Post-LHC Colliders

Established A post-LHC collider is a proposal to spend between five and thirty billion currency units over three to five decades to measure known particles more precisely, with no guarantee of discovering an unknown one. That sentence is not a criticism; it is the honest version of the physics case, and every credible proponent states it. The Large Hadron Collider found the Higgs boson in 2012 and then, across Run 1 and Run 2, excluded supersymmetric partners across most of the parameter space that motivated the machine. The next generation is being designed in the knowledge that the same could happen again.

Established Four concepts are live, and they are not variations on one design. The Future Circular Collider (FCC) is a roughly 91-kilometre ring at CERN, run first as an electron-positron Higgs and electroweak factory (FCC-ee) and, decades later, possibly as a 100-tera-electronvolt proton machine (FCC-hh). The Circular Electron Positron Collider (CEPC) is the Chinese counterpart at similar scale. The International Linear Collider (ILC) is a 20-kilometre linear electron-positron machine designed for Japan and unapproved for over a decade. A muon collider is a 10-TeV-scale machine that does not yet exist as engineering, only as a design study plus a list of unsolved problems.

Frontier The question this brief tries to settle is not which machine is best but what each one buys per unit of money, power and calendar time — and which of the four has a demonstrated path from today’s hardware to the machine. On that test the ordering is not the same as the ordering by physics reach. The lepton machines have solved physics and unsolved politics. The hadron machine has solved politics and unsolved magnets. The muon machine has neither, and the largest upside.

Established A concept study is not a build commitment, and the distinction is where most public confusion lives. CERN’s FCC Feasibility Study delivered its report in 2025; that report is an input to the European Strategy for Particle Physics update, which is an input to a CERN Council decision, which would itself be followed by host-state permitting, cost-sharing negotiation and a construction start no earlier than the 2030s. Four sequential gates, each of which has killed a collider before. The Superconducting Super Collider passed three of them and died at the fourth.

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.

Established The LHC’s measured record is the baseline every proposal is scored against. Proton-proton collisions at 13.6 tera-electronvolts in the centre of mass, in a 26.7-kilometre ring, at instantaneous luminosities around 2 × 10³⁴ per square centimetre per second. Run 2 delivered roughly 140 inverse femtobarns to each of ATLAS and CMS. The Higgs boson mass is now known to about 0.1 per cent, near 125.2 giga-electronvolts. Its couplings to the heaviest fermions and to the weak bosons are measured at the ten-per-cent level and agree with the Standard Model.

Established The same record is a long list of things not found. Gluino masses below roughly 2 TeV are excluded in standard scenarios; squarks, heavy resonances, leptoquarks and dark-matter mediators are excluded across wide swathes. No statistically robust deviation from the Standard Model has survived the full Run 2 dataset. This is the single most important fact for anyone costing the next machine: the LHC’s discovery of the Higgs was a confirmation of a fifty-year-old prediction, and its search programme returned nulls.

Established The High-Luminosity LHC is the actual next collider, and it is already being installed. The upgrade targets levelled luminosity of 5 to 7.5 × 10³⁴ and an integrated 3,000 inverse femtobarns per experiment over roughly a decade of running — more than twenty times the Run 2 dataset. The long shutdown to install it began in the mid-2020s, with physics running from around 2030. Anyone proposing an FCC decision in the late 2020s is proposing it in the middle of the HL-LHC installation, not after its results.

Frontier The HL-LHC’s flagship deliverable, Higgs self-coupling, will be measured badly. Combined ATLAS and CMS projections put the constraint on the trilinear coupling at roughly the 50-per-cent level, with di-Higgs production reaching evidence rather than observation in most scenarios. A 50-per-cent measurement of the term that fixes the shape of the electroweak potential is a real result and an unsatisfying one; it is the strongest single argument for a machine that can do better.

Established FCC-ee’s case is statistics, and the statistics are extraordinary. The feasibility study describes a roughly 91-kilometre ring with four interaction points, running at the Z pole with luminosities of order 10³⁶ per square centimetre per second — giving of order 10¹² Z bosons, five orders of magnitude beyond LEP — then at the WW threshold, then at 240 GeV for order a million Higgs-strahlung events, then at the top threshold. Higgs couplings land at the few-per-mille level, electroweak precision observables improve by one to two orders of magnitude.

