# DISCOVERIES — physical.md (D001–D025)

*Physics and chemistry. Each item names a blocker of a specific kind, and prefers the blocker
"two measurements that were never taken on the same sample" over "the instrument is expensive".
Each question is answerable, and each decisive measurement is meant to be attempted, not admired.*

### D001 — How far can a liquid be pulled apart before it cavitates?
**Question.** For a water sample whose dissolved gas and particle content are characterised, how negative must the pressure be before a cavity nucleates?
**Why unresolved.** Concept blocker: the threshold is not a material constant but a property of whichever nucleus is present, so measurements on different samples are measurements of different things, and the reported tensions span orders of magnitude for that reason, not through instrument error. Instrument blocker: the tension at the instant of nucleation is inferred from a pressure transient or from the subsequent bubble dynamics, never read at the nucleation site, and the nuclei are not counted in the same run.
**Decisive measurement.** One sealed sample, its gas content set by equilibration and its particle count measured by light scattering, taken into tension three ways — slow cooling of a rigid sealed tube, a focused acoustic standing wave, and a piston-driven microcell — with the nucleation pressure recorded in each and the surviving nucleus population re-measured after each attempt.
**Counts as an answer if.** The three thresholds converge once the nucleus population is accounted for, or the residual spread is attributable to a named nucleus species with a measured size distribution.
**Why it matters.** Cavitation limits sonochemistry, pump design and every claim about metastable water; a tension that is a property of the apparatus rather than the liquid changes what the word means.
### D002 — At what density does a supercritical fluid begin to propagate shear?
**Question.** At fixed temperature, is there a density at which a supercritical fluid supports a propagating transverse acoustic mode?
**Why unresolved.** Concept blocker: a fluid has no static shear modulus, yet above the inverse structural relaxation frequency it carries shear for a few periods, and no observable has been agreed to mark the onset, so each measurement is interpreted by the criterion its authors prefer. Instrument blocker: the transverse current correlation is weak, lies beneath the longitudinal branch, and requires inelastic X-ray scattering at millielectronvolt resolution with a resolution function narrow enough to separate a propagating mode from an overdamped one.
**Decisive measurement.** Inelastic X-ray scattering of the dynamic structure factor of argon or carbon dioxide along an isotherm, over a pressure range that crosses the line where transverse modes are predicted to disappear, at wavevectors where the transverse and longitudinal branches separate, tracking the mode frequency, width and lifetime against density at each wavevector.
**Counts as an answer if.** A threshold density with uncertainty at which the transverse mode lifetime exceeds one period, or a demonstration that the excitation is overdamped at every density reached.
**Why it matters.** It decides whether the liquid-like and gas-like supercritical regions are separated by a real dynamical boundary, which is how supercritical solvents are modelled in extraction and reaction engineering.
### D003 — Is the reptation tube a measured length or a fitted one?
**Question.** On one monodisperse polymer, do three independent routes give the same tube diameter?
**Why unresolved.** Concept blocker: the tube is not an object in the liquid but the region a chain cannot leave because of topological constraints, and its diameter is normally obtained from the plateau modulus through a formula that already assumes the tube model, so rheology cannot test it. Access blocker: neutron spin echo and single-chain tracking avoid the plateau modulus, but they have rarely been applied to the same polymer at the same molecular weight, and each conversion to a tube diameter carries its own assumption.
**Decisive measurement.** One monodisperse polymer, its tube diameter extracted three ways: from the plateau modulus, from the time at which the mean-square displacement crosses from square-root to quarter-power growth in neutron spin echo, and from the transverse confinement width of a fluorescently labelled chain tracked inside a matrix of a different length.
**Counts as an answer if.** Three diameters whose uncertainties overlap, or a stated ordering, which would show that the tube diameter is model-dependent.
**Why it matters.** The entanglement molecular weight is a design parameter for every polymer melt, and it is currently taken from one of these routes alone.
### D004 — Does shear thickening begin where particle contacts become frictional?
**Question.** In a dense suspension, does the onset of discontinuous shear thickening occur at the stress at which the particle contacts become frictional?
**Why unresolved.** Concept blocker: the accepted picture is a transition from lubricated to frictional contacts, but the contact friction coefficient at the particle scale is not the macroscopic one, and the transition stress is inferred from bulk rheology rather than measured at a contact. Instrument blocker: bulk rheometry gives the onset stress but nothing about a single contact, while colloidal-probe force microscopy gives the contact law but not the bulk transition, and the two have not been performed on one particle batch.
