Incoprea Research

Original Theories Volume XXIV · science index

189 retained entries from the original 219. Original entry numbers are preserved. These are working hypotheses, not findings or proofs.

Volcanic arcs

• Theory 39 · Arc Position Is Depth Against Wedge Flow
  The position of an arc is set by the ratio of slab depth to mantle wedge flow rate, so faster wedge flow shifts volcanism away from the trench.
• Theory 38 · Arcs Need a Wet Slab
  Arc volcanism begins only above a threshold in slab water content and dip, so a dry shallow slab produces no arc.
• Theory 37 · Arcs Erupt at Dehydration Rate
  Arc volcanism rate is set by the rate at which the subducting slab releases water rather than by convergence rate.

Asphalt rutting

• Theory 144 · Stability Is Binder Against Aggregate
  Pavement stability is set by the ratio of binder film thickness to aggregate interlock, so too much binder lubricates the skeleton.
• Theory 142 · Rutting Follows Accumulation
  Rut depth is set by the rate at which permanent deformation accumulates per load cycle rather than by total traffic.
• Theory 143 · Rutting Needs a Softening Threshold
  Rutting accelerates above a threshold in pavement temperature, so a small rise in climate produces a large rise in damage.

Balance

• Theory 68 · Motion Sickness Needs Conflict
  Motion sickness occurs above a threshold in the ratio of vestibular to visual motion signals, so passive motion in a still visual field is the worst case.
• Theory 67 · Balance Follows Angular Rate
  The sense of rotation is set by the rate of angular displacement rather than by its extent, so a slow full turn feels like no motion.
• Theory 69 · Sway Is Noise Against Stiffness
  Postural sway amplitude is set by the ratio of sensory noise to ankle stiffness, so a person with noisy proprioception sways more at the same strength.

Beer foam

• Theory 135 · Bitterness Is Iso-Alpha Against Sugar
  Perceived bitterness is set by the ratio of iso-alpha acids to residual sugar, so the same IBU tastes different across styles.
• Theory 133 · Foam Forms at Pour Rate
  Foam volume is set by the rate of gas release during pouring rather than by carbonation level.
• Theory 134 · Stability Needs Protein
  Foam persists only above a threshold in the ratio of hydrophobic protein to lipid, so trace fat destroys foam that protein would hold.

Blushing

• Theory 57 · Intensity Is Inflow Against Return
  Blush intensity is set by the ratio of arterial inflow to venous return, so a blush fades when venous drainage improves rather than when inflow stops.
• Theory 55 · Blush Onset Is Sympathetic
  Blush onset speed is set by the rate of sympathetic outflow rather than by the intensity of the emotion.
• Theory 56 · Visibility Is a Skin Ratio
  A blush becomes visible above a threshold in the ratio of vasodilation to skin thickness, so the same response is obvious in one person and invisible in another.

Bread staling

• Theory 111 · Crust Softening Is Humidity
  Crust softness is set by the ratio of internal moisture migration to ambient humidity, so bread in dry air loses crust crispness while sealed bread loses crumb softness.
• Theory 109 · Staling Follows Retrogradation
  Bread staling rate is set by the rate of starch retrogradation rather than by moisture loss, so bread kept sealed still stales.
• Theory 110 · Staling Peaks Near Freezing
  Staling is fastest above a threshold just above freezing, because retrogradation is maximised where mobility is low but not arrested.

Bridges

• Theory 213 · Bearing Life Is Load Against Capacity
  Bearing life is set by the ratio of applied load to rated capacity raised to a power, so modest overloads consume life disproportionately.
• Theory 212 · Damage Needs a Seizure Threshold
  Structural damage occurs above a threshold in the ratio of restrained movement to joint tolerance, so a seized joint transfers force into the deck.
• Theory 211 · Joint Movement Follows Thermal Rate
  Expansion joint movement is set by the rate of temperature change rather than by the temperature range, so a fast cold snap drives joints harder than a slow cold winter.