Frontier The FCC cost number that circulates, about 15 billion Swiss francs, is the tunnel plus the electron-positron machine, not the programme. The hadron stage is costed separately and later, and its magnets do not exist. Treating the quoted figure as the price of 100-TeV proton physics is the most common error in public discussion of the project. A contested number deserves its range: published estimates for the civil engineering and FCC-ee machine cluster in the low-to-mid teens of billions of francs, and no independent audit of that estimate has been published.

Established Site power is a first-order design parameter, not a footnote. CERN’s present consumption is of order 1.3 terawatt-hours per year. FCC-ee operating points are quoted in the range of roughly 220 to 350 megawatts of site power depending on energy, implying annual consumption comparable to a small city’s. A machine whose electricity bill scales with its physics reach is exposed to European power prices in a way the LHC never was, and that exposure has no technical fix.

Frontier CEPC is the same physics on a different political clock. The Chinese proposal reached technical design report maturity for the accelerator in the mid-2020s, at a quoted construction cost in the neighbourhood of 36 billion renminbi, and has been submitted for consideration in national five-year planning. Whether it is approved is a decision of the Chinese state, not of a scientific collaboration, and the approval question was live but unresolved as of early 2026.

Established The ILC has been technically ready and politically stalled for more than a decade. A 250-GeV first stage with superconducting radio-frequency cavities, an internationally reviewed design, and a Japanese government that has repeatedly declined to host it. The programme continued through a reduced-scope technology network rather than a construction project. A design does not decay, but an assembled community does; the ILC is the field’s standing demonstration that readiness is not sufficiency.

Frontier The muon collider is where the physics-per-metre argument is strongest and the engineering weakest. Muons are point particles, so a 10-TeV muon collider delivers parton-level energy comparable to a far larger proton ring, in a tunnel of roughly ten kilometres. They also decay with a 2.2-microsecond rest lifetime, which means the entire machine is a race against the clock and every component sits inside a shower of decay products. The 2023 US Particle Physics Project Prioritization Panel report treated it as a long-horizon aspiration warranting R&D, not as a project.

Established Ionization cooling has been demonstrated once, partially. The Muon Ionization Cooling Experiment published a measured reduction in transverse emittance in 2020. What it did not do is reaccelerate the cooled beam, cool in all six dimensions, or operate as a repeating cell. The gap between that result and a working cooling channel — hundreds of cells, high-gradient radio-frequency cavities operating inside multi-tesla solenoid fields, a six-dimensional emittance reduction of order 10⁵ to 10⁶ — is the largest unbridged gap in any live collider concept.

Established The anomaly that motivated much of the last decade’s new-physics expectation has largely evaporated. The muon anomalous magnetic moment programme at Fermilab reached roughly 127 parts per billion on the experimental side, while the theory community’s 2025 consensus moved to lattice-based hadronic vacuum polarisation, bringing the Standard Model prediction into agreement with the measurement. The residual disagreement is now between two theory methods rather than between theory and experiment. Any collider case built on that anomaly needs rewriting, and honest proponents have rewritten it.

Frontier Is there a target the Standard Model itself guarantees? Yes, and it is thin: the Higgs self-coupling, the Higgs total width, the electroweak vacuum’s stability, and whether the top-Higgs sector is consistent at the per-mille level. These are guaranteed measurements, not guaranteed discoveries. The honest frontier question is whether a guaranteed measurement of a parameter with no predicted anomaly is worth fifteen billion francs, and that is a values question wearing a physics costume.

Frontier Does precision beat energy at fixed cost? An electroweak factory probes new physics indirectly through loop effects, with sensitivity to mass scales of tens of TeV for strongly coupled new states. A 100-TeV hadron machine probes directly to roughly 30 to 50 TeV for coloured states. The two are not substitutes: indirect sensitivity tells you something is there, direct production tells you what. Which comes first is contested inside the field, and the contest tracks national programme interests closely enough to be worth noticing.

Speculative Could a muon collider leapfrog the sequence entirely? If six-dimensional cooling works at the required factor, a 10-TeV muon machine in a small ring delivers hadron-collider reach with lepton-collider cleanliness, at lower site power than FCC-hh. That is the single most consequential conditional in the field. It rests on a demonstration nobody has performed.