**Decisive measurement.** One batch of monodisperse particles, its thickening onset measured by shear rheology across volume fractions, and the pairwise friction coefficient between two particles of that batch measured by colloidal-probe force microscopy in the same liquid at the same normal stress, with the measured friction transition compared with the measured onset.
**Counts as an answer if.** The onset coincides with the measured friction transition across volume fractions, or the onset occurs at a lower stress that identifies a lubrication-to-contact transition independent of friction.
**Why it matters.** Shear thickening causes clogging and impact hardening in suspensions from concrete to blood; a measured contact law would let the onset be predicted rather than fitted separately for each system.
### D005 — Is the hydrophobic force the same at two length scales?
**Question.** Is the attraction measured between two macroscopic hydrophobic surfaces the same interaction as the one measured between two single hydrophobic molecules at the same separation?
**Why unresolved.** Instrument blocker: the macroscopic force is measured between surfaces at separations from a few to a hundred nanometres, the single-molecule force by atomic force microscopy or optical tweezers at sub-nanometre separations, and the ranges barely overlap. Concept blocker: the macroscopic attraction is often attributed to nanobubbles or to a dewetted layer between the surfaces, neither of which exists between two isolated molecules, so the two measurements may be of different phenomena rather than of one force.
**Decisive measurement.** A hydrophobic surface carrying a sparse, known density of hydrophobic tethers, its force measured in one apparatus against a macroscopic hydrophobic counter-surface and against a single functionalised tip, using tether density to bridge the length scales in one liquid at one temperature.
**Counts as an answer if.** The force per unit area at a given separation agrees between the two probes once tether density is accounted for, or the macroscopic force is explained by a measured bubble population.
**Why it matters.** Hydrophobic attraction is invoked for protein folding, colloid stability and membrane assembly; if the macroscopic version is a bubble artefact, a large literature is measuring the wrong phenomenon.
### D006 — Is the charge of a colloid in a nonpolar solvent a fixed number?
**Question.** In a low-permittivity solvent, is the charge on a colloidal particle set by its surface chemistry alone, or does it change with particle and surfactant concentration?
**Why unresolved.** Concept blocker: charge in such solvents comes from inverse micelles and trace water, so it is regulated by an equilibrium between the particle surface and the micelle population, and it is not a single-valued property if it depends on the suspension's composition. Instrument blocker: electrophoresis measures mobility in an applied field that perturbs the ion distribution being measured, and standard models assume a thin double layer that does not exist when the screening length exceeds the particle radius.
**Decisive measurement.** Optical-tweezers force–distance curves between isolated pairs of particles in one solvent, extracting the charge from the screened Coulomb interaction at several particle and surfactant concentrations, and comparing it with the charge inferred from electrophoresis and from the suspension's conductivity.
**Counts as an answer if.** A charge per particle with uncertainty, together with its dependence on concentration expressed as a slope, or a charge independent of both concentrations within error.
**Why it matters.** Nonpolar colloidal stability governs paint, toner, ink and battery slurries, and every stability model takes the particle charge as a fixed input.
### D007 — Does Onsager reciprocity survive outside the linear regime?
**Question.** When a thermodynamic driving force is large, does the measured ratio of a pair of conjugate cross-coefficients stay equal to one?
**Why unresolved.** Concept blocker: the reciprocal relations are proved in the linear regime, where fluxes are proportional to forces and the coefficients are constants, while every practical cross-effect is used at gradients where the flux–force relation is nonlinear, and the coefficient is then defined by a local linearisation whose validity is assumed. A test needs two quantities both defined at the same finite driving force, and no convention for that has been agreed.
**Decisive measurement.** A thermoelectric sample in which the Seebeck coefficient (voltage per unit temperature difference) and the Peltier coefficient (heat per unit current) are measured over two decades of driving force, with both directions of current and of heat flow reversed; reciprocity predicts that the Peltier coefficient equals the Seebeck coefficient times the absolute temperature at every force.
**Counts as an answer if.** The ratio of measured to predicted Peltier coefficient, with uncertainty, plotted against driving force: constant at one, or departing with a measurable slope and threshold.
