# Volume X — installment 1, theories 31-60 (new file)
THEORIES = [
{"n":31,"slug":"grasp-friction-curvature","field":"Robotics & Autonomy","title":"Grasp Is a Friction Ratio","claim":"Grasp success is set by the ratio of available friction to object curvature rather than by grip force alone, so a curved smooth object can slip despite high force.","mechanism":"Contact area falls with curvature, so the friction cone narrows; the ratio of friction to curvature sets whether a stable grasp exists at any force.","predictions":["Success should collapse at a curvature threshold.","Increasing force should not rescue low-friction curved objects."],"refute":"Success tracking grip force would remove the ratio."},
{"n":32,"slug":"slam-loop-closure-density","field":"Robotics & Autonomy","title":"SLAM Drift Is Closure Density","claim":"Localisation drift is set by the density of loop closures rather than by sensor quality, so a good sensor without closures drifts more than a poor one with them.","mechanism":"Drift accumulates between closures; closures bound it. The spacing sets the worst-case error regardless of per-step noise.","predictions":["Drift should scale with closure spacing.","Improved sensors should not fix sparse closures."],"refute":"Drift tracking sensor quality would remove the closure term."},
{"n":33,"slug":"capture-point-margin","field":"Robotics & Autonomy","title":"Balance Is a Margin","claim":"Humanoid balance recovery is set by the capture point margin rather than by the centre of mass position, so a robot inside its support polygon can still fall.","mechanism":"The capture point includes velocity, so a moving robot's stabilisable region differs from its static footprint.","predictions":["Falls should occur inside the support polygon.","Margin should predict recovery success."],"refute":"Falls tracking centre of mass position would restore the static criterion."},
{"n":34,"slug":"swarm-communication-density","field":"Robotics & Autonomy","title":"Swarms Need Density","claim":"Swarm coordination emerges only above a threshold in communication neighbour density, below which the group fragments into independent agents.","mechanism":"Flocking requires each agent to have enough neighbours to estimate the local order; below the threshold, estimates are too noisy to sustain alignment.","predictions":["Coordination should appear at a density threshold.","Adding range without density should not help."],"refute":"Coordination scaling smoothly with range would remove the threshold."},
{"n":35,"slug":"transfer-embodiment-similarity","field":"Robotics & Autonomy","title":"Transfer Follows Embodiment","claim":"Manipulation policies transfer between robots only when the ratio of task-relevant to embodiment-specific degrees of freedom exceeds a threshold.","mechanism":"A policy learned with embodiment-specific cues must relearn them on a new body; the more of the policy that is task-general, the better transfer.","predictions":["Transfer should track the ratio.","Policies dominated by body-specific cues should fail."],"refute":"Transfer independent of the ratio would favour generic pretraining."},
{"n":36,"slug":"drone-endurance-disc-loading","field":"Robotics & Autonomy","title":"Endurance Is Disc Loading","claim":"Multirotor endurance is set by the ratio of payload to disc loading rather than by battery capacity, so a larger rotor can outlast a larger battery.","mechanism":"Hover power scales with disc loading; adding battery mass raises loading, so capacity gains are partly self-defeating.","predictions":["Endurance should peak at a loading ratio.","Bigger batteries should reduce endurance past a point."],"refute":"Endurance tracking capacity monotonically would remove the loading term."},
{"n":37,"slug":"teleoperation-latency-tolerance","field":"Robotics & Autonomy","title":"Latency Tolerance Is Task Error","claim":"Tolerable teleoperation latency is set by the task's error tolerance rather than by the operator's skill, so the same link supports coarse and blocks fine work.","mechanism":"Latency converts into positional error proportional to speed; the task's tolerance sets when that error exceeds acceptable.","predictions":["Tolerance should scale with task tolerance.","Skilled operators should not exceed the limit."],"refute":"Tolerance tracking operator skill would remove the task dependence."},
