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A closed-form bound. True of any material obeying the stated physics.

• Recovery is triggered selectively, with no loss during use.<5% molecular-weight loss on accelerated ageing; >90% monomer release in 4 h.derived+

  The duty cycle demands 10^6.08 selectivity; a purely thermal trigger can supply 10^1.96. The 4.12-order deficit is independent of activation energy — Ea cancels out of the ratio entirely — so no catalyst choice closes it. Thermal-only closure would need a 133.5 °C wash.

  What this removes from the plan

  Year-1 experiment 2 should not screen thermal triggers at all. It should measure the chemical contrast a second variable supplies, because that is the only term left.

  computed byrequiredSelectivityOrdersthermalSelectivityCeilingOrdersselectivityCeilingthermalClosureTemperatureC

• The recovery trigger is absent from the supply chain.A trigger condition never encountered in manufacture, storage or use.derived+

  If hydroxide supplies the missing contrast, the wash must run at pH 11.12 or above. That figure is polymer-independent: it follows from the duty cycle and the order of the reaction in hydroxide, not from any particular backbone.

  What this removes from the plan

  Fixes the wash pH before any polymer is synthesised, and makes food-contact and alkali-stability screening a first-year question rather than a later surprise.

  computed byminimumWashPHCAUSTIC_WASH_PH

• The material survives melt processing intact.Converting window at extrusion temperature with no measurable depolymerisation.derived+

  The catalysed linkage must carry at least 58.2 kJ/mol of activation energy to survive the melt residence budget. Together with the 106.6 kJ/mol ceiling above which the wash cannot act, this leaves a genuine but narrow window — and the extruder is its severest leg.

  What this removes from the plan

  Turns "does it extrude" into a pass/fail on a measured activation energy, obtainable by TGA on grams of material rather than by a converting trial on kilograms.

  computed bycatalyticBurdenminimumProcessingBarriermaxFeasibleActivationEnergy

• Barrier performance matches incumbent packaging.OTR and WVTR at or below incumbent, at defined temperature and humidity.derived+

  Barrier improvement is capped at roughly 27× the amorphous value once crystallinity is held below what recovery tolerates. The cap is structural: crystallinity and comonomer content are interchangeable through f_eff = f(1−χ), so barrier bought by crystallising is paid for in recoverable fraction.

  What this removes from the plan

  Year-1 experiment 1 can compute its own kill criterion before the first film is cast: if the incumbent needs more than the cap, the material family is rejected on paper.

  computed bymaxBarrierAtRecoveryLimitcrystallinityCeilingForRecoveryeffectiveCleavableFractionrelativePermeability

• Recovered carbon returns to virgin-specification monomer.≥99% monomer purity and near-zero mass loss, over consecutive loops.derived+

  A loop that loses nothing concentrates everything. At 99.9% recovery the steady-state impurity level is 1000× the per-cycle input — the better the yield, the worse the accumulation, which inverts the intuition the target is written with.

  What this removes from the plan

  A five-cycle demonstration is a trap: it reports a small fraction of the steady state and reads as success. The number of cycles needed is itself computable and should be stated in the protocol before the loop is run.

  computed bypurgeConcentrationFactorsteadyStateImpuritycyclesToSteadyState

• Unrecovered material is valorised rather than lost.A net-positive electron balance from fragments the process cannot recover.derived+

  Two published routes differ in sign. Ring-opened polyester nets +2 electrons per repeat unit; melt-grafted polyethylene nets −0.28 and so consumes more than it returns. The discriminator is whether the culture can eat the fragment, not what the cutting costs.

  What this removes from the plan

  Removes coulombic-efficiency optimisation from the critical path. No efficiency rescues a fragment with zero bioavailability, so the first measurement is edibility.

  computed bynetElectronsPerRepeatUnitcutCostAsFractionOfContentPUBLISHED_ROUTESbreakEvenCoulombicEfficiency

• A candidate satisfies every constraint at once, not one headline property.≥3 jointly validated functions or constraints per flagship material.derived+

  The joint screen takes eight inputs and returns a verdict only when all are present, refusing to score a candidate on a subset. Constraints that are individually satisfiable are jointly binding through shared variables — crystallinity appears in three of them.

  What this removes from the plan

  Screening order stops being arbitrary: the constraint that binds hardest is evaluated first, and candidates die on paper in the cheapest possible order.

  computed byassessFeasibilityevaluateCandidatecandidateFromEvidencescreenCorpus

• Loop closure3/8 computed+

  Whether carbon actually returns, and what accumulates when it does.

  • Monomer yield per cycle (%)
  • Mass loss per cycle (%)
  • Steady-state impurity concentration factor (×)purgeConcentrationFactor
  • Cycles to reach a stated fraction of steady statecyclesToSteadyState
  • Whether a proposed cycle count is informative or a trapassessCycleTest
  • Molecular-weight retention across loops
  • Catalyst recovery fraction per cycle (%)
  • Purge stream volume and its disposal route
• Recovery selectivity5/7 computed+

  The contrast between conditions of use and conditions of recovery.