**Why it matters.** Thermoelectric device models, thermal-diffusion separations and electrokinetic energy conversion all use coefficients measured near equilibrium at conditions far from it.
### D008 — Does calorimetry reproduce the isosteric heat at every loading?
**Question.** In a microporous adsorbent, does the heat of adsorption measured directly by calorimetry agree with the isosteric heat derived from isotherms at several temperatures, over the full loading range?
**Why unresolved.** Concept blocker: the isosteric heat assumes a reversible, differentiable equilibrium, which fails in materials with gate-opening transitions or hysteresis, and the failure is invisible in the isotherm itself. Instrument blocker: calorimetry measures an integral heat on a sample that must be outgassed identically, while isotherms are usually measured on a different aliquot, so the two describe different solids.
**Decisive measurement.** One sample, split after a single activation, measured in a calorimeter coupled to a dosing system so that the differential heat and the isotherm are taken in the same run on the same material over the whole loading range.
**Counts as an answer if.** The two heats agree within error at all loadings, or they diverge in a loading window that coincides with a structural transition seen by diffraction on the same sample.
**Why it matters.** Heats of adsorption set the energy penalty of gas storage and separation; a systematic divergence would mean the isotherm-derived values by which materials are ranked are wrong by more than the differences between the materials.
### D009 — Does confinement change a reaction's equilibrium constant?
**Question.** At the same temperature and the same bulk fugacities, is the equilibrium composition of a gas-phase reaction different inside a molecular-scale pore?
**Why unresolved.** Concept blocker: the equilibrium constant is defined relative to a standard state, and inside a pore the reference chemical potential includes a confinement free energy, so the constant appears to shift unless the standard state is redefined; there is no agreed standard state for an adsorbed phase, so "the equilibrium constant in a pore" is not yet a defined quantity. Access blocker: experiments report both shifts and no shifts, and the two cannot be separated because pore occupancy and bulk fugacity are not measured independently.
**Decisive measurement.** The nitrogen dioxide / dinitrogen tetroxide equilibrium inside a zeolite of known pore size, measured by gravimetry and infrared absorbance at controlled temperature and gas fugacity, with the same measurement on the free gas in the same apparatus, extracting the standard free-energy shift and the dimer fraction jointly.
**Counts as an answer if.** A shift of standard free energy in kilojoules per mole with uncertainty, or a bound showing the equilibrium composition is unchanged at the same fugacity within error.
**Why it matters.** Catalysis in zeolites and metal–organic frameworks is designed on bulk thermodynamics; a shift of a few kilojoules per mole changes selectivity substantially.
### D010 — Does a redox couple's Seebeck coefficient equal its reaction entropy?
**Question.** For one redox couple at one concentration, does the measured thermogalvanic Seebeck coefficient equal the reaction entropy measured calorimetrically, once the Soret contribution of the electrolyte is accounted for?
**Why unresolved.** Concept blocker: the Seebeck coefficient of a thermocell contains the reaction entropy plus a thermodiffusion term from the electrolyte, and the two have never been separated by independent measurement, so the standard design rule is an assumption about which dominates. Access blocker: the calorimetric entropy needs the same couple at the same concentration and supporting electrolyte as the thermocell, and the Soret term needs a concentration-gradient measurement in the same cell.
**Decisive measurement.** One thermocell across a temperature difference, its Seebeck coefficient measured over a concentration series; the same couple's reaction entropy from isothermal calorimetry; and the Soret coefficients of the redox species from a thermodiffusion cell, so that the three terms are closed rather than fitted.
**Counts as an answer if.** The Seebeck coefficient equals the calorimetric reaction entropy divided by the charge transferred, with the measured Soret term accounting for the residual, or the residual names a missing contribution.
**Why it matters.** Thermogalvanic cells are proposed for harvesting low-grade heat, and whether the entropy or the transport term dominates decides the electrode and electrolyte design.
### D011 — Does an electrocatalytic rate track the local field?
**Question.** At a working electrode and at fixed potential and temperature, does the rate of an electrocatalytic step follow the local electric field measured at that same surface?
**Why unresolved.** Concept blocker: rates are plotted against applied potential, which is not the field at the reaction site; the field is screened by the double layer and by the electrolyte, so two experiments at the same potential can have different fields. Instrument blocker: the local field is measurable through the vibrational Stark shift of a probe, but the probe must sit on the catalytically active surface, and its coverage changes the catalysis being measured.