{"n":38,"slug":"soft-actuator-pressure-stiffness","field":"Robotics & Autonomy","title":"Soft Actuators Are a Pressure Ratio","claim":"Soft actuator stroke is set by the ratio of chamber pressure to wall stiffness rather than by pressure alone, so a stiffer body can deliver less motion at higher pressure.","mechanism":"Inflation competes with wall deformation; the ratio sets how much energy goes into bending versus stretching.","predictions":["Stroke should collapse onto the ratio.","Stiffer walls should reduce stroke at fixed pressure."],"refute":"Stroke tracking pressure at fixed stiffness would remove the ratio."},
{"n":39,"slug":"stride-frequency-optimum","field":"Robotics & Autonomy","title":"Gait Has a Frequency Optimum","claim":"Legged locomotion efficiency peaks at a stride frequency set by the ratio of natural leg frequency to speed, not at the frequency that minimises cost of transport empirically.","mechanism":"At resonance, elastic energy recovery is maximal; deviating either way raises the cost of swinging and supporting.","predictions":["Efficiency should peak at the ratio.","Changing leg stiffness should shift the optimum."],"refute":"Efficiency peaking independently of natural frequency would remove the resonance account."},
{"n":40,"slug":"robot-safety-energy-mass","field":"Robotics & Autonomy","title":"Safety Is an Energy Ratio","claim":"Robot safety certification thresholds are set by the ratio of kinetic energy to impact area rather than by mass or speed alone.","mechanism":"Injury severity depends on pressure at impact, which is energy divided by contact area; two robots at the same speed differ by their end effector.","predictions":["Injury severity should track the ratio.","Lighter robots with small effectors should be riskier."],"refute":"Severity tracking mass would remove the area term."},
{"n":41,"slug":"buffer-bdp-ratio","field":"Networks & Telecommunications","title":"Buffers Follow Bandwidth-Delay","claim":"Network throughput collapses when buffer size falls below a critical fraction of the bandwidth-delay product, rather than degrading smoothly.","mechanism":"A buffer smaller than the product cannot hold a full window, so the sender stalls each round trip and utilisation falls.","predictions":["Throughput should collapse below a buffer fraction.","Enlarging the buffer should restore throughput abruptly."],"refute":"Smooth throughput decline with buffer would remove the threshold."},
{"n":42,"slug":"mmwave-blockage-density","field":"Networks & Telecommunications","title":"Millimetre Coverage Is Blockage","claim":"Millimetre-wave coverage is set by blockage density rather than by path loss, so a dense low-rise area can outperform an open area with few reflectors.","mechanism":"Coverage depends on the probability of a clear line of sight or a usable reflection; density sets both, in opposite directions.","predictions":["Coverage should track blockage density non-monotonically.","Open areas should underperform at intermediate density."],"refute":"Coverage tracking path loss alone would remove the blockage term."},
{"n":43,"slug":"fiber-route-circuity","field":"Networks & Telecommunications","title":"Latency Is Route Circuity","claim":"Network latency is set by the ratio of physical route length to great-circle distance rather than by nominal distance.","mechanism":"Propagation is fixed by glass length; routes that wander add latency that no protocol can remove.","predictions":["Latency should track circuity.","Direct routes should win regardless of nominal distance."],"refute":"Latency tracking nominal distance would remove the routing term."},
{"n":44,"slug":"spectrum-interference-correlation","field":"Networks & Telecommunications","title":"Spectrum Efficiency Is Correlation","claim":"Achievable spectral efficiency is set by the correlation of interference across antennas rather than by signal-to-noise ratio.","mechanism":"Correlated interference occupies a subspace and cannot be nulled; uncorrelated interference can be separated spatially.","predictions":["Efficiency should fall as interference correlation rises.","Adding antennas should not help beyond a point."],"refute":"Efficiency tracking SNR alone would remove the correlation term."},