Cheese ripening

• Theory 114 · Rind Is Drying Against Sealing
  Rind formation is set by the ratio of surface drying to interior moisture supply, so a humid cave produces a thin rind and a dry one a thick.
• Theory 112 · Ripening Follows Enzyme Rate
  Cheese ripening rate is set by the rate of proteolysis rather than by age, so two cheeses of the same age differ in maturity.
• Theory 113 · Ripening Stops on Salt
  Ripening ceases above a threshold in salt-to-moisture ratio, so a heavily salted cheese arrests rather than matures.

Chocolate tempering

• Theory 123 · Snap Is Fat Against Sugar
  The snap of chocolate is set by the ratio of fat crystal network to sugar particle packing, so the same recipe snaps differently with different conching.
• Theory 122 · Tempering Needs Seed Crystals
  Tempering succeeds only above a threshold in the ratio of seed crystals to melt volume, so insufficient seeding produces unstable crystal forms.
• Theory 121 · Tempering Follows Cooling Rate
  Correct temper is set by the rate of cooling through the crystallisation range rather than by the final temperature.

Coffee extraction

• Theory 116 · Channeling Needs a Pressure Threshold
  Channeling begins above a threshold in the ratio of pump pressure to bed permeability, so the same grind channels in one basket and not another.
• Theory 115 · Extraction Follows Flow
  Coffee extraction rate is set by the flow rate through the bed rather than by contact time, so a fast shot can extract more than a slow one.
• Theory 117 · Strength Is Solubles Against Water
  Brew strength is set by the ratio of solubles extracted to water retained, so under-extracted coffee can taste strong if little water is left.

Concrete curing

• Theory 141 · Creep Is Load Against Age
  Creep strain is set by the ratio of sustained load to age at loading, so concrete loaded young creeps far more than the same concrete loaded late.
• Theory 139 · Strength Follows Hydration Rate
  Concrete strength gain is set by the rate of cement hydration rather than by curing time, so warm concrete matures in days and cold concrete in months.
• Theory 140 · Porosity Needs a Water Threshold
  Concrete becomes permeable above a threshold in the ratio of water to cement, so a small excess water produces a large loss of durability.

Steel corrosion

• Theory 153 · Damage Is Anode Against Cathode
  Corrosion penetration is set by the ratio of anodic to cathodic area, so a small anode coupled to a large cathode corrodes very fast.
• Theory 152 · Pitting Needs a Chloride Threshold
  Pitting corrosion begins above a threshold in the ratio of chloride to alkalinity at the steel surface, so a well-passivated steel tolerates more chloride.
• Theory 151 · Corrosion Follows Oxygen Supply
  Atmospheric corrosion rate of steel is set by the rate at which oxygen reaches the surface rather than by humidity alone.

Déjà vu

• Theory 82 · Déjà Vu Is a Timing Mismatch
  Déjà vu occurs when the familiarity signal arrives faster than the recollection signal, so the mismatch is a rate difference rather than a memory error.
• Theory 84 · Frequency Is Fatigue Against Arousal
  Déjà vu frequency is set by the ratio of fatigue to arousal, peaking where the two combine rather than at either extreme.
• Theory 83 · It Needs a Novelty Threshold
  Déjà vu requires a threshold in scene novelty, appearing where the environment is familiar enough to match but novel enough to require checking.

River deltas

• Theory 26 · Avulsion Follows a Slope Ratio
  Delta avulsion occurs above a threshold in the ratio of channel slope to floodplain slope, so a channel slightly steeper than its surroundings eventually switches.
• Theory 27 · Delta Shape Is a Force Ratio
  Delta shape is set by the ratio of fluvial to marine energy, so the same sediment load builds a birdfoot, a fan or a cusp depending on wave and tide strength.
• Theory 25 · Deltas Grow at Supply Rate
  Delta progradation rate is set by the rate of sediment supply relative to accommodation creation, not by total supply.

Deep scattering layer

• Theory 15 · Amplitude Is Food Against Risk
  Migration amplitude is set by the ratio of surface food to predation risk, so populations in risky water migrate less despite abundant food.
• Theory 13 · Migration Tracks Light Change
  The speed of diel vertical migration is set by the rate of change of light at depth rather than by absolute light level.
• Theory 14 · Layers Form on Predator Density
  A coherent scattering layer forms above a threshold in predator density, so sparse populations disperse rather than aggregate.

