is the person who keeps it that way?
2. Where have we already closed a loop without calling it that, because it simply paid? What made it pay?
3. Which of our products would be easiest to take apart, and who designed it that way, and what were they thinking about when they did?

Dream — what becomes possible

1. If every bill of materials carried the return assay beside the input price, what would our designers choose differently next month?
2. Imagine our largest arising sold under a specification at a formula price. What does that line look like in the accounts, and who is proud of it?
3. If we knew the mean life of everything we sell, what would we be able to tell customers that nobody in our industry can tell them today?

Design — what we build

1. What single separation, done once at the point of arising, would raise the grade of our biggest stream the most?
2. Which specification are our returns aimed at — and if nobody has decided, who should, and by when?
3. What would we have to measure for a month to know our own ρc and Y rather than an industry average?

Destiny — how it holds

1. What would keep this running if the primary price fell by a third, and which of those protections could we write into the first contract?
2. Who else would have to be in the scheme for the monitoring to be trusted by everyone in it?
3. What is the first sign we would see if our reported recovery rate had drifted away from the physical one — and who would be looking?

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WORKS CITED

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Ashby, M. F. (2012). Materials and the Environment: Eco-Informed Material Choice, 2nd edn. Butterworth-Heinemann.

Bjørn, A. and Hauschild, M. Z. (2013). "Absolute versus Relative Environmental Sustainability: What Can the Cradle-to-Cradle and Eco-Efficiency Concepts Learn from Each Other?" Journal of Industrial Ecology, 17(2), 321–332.

Braungart, M., McDonough, W. and Bollinger, A. (2007). "Cradle-to-cradle design: creating healthy emissions." Journal of Cleaner Production, 15(13–14), 1337–1348.

Circle Economy. The Circularity Gap Report. Editions 2018, 2020, 2023 and

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Daehn, K. E., Cabrera Serrenho, A. and Allwood, J. M. (2017). "How Will Copper Contamination Constrain Future Global Steel Recycling?" Environmental Science & Technology, 51(11), 6599–6606.

Ellen MacArthur Foundation (2013). Towards the Circular Economy, Vol. 1.

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Geyer, R., Kuczenski, B., Zink, T. and Henderson, A. (2016). "Common Misconceptions about Recycling." Journal of Industrial Ecology, 20(5), 1010–1017.

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Note on figures. Every number above is computed in lib/verify/IV_02.py with its inputs printed beside it, and reproducible with python3 lib/verify.py IV.02. Recovery rates are end-of-life rates excluding new scrap; where a published rate includes new scrap the text says so. Energy intensities are primary energy per kilogram of finished material from Gutowski et al. (2013) and Ashby (2012); process energies for secondary routes are stated per kilogram of feed, which is the convention that makes the yield threshold visible.