{"n":45,"slug":"cdn-locality-ratio","field":"Networks & Telecommunications","title":"Caching Is a Locality Ratio","claim":"Content delivery cost is set by the ratio of cache size to demand locality rather than by cache capacity.","mechanism":"Hit rate depends on whether demand concentrates within the cache; a large cache facing diffuse demand behaves like a small one.","predictions":["Cost should track the ratio.","Larger caches should fail on diffuse demand."],"refute":"Cost tracking capacity would remove the locality term."},
{"n":46,"slug":"mesh-articulation-count","field":"Networks & Telecommunications","title":"Mesh Resilience Is Articulation","claim":"Mesh network resilience is set by the number of articulation points rather than by node count or redundancy.","mechanism":"An articulation point is a single node whose loss disconnects the graph; redundancy elsewhere does not compensate.","predictions":["Outage risk should track articulation count.","Adding redundant edges away from articulations should not help."],"refute":"Resilience tracking redundancy would remove the structural term."},
{"n":47,"slug":"constellation-elevation-distribution","field":"Networks & Telecommunications","title":"Constellation Capacity Is Elevation","claim":"Satellite constellation capacity is set by the distribution of elevation angles rather than by satellite count.","mechanism":"Low-elevation links suffer longer paths and more blockage; capacity depends on how much of the sky is seen at usable angles.","predictions":["Capacity should track the elevation distribution.","Adding satellites at low elevation should add little."],"refute":"Capacity tracking count would remove the geometry."},
{"n":48,"slug":"wifi-airtime-contention","field":"Networks & Telecommunications","title":"Wi-Fi Loss Is Airtime Share","claim":"Wi-Fi contention loss is set by the ratio of offered airtime to available airtime rather than by the number of stations.","mechanism":"Throughput depends on how much channel time each station can claim, so many idle stations cost little while few busy ones cost a lot.","predictions":["Loss should track airtime share.","Station count should predict poorly at low load."],"refute":"Loss tracking station count would remove the airtime term."},
{"n":49,"slug":"sync-error-chain-depth","field":"Networks & Telecommunications","title":"Clock Error Is Chain Depth","claim":"Time synchronisation error is set by the depth of the distribution chain rather than by the quality of the master clock.","mechanism":"Each hop adds asymmetry and jitter; the sum scales with depth even when each hop is good.","predictions":["Error should scale with depth.","A better master should not fix a deep chain."],"refute":"Error tracking master quality would remove the depth term."},
{"n":50,"slug":"reachability-exposure-ratio","field":"Networks & Telecommunications","title":"Exposure Is Reachability","claim":"Network exposure is set by the ratio of reachable to total hosts rather than by the number of hosts.","mechanism":"Only reachable hosts can be attacked; a large network with tight segmentation is smaller than its address space.","predictions":["Exposure should track the ratio.","Growing the network with segmentation should not raise exposure."],"refute":"Exposure tracking host count would remove the segmentation term."},
{"n":51,"slug":"disinfection-ct-repair","field":"Water & Sanitation","title":"Disinfection Beats Repair","claim":"Disinfection efficacy is set by the ratio of contact time-times-concentration to the organism's repair rate rather than by CT alone.","mechanism":"Organisms repair damage during and after exposure; efficacy depends on whether damage accumulates faster than repair.","predictions":["Efficacy should collapse at high repair rates.","CT should over-predict kill for repair-capable organisms."],"refute":"Efficacy tracking CT alone would remove the repair term."},
{"n":52,"slug":"membrane-critical-flux","field":"Water & Sanitation","title":"Fouling Begins Below Critical Flux","claim":"Membrane fouling is set by the ratio of operating flux to critical flux rather than by transmembrane pressure.","mechanism":"Below critical flux, deposition is reversible; above it, a cake forms that pressure cannot remove.","predictions":["Fouling should begin above the critical ratio.","Higher pressure should worsen fouling above it."],"refute":"Fouling tracking pressure would remove the flux threshold."},