Dust storms

• Theory 04 · Dust Follows Crust Breakdown
  Dust emission rate is set by the rate at which surface crust is disrupted, not by wind speed alone, so a high-wind day on intact crust emits little.
• Theory 06 · Load Is Emitted Against Settled
  Atmospheric dust load is set by the ratio of emission to deposition rate, so a long-lived plume requires weak deposition as much as strong emission.
• Theory 05 · Storms Ignite on a Shear Threshold
  Dust storms ignite above a threshold in the ratio of wind shear to crust strength, so the same wind produces a storm on one surface and nothing on another.

Ocean eddies

• Theory 07 · Eddies Grow at Instability Rate
  Eddy kinetic energy is set by the rate of baroclinic instability growth rather than by the available potential energy.
• Theory 09 · Eddy Size Is a Rossby Ratio
  Eddy diameter is set by the ratio of the Rossby radius to the beta effect, so high-latitude eddies are smaller than tropical ones at the same stratification.
• Theory 08 · Eddies Need Shear Anisotropy
  Eddy formation requires a threshold in the ratio of horizontal to vertical shear, so strong shear in the wrong direction suppresses eddies.

Elevator scheduling

• Theory 196 · Waiting Follows Arrival Rate
  Average elevator wait is set by the rate of passenger arrivals relative to car capacity rather than by building height.
• Theory 197 · Bunching Needs a Demand Threshold
  Elevator bunching occurs above a threshold in demand, where cars cluster and service degrades abruptly.
• Theory 198 · Capacity Is Round Trip Against Interval
  System capacity is set by the ratio of round-trip time to the target interval, so a faster car does not increase capacity if the interval is fixed.

Emergency response

• Theory 207 · Coverage Is Travel Against Demand
  Effective coverage is set by the ratio of travel time to incident density, so dense areas need more stations for the same response time.
• Theory 205 · Response Follows Dispatch Rate
  Response time is set by the rate at which units are dispatched and cleared rather than by the number of units.
• Theory 206 · Collapse Needs a Surge Threshold
  Response capability collapses above a threshold in the ratio of incidents to capacity, because queues compound.

Glass tempering

• Theory 147 · Strength Is Flaw Against Stress
  Glass strength is set by the ratio of flaw size to applied stress, so a single deep scratch negates any tempering.
• Theory 145 · Tempering Follows Cooling Rate
  Residual stress in tempered glass is set by the cooling rate through the transition range, so faster quenching produces stronger glass.
• Theory 146 · Tempering Needs a Thickness Floor
  Tempering fails below a threshold in thickness, because the temperature gradient cannot develop across a thin sheet.

Glacial lake outbursts

• Theory 29 · Breach Needs a Freeboard Threshold
  Outburst occurs above a threshold in the ratio of lake depth to dam freeboard, so a deep lake behind a high dam can be safe while a shallow one behind a low dam fails.
• Theory 28 · Outburst Timing Is Growth Against Strength
  The timing of a glacial lake outburst is set by the rate of lake growth relative to moraine strength, not by lake size.
• Theory 30 · Peak Flow Is Volume Against Breach
  Peak discharge is set by the ratio of lake volume to breach width, so a large lake draining through a narrow breach produces a sharper flood than a small lake through a wide one.

Goosebumps

• Theory 59 · Reflex Needs a Cold Threshold
  Piloerection occurs above a threshold in the ratio of cold exposure to insulation, so a well-clothed person does not respond at the same temperature.
• Theory 58 · Piloerection Tracks Cooling Rate
  Goosebumps appear at the rate of skin cooling rather than at a fixed temperature, so a fast draft triggers them where slow cooling does not.
• Theory 60 · Bump Density Is Follicles per Area
  Goosebump prominence is set by the ratio of follicle density to skin area, so the same contraction is coarser on the forearm than on the neck.

Habit formation

• Theory 92 · Automaticity Needs a Cue Threshold
  A behaviour becomes automatic only above a threshold in cue consistency, so the same number of repetitions in varied contexts produces no habit.
• Theory 91 · Habits Form at a Rate
  Habit strength grows with the rate of repetition in a stable context rather than with the total number of repetitions, so massed practice forms weak habits.
• Theory 93 · Persistence Is Reward Against Effort
  Habit persistence is set by the ratio of reward to effort, so a habit with high effort persists only while the reward is high.