  • Selectivity orders demanded by the duty cyclerequiredSelectivityOrders
  • Selectivity orders a thermal trigger can supplythermalSelectivityCeilingOrders
  • Minimum wash pH for hydroxide to close the deficitminimumWashPH
  • Wash temperature at which thermal contrast alone would sufficethermalClosureTemperatureC
  • Per-mechanism contribution to the achieved contrastselectivityLedger
  • Measured shelf-life molecular-weight loss (%)
  • Measured monomer release within the recovery window (%)
• Processing survival4/6 computed+

  The extruder is the severest thermal leg the material ever sees.

  • Activation energy the linkage must carry to survive the meltcatalyticBurden
  • Upper activation energy above which the wash cannot actmaxFeasibleActivationEnergy
  • Activation energy inferred from a thermogravimetric rampactivationEnergyFromTga
  • Maximum processing temperature the window permitsmaxProcessingTemperatureC
  • Melt strength and converting window
  • Residual monomer after extrusion (ppm)
• Packaging performance4/9 computed+

  Parity with the incumbent, which is the only bar that matters commercially.

  • Barrier improvement ceiling at the recovery limit (×)maxBarrierAtRecoveryLimit
  • Crystallinity ceiling that recovery toleratescrystallinityCeilingForRecovery
  • Relative permeability from morphology (Nielsen tortuosity)relativePermeability
  • Glass transition of a candidate compositionfoxGlassTransition
  • Oxygen and water-vapour transmission rate
  • Heat-seal initiation, hot tack, seal integrity
  • Tear, puncture and flex-crack durability
  • Haze, odour, colour and their drift on ageing
  • 90 °C hot-fill retention
• Contamination tolerance1/6 computed+

  Removing sorting is the clause that separates this from existing recycling.

  • Monomer yield from printed, food-contaminated film (%)
  • Purification energy per kilogram of monomer
  • Solvent demand and recovery fraction
  • Purification efficiency required to hold the looprequiredPurificationEfficiency
  • Selectivity against non-target polymers in the same stream
  • Tolerance to adhesives, inks, labels and closures
• Feasibility boundaries6/6 computed+

  Where the physics forbids a target outright. The cheapest result a programme can get.

  • Whether a thermal trigger alone can ever close the duty cycleselectivityCeiling
  • Joint feasibility across all eight design inputs at onceassessFeasibility
  • Feasible activation-energy window, and whether it is emptyfeasibleBarrierWindow
  • Minimum cleavable fraction for monomer-dominated productsminimumCleavableFractionForMonomer
  • Fragment floor imposed by chain architectureaccessibleFragmentFloorDp
  • Sign of the electron balance for a valorisation routenetElectronsPerRepeatUnit
• Predictive accuracy5/7 computed+

  Whether a computed number is fit to make a decision with.

  • Error on an anchored polymerisation enthalpy (kJ/mol)SOLVATION_CORRECTION
  • Error correlation ρ across a ring-openingCORRECTED_CALIBRATION
  • Enthalpy error propagated to a ceiling temperature (K)ceilingTemperatureErrorK
  • Per-atom accuracy a target error would demandrequiredPerAtomAccuracyMeV
  • Which design inputs atomistic simulation can reach at allreachSummary
  • Prediction interval coverage against held-out measurements
  • Accuracy on monomer families outside the training set
• Avoidable experimentation3/6 computed+

  Specification §21 — experiments performed despite sufficient prior evidence.

  • Planned experiments removed or narrowed by a derived boundexperimentsChanged
  • Candidates rejected on paper before synthesisscreenCorpus
  • Constraint that binds hardest, setting the screening orderevaluateCandidate
  • Repeated-dead-end rate across the programme
  • Fraction of experiments selected with quantified expected information gain
  • Percentage of failed experiments producing reusable information
• Evidence quality and provenance3/5 computed+

  A claim without a grade is a claim that cannot be checked.

  • Sources carrying a DOI and a content hashSOURCES
  • Specification claims graded on the evidence ladderALIGNMENT
  • Grade of a derived result, capped at its weakest inputweakestGrade
  • Fraction of claims resting on a single source
  • Capture rate for failures and anomalies
• Safety and migration2/6 computed+

  Food contact is a regulatory gate, not a performance metric.

  • Migrated fraction of a mobile species over shelf lifemigratedFraction
  • Migration in parts per billion against a stated limitmigrationPpb
  • Residual catalyst, oligomer and degradation products
  • Migration after repeated loops, not only first use
  • Substances of concern designed out rather than diluted
  • Environmental fate of unrecovered material
• Energy, carbon and cost0/6 computed+

  The clause the whole outcome is judged on, and the least instrumented here.

  • Total cost per use, including collection and capital
  • Energy per kilogram of recovered monomer
  • Greenhouse-gas balance without offsets
  • Renewable fraction of process energy
  • Cost per use versus virgin at matched performance
  • Capital intensity per tonne of annual capacity
• Scale-up and translation0/5 computed+

  Whether anything demonstrated survives leaving the bench.

  • Functional retention at ≥100× production scale (%)
  • Independent reproduction rate within stated uncertainty (%)
  • Laboratory-to-pilot time
  • Converting-line compatibility on existing equipment
  • Freedom to operate and licensing position