Speculative Is there a cheaper path to high energy? Plasma-wakefield acceleration reaches gradients three orders of magnitude above radio-frequency cavities in metre-scale stages, and has produced high-quality beams at the giga-electronvolt level. Converting that into a collider requires staging hundreds of modules with preserved emittance, positron acceleration that remains unsolved, and a luminosity argument nobody has closed. It is a serious research programme and not a credible alternative on a 2050 timescale.

Established For FCC-hh, the bottleneck is a magnet that does not exist in series production. A 100-TeV proton ring in a 91-kilometre tunnel requires dipoles near 14 to 16 tesla. Niobium-tin accelerator dipoles have reached roughly 14.5 tesla in single short-model magnets in laboratory conditions; the step from a record model to thousands of kilometres of bore-quality, quench-protected, series-produced magnet is where accelerator programmes historically lose a decade. Rare-earth barium copper oxide tape offers higher fields but at conductor costs and mechanical stresses that the collider community itself has publicly questioned.

Established For FCC-ee, the bottleneck is synchrotron radiation power, and it is a hard physical wall. Radiated power per turn scales as the fourth power of energy over the ring radius, which is why the electron machine tops out near the top-quark threshold in a 91-kilometre ring and why the ring is 91 kilometres rather than 27. The consequence is that the same tunnel must be reused for a hadron machine to reach higher energies at all — the two-stage argument is a physics constraint before it is a financial one.

Established For the muon collider, the bottlenecks are cooling, neutrino radiation and detector background, in that order. Cooling is the existential one. Neutrino radiation is a genuine siting constraint: the decay of stored muons produces a collimated neutrino flux that deposits dose where it exits the earth, which for a 10-TeV machine forces beam-wobbling systems and site-boundary analysis rather than being ignorable. Beam-induced background from decay electrons floods the detector, requiring tungsten shielding nozzles that remove a substantial part of the forward acceptance.

Established Detector conditions at HL-LHC already strain the state of the art, and the successors are worse. HL-LHC runs at 140 to 200 simultaneous interactions per bunch crossing, which is why timing detectors with tens of picoseconds of resolution moved from exotic to mandatory. FCC-hh projections run into the high hundreds or thousand-interaction regime with radiation doses an order of magnitude above HL-LHC. Silicon that survives those fluences for a decade is a materials programme, not a purchase.

Established Civil engineering is not the easy part. A 91-kilometre tunnel under the Geneva basin with of order eight surface sites generates several million cubic metres of excavated material, requires land acquisition across an international border, and depends on geology that the feasibility study itself flags as partially characterised. Tunnel-boring risk is the most reliably underestimated line in megaproject accounting, a pattern documented across hundreds of projects and summarised in this corpus in Megaproject Governance.

Established Superconductor supply is now shared with fusion, and fusion is winning the queue. Rare-earth barium copper oxide tape production expanded sharply through the 2020s, driven by compact tokamak programmes rather than accelerators; a single supplier has publicly reported delivering thousands of kilometres of tape into the fusion sector. A collider committing to high-temperature superconducting magnets in the 2030s would be entering a market it does not dominate and did not create — a reversal of the historical relationship documented in High Temperature Superconductors.

Established Niobium-tin conductor remains a specialist industry with few qualified producers. The HL-LHC upgrade itself absorbed a large share of world accelerator-grade niobium-tin capacity. Scaling to an FCC-hh dipole inventory is a factor-of-many expansion of an industry whose customers are exclusively public research programmes, which means no private demand underwrites the capacity between orders.

Frontier The dependency that is easiest to forget is people. An accelerator physicist trained on LHC construction in 1998 retired in the 2020s. A decision taken in the late 2020s for a machine operating in the 2050s spans two full career generations, and the intervening years offer graduate students no construction project to learn on. The ILC’s stall is the natural experiment: technical readiness persisted, assembled expertise dispersed.

Established Power procurement is a dependency with a political tail. Several hundred megawatts of continuous industrial demand in a European grid with decarbonisation targets is a negotiation with governments and utilities, not a line item. A machine that runs only when power is cheap is a machine with a reduced duty cycle and reduced integrated luminosity, which converts an energy-policy variable directly into a physics result.