Hibernation

• Theory 49 · Arousals Track Metabolic Debt
  The frequency of hibernation arousals is set by the rate at which metabolic debt accumulates, not by body temperature.
• Theory 50 · Entry Needs a Fat Threshold
  Hibernation entry requires a threshold in the ratio of fat reserves to body mass, so an animal below it must stay active and risk winter.
• Theory 51 · Body Temperature Is a Balance
  Hibernating body temperature is set by the ratio of heat loss to metabolic suppression, so a well-insulated hibernaculum permits deeper torpor.

Hiccups

• Theory 77 · Hiccups Stop on CO2
  Hiccups cease above a threshold in arterial CO2, which is why breath-holding terminates them.
• Theory 76 · Hiccup Rate Is Reflex Cycling
  Hiccup frequency is set by the rate of the vagal reflex cycle rather than by diaphragm irritability.
• Theory 78 · Susceptibility Is a Volume Ratio
  Hiccup susceptibility is set by the ratio of stomach volume to lung capacity, which is why they follow large meals and carbonated drinks.

Honey crystallisation

• Theory 124 · Crystallisation Follows Nucleation
  Honey crystallisation rate is set by the rate of nucleation on particles rather than by sugar concentration.
• Theory 126 · Granulation Is a Sugar Ratio
  Granulation tendency is set by the ratio of glucose to fructose, so honeys of equal total sugar differ in how fast they set.
• Theory 125 · Stability Needs a Moisture Threshold
  Honey resists fermentation only below a threshold in water content, so a small rise turns a stable product into a fermenting one.

Housing markets

• Theory 174 · Rents Track Vacancy
  Rent growth is set by the ratio of demand to vacant stock, so a small vacancy buffer stabilises rents out of proportion to its size.

Inflation

• Theory 171 · Pressure Is Demand Against Capacity
  Inflationary pressure is set by the ratio of demand to productive capacity, so the same demand is inflationary in a constrained economy and not in an elastic one.
• Theory 169 · Inflation Follows Expectation Revision
  Inflation rate is set by the rate at which expectations are revised rather than by the size of the shock.

Insurance cycles

• Theory 177 · Premium Is Risk Against Capital
  Premium adequacy is set by the ratio of expected loss to capital held, so the same risk supports a different premium in differently capitalised insurers.

Itching

• Theory 63 · Alloknesis Is Sensitisation
  Whether a light touch becomes itchy is set by the ratio of central sensitisation to peripheral input, so the same touch is neutral in one state and unbearable in another.
• Theory 61 · Itch Follows Firing Rate
  Itch intensity is set by the firing rate of a dedicated population of pruriceptors, not by the number recruited, so a small persistent signal itches more than a large brief one.
• Theory 62 · Scratching Needs a Gain Threshold
  Scratching is triggered above a threshold in the ratio of itch signal to inhibitory tone, so a strong descending inhibition can suppress the reflex entirely.

King tides

• Theory 23 · Nuisance Flooding Is a Drainage Ratio
  Nuisance flooding begins above a threshold in the ratio of high tide to drainage capacity, so a city with better outfalls floods later at the same sea level.
• Theory 24 · Flood Duration Is Range Against Outfall
  Flood duration is set by the ratio of tidal range to outfall capacity, so a large-range coast drains slowly even with good infrastructure.
• Theory 22 · Flooding Follows Sea-Level Rate
  King tide flooding frequency is set by the rate of sea-level rise relative to the perigean cycle rather than by the absolute level.

Laughter

• Theory 106 · Laughter Follows Surprise Rate
  Laughter is elicited by the rate at which a situation is reframed rather than by the content of the joke, so pacing determines whether it lands.
• Theory 108 · Relief Is Tension Against Resolution
  The relief in laughter is set by the ratio of tension built to resolution offered, so a long build with a weak punchline produces discomfort rather than amusement.