**Decisive measurement.** A low coverage of a Stark-active spectator on a single-crystal electrode, its Stark tuning rate calibrated in the same cell, read simultaneously with the turnover rate of a reactant while ionic strength is varied so that applied potential and local field move independently.
**Counts as an answer if.** The rates collapse onto a single function of the measured local field across ionic strengths, or they do not, in which case the field is not the controlling variable and the potential acts through coverage instead.
**Why it matters.** Field-driven catalysis is invoked for carbon dioxide reduction, for enzyme active sites and for reactions at interfaces; a measured field would turn it from a plausible mechanism into a design parameter.
### D012 — Does the hydrated electron's optical radius match its structural radius?
**Question.** Is the cavity radius of the hydrated electron inferred from its optical absorption the same as the radius measured by scattering from the same irradiated water?
**Why unresolved.** Concept blocker: the optical absorption energy is inverted through a continuum cavity model that assumes a sharp radius and a dielectric continuum, which are precisely the quantities in question. Instrument blocker: structural probes of radiolytically generated electrons have far lower concentration and signal than the optical measurement, so they have been performed on different systems at different doses.
**Decisive measurement.** Pulse radiolysis of a thin water jet, with the same jet and the same dose probed at the same delay by transient X-ray scattering and by transient absorption; the pair distribution around the electron gives a radius, and the optical spectrum gives the radius that the cavity model requires.
**Counts as an answer if.** The two radii agree, or the structural one is significantly smaller, which would make the optical radius an effective quantity rather than a geometric one.
**Why it matters.** The hydrated electron is the primary reductant in radiation chemistry and in photocatalytic water splitting, and its size sets every rate constant estimated from it.
### D013 — Does a solute feel the solvent's whole dielectric spectrum?
**Question.** Is the reaction field at a dissolved probe predicted by the solvent's full measured dielectric loss spectrum rather than by a two-frequency approximation built from its static constant and refractive index?
**Why unresolved.** Assumption blocker: reaction-field models collapse a solvent's broad, structured loss spectrum into one or two frequencies, and that choice sits in the model rather than in the data. Instrument blocker: the field is inferred from a spectral shift that also depends on the probe's cavity radius and polarisability, so the two unknowns are fitted together and the fit absorbs the error.
**Decisive measurement.** One rigid probe with a known vibrational Stark tuning rate (a nitrile or carbonyl stretch), its shift measured in a series of solvents whose dielectric loss spectra are measured from hertz to terahertz, with a single solvent-independent cavity radius required to reproduce every shift.
**Counts as an answer if.** The shifts collapse onto the prediction from the measured spectra with no per-solvent parameter, or the residuals isolate a specific solvation term, such as hydrogen bonding or charge transfer, that the continuum field cannot carry.
**Why it matters.** Solvatochromism, electron-transfer rates and pKa shifts in mixed solvents all use the continuum field; if it is wrong by a factor that varies with solvent, those predictions inherit the error.
### D014 — Does vibrational excitation change a rate in solution?
**Question.** When a reactant's vibration is excited in solution, does its reaction rate rise by the amount the gas-phase barrier predicts?
**Why unresolved.** Instrument blocker: state-selected excitation needs an infrared or Raman pump on a molecule whose vibrational energy relaxes within picoseconds in solution, often faster than a bimolecular encounter, so the excited population may be gone before it reacts. Concept blocker: energy can be redistributed to the solvent before the barrier is crossed, so a null result is ambiguous between no vibrational control and relaxation that is simply too fast.
**Decisive measurement.** Stimulated Raman pumping of a stretch of the reactant in a series of solvents spanning vibrational relaxation times from a few to hundreds of picoseconds, with the reaction followed by transient absorption and the relaxation measured on the same sample, so that the rate enhancement is plotted against the measured relaxation time rather than against solvent identity.
**Counts as an answer if.** The enhancement extrapolates to the gas-phase prediction as relaxation slows, or it vanishes in every solvent and vibrational control is absent in the condensed phase.
**Why it matters.** Mode-selective chemistry is the goal of laser-driven synthesis; whether it survives a solvent decides whether it can ever be a preparative method.
### D015 — Is aromatic stabilization one measurable energy?
**Question.** Do the thermochemical and the magnetic measures of aromatic stabilization rank a set of molecules in the same order?