Established The decisive experiment for this whole field is a full six-dimensional muon ionization-cooling cell, with radio-frequency reacceleration, operated in a beam and measured. Not a simulation, not a single-pass emittance reduction, but a repeating cell demonstrating the cooling factor per unit length that the design studies assume. If it works, the 10-TeV muon collider becomes an engineering programme with a cost estimate and the circular-ring sequence loses its monopoly on high energy. If it fails, or if the achievable gradient inside a multi-tesla solenoid falls short, the muon route is a research topic and the field’s only path to 10 TeV parton collisions runs through a 100-kilometre tunnel and 16-tesla magnets.

Established No facility is currently funded to perform that demonstration. The international design collaboration has produced parameter sets and a staged R&D plan; what it does not have is a committed demonstrator with a construction budget and a date. That is a statement about funding, not about difficulty, and it is why this brief records the horizon as unscheduled rather than as a decade away.

Frontier The second experiment is a full-length, series-representative 16-tesla dipole, built by industry rather than by a laboratory, and cycled to accelerator duty. Short models at record fields prove physics; a full-length magnet built to a production drawing proves a factory. The distinction is exactly the one that separated the Superconducting Super Collider’s magnet programme from its budget.

Established The third is already running and costs nothing extra: the HL-LHC itself. Three thousand inverse femtobarns will either produce a deviation or will not. A null result across the full dataset is not a neutral outcome for the next machine — it strengthens the precision case and weakens the energy-frontier case simultaneously, and planners should say in advance which way they would update.

Frontier The fourth is a policy result, and it is the one that actually determines what gets built. A CERN Council decision with a cost-sharing schedule, host-state permits and a construction start date is the observation that converts a feasibility study into a project. Every collider that failed in the last forty years failed at this step rather than at a technical one.

Established The FCC-ee machine is conventional engineering at unprecedented scale, which is a different risk profile from novel engineering at small scale. Normal-conducting arc magnets, superconducting radio-frequency cavities of proven design, a twin-aperture layout, top-up injection from a booster in the same tunnel. Nothing in it requires an invention. Everything in it requires that a 91-kilometre machine behave like the 27-kilometre machine it resembles, and beam-dynamics surprises at that scale are the historical norm rather than the exception.

Established Beam power and machine protection dominate the hadron design. The LHC stores hundreds of megajoules per beam; FCC-hh would store of order ten times that. A stored beam capable of drilling through tens of metres of copper must be extracted reliably in microseconds every time, for decades. Machine protection is the discipline where a collider’s availability — and therefore its integrated luminosity, and therefore its physics — is actually decided.

Established Muon collider engineering is dominated by things that are radioactive, hot and fast at once. A multi-megawatt proton driver striking a target to make pions, a capture solenoid in an extreme radiation field, a cooling channel with high-gradient cavities inside solenoid fields where breakdown physics differs from the field-free case, and rapid-cycling acceleration that must complete before the beam decays. Each subsystem has a laboratory precedent; none has been operated in series.

Frontier Detector engineering for either successor is a twenty-year lead item and is routinely underbudgeted. Timing layers at tens of picoseconds, radiation-hard silicon to fluences beyond present qualification, trigger and data-acquisition systems handling rates that make HL-LHC look modest, and reconstruction software whose computing cost scales worse than linearly with pileup. Detector collaborations are typically funded nationally while the machine is funded internationally, which puts the two on different schedules by construction.

Established Collider magnet programmes and fusion magnet programmes now draw on the same conductor industry. That is a change of direction: accelerator physics created the market for niobium-titanium and niobium-tin, and fusion has created the market for rare-earth barium copper oxide tape. The industrial base question is treated in Superconducting Infrastructure and the materials question in High Temperature Superconductors; this brief takes both as given and asks only whether a collider can buy at the volumes it needs.

Frontier Non-collider probes now cover parameter space colliders cannot reach, and cost three orders of magnitude less. Precision tabletop searches, neutrino observatories and astrophysical constraints exclude regions of coupling space that no accelerator will approach. The relationship is complementary rather than competitive, but the budget relationship is not: see Neutrino Astronomy for the observatory branch and Quantum Gravity for the tabletop one.

Established The cost-scaling problem is shared with other frontier instruments. Ground-based astronomy faces a construction cost that rises steeply with aperture, which is why the largest telescope under construction is 39 metres rather than 100; the collider analogue is that energy reach rises slowly with tunnel length and cost rises fast. Mega-Telescopes documents the scaling exponent in its own field.