Lubricants

• Theory 160 · Film Forms at Entrainment Rate
  Lubricating film thickness is set by the rate at which surfaces entrain oil into the contact rather than by oil viscosity alone.
• Theory 161 · Separation Needs a Speed Threshold
  Full film separation requires a speed above a threshold, below which asperity contact and wear occur.
• Theory 162 · Regime Is Viscosity Against Load
  The lubrication regime is set by the ratio of viscous film thickness to surface roughness, so the same oil protects a smooth surface and fails on a rough one.

Marine snow

• Theory 10 · Flux Follows Aggregation
  Marine snow flux is set by the aggregation rate of particles rather than by surface production, so a productive but dispersed bloom exports little.
• Theory 12 · Export Efficiency Is Sink Against Decay
  Export efficiency is set by the ratio of sinking velocity to remineralisation rate, so the same production exports differently in warm and cold water.
• Theory 11 · Export Needs Large Aggregates
  Carbon export occurs above a threshold in aggregate size, because small particles sink too slowly to escape remineralisation.

Meat tenderising

• Theory 131 · Collagen Melts on a Threshold
  Tough cuts become tender only above a threshold in the ratio of time to temperature, so fast high heat leaves collagen intact.
• Theory 132 · Juiciness Is Water Against Fat
  Perceived juiciness is set by the ratio of retained water to fat content, so a lean cut needs more water retention to match a fatty one.
• Theory 130 · Tenderness Follows Proteolysis
  Meat tenderisation rate is set by the rate of proteolysis of myofibrils rather than by temperature alone.

Monsoons

• Theory 03 · Strength Is an Evaporation Split
  Monsoon strength is set by the ratio of oceanic to terrestrial evaporation rather than by total evaporation.
• Theory 01 · Onset Is a Rate, Not a Peak
  Monsoon onset is set by the rate at which the land-sea thermal contrast develops rather than by its eventual peak.
• Theory 02 · Monsoons Fail on Recycling
  Monsoon collapse occurs below a threshold in soil-moisture recycling, so rainfall fails abruptly rather than declining with the large-scale flow.

Power outages

• Theory 209 · Cascades Need a Margin Threshold
  Cascading failure occurs only where reserve margin falls below a threshold, so a well-margined grid absorbs the same fault.
• Theory 208 · Outages Propagate at a Rate
  The size of a blackout is set by the rate of cascade propagation relative to operator intervention, not by the initial fault.
• Theory 210 · Restoration Is Damage Against Crews
  Restoration time is set by the ratio of damage to crew capacity, so a large event with adequate crews can be faster than a small one without.

Pain

• Theory 74 · Chronic Pain Is a Threshold Shift
  The transition to chronic pain occurs when central sensitisation lowers the threshold below normal input levels, so pain persists without ongoing injury.
• Theory 75 · Pain Is Excitation Against Inhibition
  Perceived pain is set by the ratio of ascending excitation to descending inhibition, so the same injury is felt differently depending on context.
• Theory 73 · Pain Follows Stimulus Rate
  Pain intensity is set by the rate at which nociceptors fire, with slow repeated stimulation producing more pain than a single larger one.

Paper ageing

• Theory 157 · Paper Ages by Hydrolysis
  Paper embrittlement rate is set by the rate of acid hydrolysis of cellulose rather than by age.
• Theory 158 · Yellowing Needs a Lignin Threshold
  Yellowing occurs above a threshold in lignin content, so papers below it age by a different route entirely.
• Theory 159 · Lifetime Is Moisture Against Temperature
  Paper lifetime is set by the ratio of moisture to temperature, so a cool humid store can be worse than a warm dry one.

Patents

• Theory 189 · Value Is Breadth Against Depth
  Patent value is set by the ratio of claim breadth to technical depth, so broad claims on shallow work are worth less than narrow claims on deep work.
• Theory 187 · Filing Follows R&D Rate
  Patent filing rate is set by the rate of R&D spending rather than by its cumulative level, so a sustained programme files more than a large one-off.
• Theory 188 · Grants Need a Novelty Threshold
  A patent is granted only above a threshold in the ratio of inventive step to prior art density, so crowded fields require larger steps.