**Why unresolved.** Concept blocker: aromaticity is defined by several non-equivalent criteria — thermochemical, magnetic, geometric — which disagree for molecules with competing ring currents, and no agreed scalar exists, so a measurement of one cannot test another. Access blocker: the thermochemical criterion needs heats of hydrogenation or combustion on isolable compounds, while the magnetic criterion needs measured shielding tensors on the same compounds, and the sets of molecules chosen for the two purposes barely overlap.
**Decisive measurement.** A set chosen so that the two criteria are predicted to disagree, each compound measured in the gas phase by calorimetry to a common reference and by its measured ring-current shielding, from nuclear magnetic resonance shift anisotropies or from magnetically induced current densities computed on the measured tensor.
**Counts as an answer if.** A single ordering is common to both criteria, or the disagreement can be expressed as a second, independently measurable parameter such as a ring-current strength.
**Why it matters.** "Aromatic" is used across organic chemistry to predict stability and reactivity; a quantity that reverses when the criterion changes is not a predictor, and the word is doing work the measurement cannot support.
### D016 — Do enantiomers differ in energy by the parity-violating amount?
**Question.** Do the two enantiomers of a chiral molecule have a measurable energy difference arising from the electroweak interaction?
**Why unresolved.** Instrument blocker: the predicted difference is many orders of magnitude below the linewidth of molecular transitions reachable today, so it cannot be resolved by ordinary spectroscopy and is usually reported only as an upper bound. Concept blocker: the effect grows steeply with nuclear charge, and the molecules that enhance it most are exactly those with congested spectra and poorly known vibrational structure, so the calculation cannot be matched to a measured line.
**Decisive measurement.** A heavy-atom chiral molecule with a symmetry-allowed vibrational or tunnelling transition, both enantiomers measured in the same apparatus by Ramsey spectroscopy after buffer-gas cooling, with the linewidth pushed below the predicted shift; a racemic sample of the same molecule as the null control.
**Counts as an answer if.** A reproducible frequency difference between enantiomers appears with the sign and magnitude of the electroweak calculation, or an upper bound below the predicted value is established.
**Why it matters.** It would be the first laboratory measurement of parity violation in a molecular energy, and it is the only known physical mechanism that could bias chemistry toward one handedness.
### D017 — How many molecules are in a critical nucleus?
**Question.** What is the number of molecules in the nucleus at the top of the nucleation barrier, counted rather than fitted?
**Why unresolved.** Instrument blocker: the critical nucleus holds tens of molecules and lives for nanoseconds, so no imaging method resolves it, and the indirect route — the nucleation theorem, which extracts the nucleus size from the slope of the logarithm of the rate against the logarithm of supersaturation — has rarely been applied over enough decades of rate for the answer to be distinguished from a fit. Concept blocker: the theorem assumes a steady state that is itself hard to verify.
**Decisive measurement.** Nucleation rates of a well-characterised system, an alkane from solution or potassium chloride from water, over six decades of supersaturation at fixed temperature in a flow tube or by droplet microfluidics, with small-angle X-ray scattering at the same supersaturations to size the nuclei directly.
**Counts as an answer if.** A nucleus size with uncertainty at a stated supersaturation, and whether the nucleation-theorem value agrees with the scattering value.
**Why it matters.** Classical nucleation theory is used with a fitted surface energy precisely because the nucleus size is unknown; a counted value replaces that fit with a measurement.
### D018 — Does a measured interfacial energy predict the ice nucleation rate?
**Question.** Is the homogeneous nucleation rate of ice from supercooled water predictable from the ice/water interfacial free energy measured independently on the same water?
**Why unresolved.** Concept blocker: classical nucleation theory converts the measured rate into the interfacial energy and then converts it back into a rate, so the two are never independent, and the direct measurement has been made on different samples by a different route. Access blocker: a direct measurement needs an isolated ice/water interface held at a known undercooling, which is difficult because the interface moves as soon as the temperature is set.
**Decisive measurement.** A water inclusion trapped inside a single ice crystal and held at fixed undercooling by pressure or by solute, its interface shape measured by confocal microscopy to give the interfacial energy from the capillary fluctuation spectrum, together with the nucleation rate in emulsified droplets of the same purity and the same water.