{"n":53,"slug":"leakage-pressure-condition","field":"Water & Sanitation","title":"Leakage Is a Pressure Ratio","claim":"Distribution leakage is set by operating pressure relative to pipe condition rather than by pressure alone.","mechanism":"Leak area grows with pressure, but the area available depends on pipe condition; the ratio determines loss.","predictions":["Leakage should track the ratio.","The same pressure should leak differently by pipe condition."],"refute":"Leakage tracking pressure at controlled condition would remove the ratio."},
{"n":54,"slug":"coagulation-charge-threshold","field":"Water & Sanitation","title":"Coagulation Is a Charge Threshold","claim":"Optimal coagulant dose is set by the charge neutralisation point rather than by turbidity, so a clearer water can need more coagulant.","mechanism":"Colloids stabilise by surface charge; dose must reach neutralisation regardless of how many particles are present.","predictions":["Dose should track charge demand, not turbidity.","Clear high-charge water should need more coagulant."],"refute":"Dose tracking turbidity would remove the charge mechanism."},
{"n":55,"slug":"desalination-recovery-saturation","field":"Water & Sanitation","title":"Recovery Is a Saturation Ratio","claim":"Desalination energy is set by recovery ratio relative to saturation concentration rather than by salinity alone.","mechanism":"Energy rises steeply as concentrate approaches saturation because osmotic pressure diverges.","predictions":["Energy should track the ratio.","Higher salinity should require lower recovery for the same energy."],"refute":"Energy tracking salinity alone would remove the recovery term."},
{"n":56,"slug":"well-specific-capacity","field":"Water & Sanitation","title":"Well Decline Has a Knee","claim":"Well yield declines abruptly once specific capacity falls below a threshold, because turbulent losses overtake laminar flow.","mechanism":"Drawdown has a linear and a quadratic term; when the quadratic dominates, small increases in pumping produce large drawdown.","predictions":["Yield should collapse below a specific capacity.","Step testing should show the transition."],"refute":"Yield declining smoothly with drawdown would remove the threshold."},
{"n":57,"slug":"aeration-transfer-efficiency","field":"Water & Sanitation","title":"Aeration Is Transfer Efficiency","claim":"Wastewater aeration cost is set by oxygen transfer efficiency relative to demand rather than by blower power.","mechanism":"Power that does not transfer oxygen is wasted; the ratio sets energy per unit of biological demand.","predictions":["Cost should track the ratio.","More power at low efficiency should raise cost."],"refute":"Cost tracking power would remove the transfer term."},
{"n":58,"slug":"lead-scale-solubility","field":"Water & Sanitation","title":"Lead Release Is a Solubility Edge","claim":"Lead release is set by whether the corrosion scale is on the soluble side of a stability boundary, not by lead concentration in the source water.","mechanism":"Scale stability depends on pH and alkalinity; crossing the boundary dissolves the passivating layer and releases accumulated lead.","predictions":["Release should jump at a boundary crossing.","Source lead concentration should not predict release."],"refute":"Release tracking source concentration would remove the scale mechanism."},
{"n":59,"slug":"rainwater-storage-demand","field":"Water & Sanitation","title":"Harvesting Is a Storage Ratio","claim":"Rainwater harvesting yield is set by storage capacity relative to demand rather than by roof area.","mechanism":"Yield depends on capturing events between draws; too little storage spills, and roof area only sets the upper bound.","predictions":["Yield should track the storage ratio.","Enlarging roofs without storage should add little."],"refute":"Yield tracking roof area would remove the storage term."},
{"n":60,"slug":"sanitation-convenience-cost","field":"Water & Sanitation","title":"Sanitation Adoption Is a Ratio","claim":"Sanitation adoption is set by the ratio of convenience to cost rather than by health messaging.","mechanism":"Households adopt what is easier than the alternative; messaging changes beliefs, not the daily cost of use.","predictions":["Adoption should track the ratio.","Health campaigns alone should underperform convenience improvements."],"refute":"Adoption tracking messaging would favour the information model."},
]