Established CERN is the only institution on earth that has built and operated a collider at this scale, and its governance is the project’s main asset. A treaty organisation with two dozen member states, a council that sets a multi-year budget in national contributions, and a track record of delivering LEP and the LHC in the same tunnel. The corpus treats the general question of why such bodies persist in Scientific Institutions Through History; the specific point here is that continuity of a funding instrument across forty years is rarer than any of the technology involved.

Established The failure mode is documented in detail and it is domestic politics, not international science. The Superconducting Super Collider was terminated by the US Congress in 1993 after roughly two billion dollars had been committed, with about 1.6 billion of that expended on construction, and the audited termination itself required further appropriations. Post-mortems by participants assign responsibility partly to the physics community’s own conduct — management structure, cost growth, and the handling of international partners — rather than to hostile outsiders alone.

Frontier The European decision architecture is deliberately slow and that is a feature with a cost. A strategy update gathers community input, an open symposium debates it, a drafting group produces recommendations, the Council adopts them, and only then does a project enter cost-sharing negotiation. The process is legitimate and transparent. It also means the field must commit to a machine before the HL-LHC has reported, and the ordering is a consequence of construction lead times, not of anyone’s preference.

Frontier Two-host competition is now a real dynamic rather than a rhetorical one. A Chinese approval decision for CEPC would change the European calculus immediately, and the reverse is equally true. This is not a scenario the strategy documents can discuss frankly in public, which is precisely why an outside brief should say it plainly: the probability that both an FCC-ee and a CEPC are built is low, and each programme’s internal case partly depends on the other not happening.

Frontier The opportunity-cost argument is the serious objection and it deserves a serious answer. Fifteen billion francs is comparable to a national research budget, and physicists outside the energy frontier have argued publicly that the same sum distributed across smaller instruments would produce more knowledge. The counter-argument is that collider funding is not fungible in practice — member-state contributions to a treaty organisation are not a pool that would otherwise go to condensed-matter physics. Both claims are partly true and neither has been tested empirically.

Established Local environmental impact is a genuine burden borne by people who get no physics. Millions of cubic metres of spoil, decades of construction traffic, surface sites on agricultural land, and groundwater effects in a populated basin. Consultation processes exist and have been used; the honest framing is that a global public good is being financed with a local private cost, and that compensation mechanisms are a matter of negotiation rather than of right.

Frontier Energy consumption is an ethical argument now in a way it was not in 1994. Several hundred megawatts of continuous demand during a decarbonisation transition invites the question of whether the physics is worth the carbon, and the answer depends entirely on the grid the machine draws from. Proponents who quote a low-carbon grid should also quote what happens if that grid is not delivered on schedule.

Frontier The strongest civilizational argument for these machines is not physics but institutional: they are proof that multi-decade cooperative projects are still possible. CERN outlasted the Cold War division of Europe and remains a working example of pooled sovereignty in a technical domain. If the next machine is not built, the lost capability is partly the accelerator and partly the demonstration that such commitments can be kept.

Speculative If the Standard Model remains unbroken through an FCC-ee programme, particle physics faces a structural question rather than a technical one. A field whose instruments cost more each generation and whose anomalies keep resolving in favour of the existing theory must eventually decide whether to keep scaling. There is no physical law guaranteeing that the next layer of nature is accessible at a price a civilization will pay, and that possibility is rarely stated inside the field’s own planning documents.

Handwave Claims that a post-LHC collider will unlock practical applications — energy sources, propulsion, materials — are assertion. No proposed application depends on knowing the Higgs self-coupling to five per cent. The case for these machines is knowledge, and dressing it as utility weakens it.

These horizons track what the machines and their gating decisions plausibly deliver, assuming no cancellation and no surprise at HL-LHC.