**Counts as an answer if.** The rate predicted from the measured interfacial energy matches the measured rate, or the prediction is off by a factor that can be assigned to the nucleation prefactor rather than to the interfacial energy.
**Why it matters.** Ice nucleation governs the freezing of tissue and of food and the design of cryoprotectants; an interfacial energy that does not predict the rate would mean the barrier is not the controlling quantity.
### D019 — Below what size does a cluster stop melting?
**Question.** Below how many atoms does a cluster cease to have a melting transition with a latent heat?
**Why unresolved.** Concept blocker: the Gibbs–Thomson relation says the melting point falls with size and would vanish at a few atoms, but at that size a cluster has no bulk to coexist with a surface, no latent heat in the thermodynamic sense, and the transition becomes a continuous rearrangement, so phase coexistence is not defined for a system with no interior. Instrument blocker: calorimetry on size-selected clusters has only recently become possible, and reading a broad heat-capacity peak as a transition requires a model.
**Decisive measurement.** Mass-selected clusters of a low-melting metal — gallium, tin or indium — deposited in vacuum onto a nanocalorimeter, with heat capacity measured across the expected melting range for sizes from tens to a thousand atoms, at a coverage low enough to keep the clusters isolated.
**Counts as an answer if.** The cluster size at which the latent-heat peak disappears, with uncertainty, and whether the peak height falls continuously to zero or vanishes abruptly.
**Why it matters.** Nanoparticle melting-point depression is used to design solders, catalysts and phase-change materials, and the extrapolation is applied at sizes where the underlying transition may not exist.
### D020 — Does a dislocation core have a measurable elastic compliance?
**Question.** Is the strain field within a few nanometres of a dislocation line measurably softer than linear elasticity predicts?
**Why unresolved.** Concept blocker: linear elasticity diverges at the core, so the core radius and core energy are fit parameters of a model rather than observables, and no agreed operational definition of a core's elastic response exists. Instrument blocker: no experiment isolates the core from the long-range strain field — diffraction averages over micrometres, and atomistic simulation supplies its own core criterion — while the measurement needs sub-nanometre displacement sensitivity inside a crystal.
**Decisive measurement.** Bragg coherent diffraction imaging of a single dislocation in a nanocrystal, reconstructing the displacement field on a one-to-two nanometre grid around the line and fitting the deviation from the elastic inverse-radius form in terms of a core radius and a core compliance, repeated for edge and screw character in the same material.
**Counts as an answer if.** A core radius with uncertainty and either a nonzero compliance ratio or an upper bound below the elastic prediction, stated per dislocation character.
**Why it matters.** Core parameters set the Peierls stress, and hence dislocation mobility and the strength of every metal; they currently enter crystal-plasticity models as tuned constants.
### D021 — Is there a minimum length for a crack to propagate?
**Question.** Below some crack length, does a crack stop propagating even when the stress intensity exceeds the bulk fracture toughness?
**Why unresolved.** Concept blocker: linear elastic fracture mechanics has no length scale — toughness is defined for a crack in a continuum, while the process zone is a few nanometres — and what replaces the stress intensity when the crack is comparable to the process zone is undefined. Instrument blocker: fracture tests at one to ten nanometres require loading inside an electron microscope, and the specimens, edge conditions and methods used so far differ enough that the reported toughness spans a wide range.
**Decisive measurement.** Pre-notched specimens of one material — a suspended graphene membrane, or single-crystal silicon — with notch lengths from a micrometre down to a few nanometres, loaded in situ in a transmission electron microscope with load and crack length recorded simultaneously.
**Counts as an answer if.** Critical stress intensity against notch length, with uncertainties, showing either a plateau above some length and a fall below it, with the crossover length, or no detectable dependence down to the smallest notch.
**Why it matters.** It sets the smallest flaw that matters in nanomechanical devices, and whether bulk toughness may be used to design them.
### D022 — Is a metal's electron temperature defined a hundred femtoseconds after excitation?
**Question.** At a hundred femtoseconds after an optical pulse, does the conduction-electron distribution in a metal have a Fermi–Dirac form with a single temperature?
**Why unresolved.** Concept blocker: the two-temperature model assumes electron–electron scattering establishes a temperature faster than electron–phonon transfer, but electron–electron scattering weakens as the electron gas cools, so at low fluence thermalisation can be slower than phonon emission and the model's central quantity would not exist. Instrument blocker: nearly all ultrafast data are fitted with that model and reported as an electron-temperature history, while the distribution itself has rarely been measured where the assumption is weakest.