• 10 yr: Frontier HL-LHC in physics running with a large fraction of its 3,000 inverse femtobarns still to come; a European strategy position and possibly a CERN Council decision on FCC-ee; a CEPC approval decision resolved one way or the other; muon-collider work still at design-study and component-test level.
• 25 yr: Speculative If approved and funded on the nominal schedule, an FCC-ee or CEPC in early physics operation, producing Higgs couplings at the per-mille level and Z-pole datasets five orders of magnitude beyond LEP. If not approved, no operating energy-frontier machine anywhere and a field living on HL-LHC legacy data.
• 50 yr: Speculative A hadron stage in the same tunnel at 80 to 100 TeV, conditional on 14-to-16-tesla magnets having reached series production, or a 10-TeV muon collider conditional on cooling having been demonstrated and industrialised. Both conditionals are load-bearing and neither is currently satisfied.
• 100 / 250+ yr: Handwave Proposals for collider energies beyond 100 TeV — plasma-wakefield staging, lunar or orbital rings, muon machines at the hundred-TeV scale — have no engineering basis at present and their cost arguments are assertion. What can be said is that the scaling of cost with energy, not the physics, is what makes these horizons speculative.

• Depends on results already mapped in this corpus: conductor availability and price as documented in High Temperature Superconductors and Superconducting Infrastructure, and the cost-forecasting record in Megaproject Governance. No physics result on the map blocks an electron-positron machine; it is buildable with today’s technology and waits only on money and permits.
• Requires (not on this map) a demonstrated six-dimensional ionization-cooling cell with radio-frequency reacceleration, without which no muon collider exists; series production of accelerator-quality dipoles near 16 tesla by industry rather than by laboratories; rare-earth barium copper oxide tape available at collider volumes and prices rather than at fusion-programme volumes; a host-state construction permit for a 91-kilometre cross-border tunnel with its surface sites; a capital commitment that survives four decades of electoral cycles in two dozen contributing states; and civil-engineering capacity to bore and dispose of several million cubic metres of spoil on schedule.
• Enables Higgs self-coupling and total-width measurements at the few-per-cent level, electroweak precision observables one to two orders of magnitude beyond LEP, indirect sensitivity to new states at tens of tera-electronvolts, and — only in the hadron or muon stages — direct production reach beyond the LHC.
• Adjacent Neutrino Astronomy and Quantum Gravity for the non-accelerator probes that cover complementary parameter space, Mega-Telescopes for the same cost-versus-scale problem in another instrument class, and Scientific Institutions Through History for why a body like CERN persists at all.

Handwave “The next collider will discover what dark matter is.” It might. There is no prediction that it will. Weakly interacting massive particles in the mass range most accessible to a hadron collider have been excluded over much of the theoretically favoured space by direct-detection experiments and by LHC searches together. A collider can produce dark-matter candidates only if they couple to Standard Model particles strongly enough, and the coupling is precisely what is unknown.

Speculative “Supersymmetry is still around the corner.” Supersymmetry remains a viable framework and its simplest natural versions are excluded. The parameter space that survives requires either heavy superpartners — which reintroduces the fine-tuning the theory was invented to remove — or compressed spectra that hide from LHC searches. Both are live research programmes; neither supports the claim that a discovery is imminent.

Established “The LHC found nothing after the Higgs.” False in an important way. The LHC measured the Higgs couplings, observed its decays to tau leptons, bottom quarks and muons, measured top-quark properties to per-cent precision, discovered dozens of conventional and exotic hadrons, and excluded vast regions of parameter space. Exclusion is a result. What the LHC did not do is find physics beyond the Standard Model, and conflating those two statements misleads in both directions.

Frontier “The muon g−2 anomaly proves new physics is nearby.” This was a defensible reading until the theory consensus shifted. With lattice determinations of the hadronic contribution adopted in the 2025 theory summary, the Standard Model prediction and the Fermilab measurement agree within uncertainties. The remaining discrepancy is between two ways of computing the same quantity. Anyone still quoting the anomaly as a motivation is quoting a superseded number.

Handwave “A concept study means the machine is being built.” A feasibility study establishes that a design closes, a site is possible and a cost can be estimated. It does not commit a franc to construction. Between study and steel lie a strategy update, a council decision, cost-sharing agreements, host-state permits and national budget votes — and the historical record of that sequence includes a cancelled machine with a partly dug tunnel in Texas.

Speculative “Plasma wakefield acceleration will make big rings obsolete.” Gradients of tens of giga-electronvolts per metre are measured and real. A collider additionally needs luminosity, beam quality preserved across hundreds of staged modules, positron acceleration, and a power efficiency nobody has demonstrated. Treating a demonstrated gradient as a demonstrated collider is the most common category error in coverage of the field.