**Decisive measurement.** Time- and angle-resolved photoemission with tens-of-femtoseconds time and tens-of-millielectronvolts energy resolution on a single-crystal gold film, over a fluence range spanning two decades, fitting a Fermi–Dirac function at each delay and recording the residuals.
**Counts as an answer if.** A threshold fluence with uncertainty above which the fit residuals exceed experimental resolution, or a Fermi–Dirac form at every fluence and delay probed.
**Why it matters.** Ultrafast thermometry, laser-machining thresholds and the interpretation of every pump–probe experiment on a metal rest on that temperature being defined.
### D023 — Does conductivity equal the value from measured phonon lifetimes?
**Question.** For a simple crystal, does the measured thermal conductivity equal the value computed from its independently measured phonon lifetimes, velocities and heat capacity?
**Why unresolved.** Instrument blocker: phonon lifetimes come from inelastic X-ray or neutron linewidths on a small crystal, conductivity from a macroscopic specimen, and the two are measured at different temperatures on different samples; at room temperature the instrumental resolution is a large fraction of the linewidth. Concept blocker: combining mode-resolved lifetimes with the measured spectral heat capacity requires a choice about normal versus umklapp processes and about which modes carry heat, and that choice is where the prediction can fail.
**Decisive measurement.** Inelastic X-ray scattering on a high-quality single crystal at the temperatures of interest, with the resolution function measured on a reference scatterer, giving mode-resolved lifetimes; heat capacity from the same spectrum; and conductivity measured on a specimen cut from the same boule.
**Counts as an answer if.** The computed conductivity reproduces the measured one within its uncertainty, or the deficit identifies a named missing channel — boundary, isotope, or a mode whose lifetime was not measured.
**Why it matters.** Phonon lifetimes are the input to every nanoscale thermal-management calculation, and they are currently taken from simulation rather than measured on the material being designed.
### D024 — Does interfacial heat flow equal the measured phonon transmission?
**Question.** Is the thermal boundary conductance of a solid–solid interface equal to the value computed from the phonon transmission measured across that same interface?
**Why unresolved.** Instrument blocker: boundary conductance is measured by time-domain or frequency-domain thermoreflectance on a buried interface, while phonon transmission is inferred from atomistic simulation or from surface-sensitive electron or helium scattering, not from a buried interface. Assumption blocker: the diffuse-mismatch and acoustic-mismatch models bracket the data, so agreement with either is not a measurement of transmission.
**Decisive measurement.** A metal–dielectric interface whose conductance is measured by thermoreflectance, grown on a membrane thin enough that grazing-incidence inelastic X-ray or neutron scattering can measure the phonon transmission across the same interface, with both measurements on one specimen.
**Counts as an answer if.** The measured conductance equals the value from the measured transmission within error, or it exceeds it by a factor that requires an electronic or inelastic channel to be named.
**Why it matters.** Interfacial heat flow limits every nanoscale device and every thermoelectric, and the model there is the least constrained of any in heat transport.
### D025 — Is the electron energy distribution in a cold plasma Maxwellian?
**Question.** In an atmospheric-pressure cold plasma, does the electron energy distribution have a single temperature, or a non-Maxwellian tail?
**Why unresolved.** Concept blocker: almost all plasma diagnostics use optical emission and invert it through a model that assumes a Maxwellian or two-temperature distribution, so the distribution is an input rather than an output, and every rate coefficient is an average over a distribution nobody has measured for that plasma. Instrument blocker: Thomson scattering measures the distribution directly, but the signal from a weakly ionised gas at one atmosphere is small and has been obtained in only a few well-equipped experiments.
**Decisive measurement.** Thomson scattering with a narrow-linewidth laser and volume-filtered collection on a dielectric-barrier discharge at one atmosphere, at several positions and phases, extracting the distribution function and comparing it with the electron temperature derived from emission on the same discharge.
**Counts as an answer if.** A measured distribution function with uncertainty, together with a statement of whether it is Maxwellian and any deviation quantified as a tail-to-bulk temperature ratio.
**Why it matters.** Plasma medicine, surface treatment and ozone generation are modelled with rate coefficients computed from an assumed distribution; a non-Maxwellian tail changes those rates by orders of magnitude.