Peer review

• Theory 218 · Decisions Need an Agreement Threshold
  A decision is reliable only above a threshold in inter-reviewer agreement, below which the outcome is largely noise.
• Theory 217 · Quality Follows Review Rate
  Review accuracy is set by the rate at which reviewers can evaluate submissions rather than by reviewer expertise.
• Theory 219 · Value Is Signal Against Noise
  The predictive value of review is set by the ratio of true quality signal to reviewer noise, so adding reviewers helps only while noise is independent.

Pickling

• Theory 136 · Preservation Follows Acidification Rate
  Pickle safety is set by the rate at which pH falls rather than by the final pH, so a slow acidification can spoil before it preserves.
• Theory 138 · Crispness Is Calcium Against Acid
  Pickle crispness is set by the ratio of calcium to acid, so a strong brine softens the tissue unless calcium is raised.
• Theory 137 · Fermentation Needs a Salt Window
  Lactic fermentation proceeds only within a salt window, so both too little and too much salt produce spoilage by different routes.

Queueing

• Theory 101 · Abandonment Needs a Patience Threshold
  Queue abandonment occurs above a threshold in the ratio of expected wait to patience, so the same wait is tolerated in one context and not another.
• Theory 100 · Waiting Follows Arrival Rate
  Perceived wait time is set by the rate at which the queue advances rather than by the number ahead, so a long fast queue feels shorter than a short slow one.
• Theory 102 · Queue Length Is Load Against Service
  Average queue length is set by the ratio of arrival rate to service rate, and it diverges as the ratio approaches one.

Rice cooking

• Theory 129 · Texture Is Amylose Against Water
  Cooked rice texture is set by the ratio of amylose to absorbed water, so the same variety can be fluffy or sticky depending on the ratio.
• Theory 127 · Cooking Follows Hydration Rate
  Rice cooking time is set by the rate at which water penetrates the grain rather than by the total water absorbed.
• Theory 128 · Gelatinisation Needs a Temperature
  Starch gelatinisation begins above a threshold temperature that depends on amylose content, so two rices cook differently at the same heat.

Rubber elasticity

• Theory 148 · Elasticity Follows Crosslink Rate
  Rubber modulus is set by the rate of crosslink formation during vulcanisation rather than by cure time.
• Theory 149 · Elasticity Needs a Network Threshold
  Rubber behaves elastically only above a threshold in crosslink density, below which it flows.
• Theory 150 · Toughness Is Filler Against Network
  Rubber toughness is set by the ratio of filler to crosslink density, so adding carbon black to an over-cured rubber makes it brittle.

Salt flats

• Theory 36 · Crust Thickness Balances Supply and Loss
  Crust thickness is set by the ratio of groundwater salt supply to evaporation, so a shallow water table builds a thicker crust than a deep one.
• Theory 34 · Crust Grows at Evaporation Rate
  Salt crust growth rate is set by evaporation rate relative to inflow, not by brine concentration.
• Theory 35 · Pans Form on an Evaporation Threshold
  A salt pan forms only above a threshold in the ratio of evaporation to inflow, so a basin with modest inflow stays a lake.

Shivering

• Theory 65 · Shivering Stops on Fuel
  Shivering ceases below a threshold in muscle glycogen, so an animal can be dangerously cold yet not shivering.
• Theory 66 · Shivering Rate Is Loss Against Insulation
  Shivering intensity is set by the ratio of heat loss to insulation, so the same cold requires more shivering in wet clothing.
• Theory 64 · Shivering Follows Cooling Rate
  Shivering onset is set by the rate of core cooling rather than by core temperature, so rapid cooling triggers it before the body is cold.

Sinkholes

• Theory 40 · Collapse Timing Is Dissolution
  Sinkhole collapse timing is set by the rate of dissolution relative to soil cohesion, not by cavity size.
• Theory 42 · Size Is Dissolution Against Infill
  Sinkhole size is set by the ratio of dissolution to sediment infill, so a fast-dissolving but rapidly filling cavity stays small.
• Theory 41 · Roofs Fail on a Span Ratio
  Collapse occurs above a threshold in the ratio of cavity span to roof strength, so a wide shallow cavity fails before a narrow deep one.

Ceramic sintering

• Theory 154 · Densification Follows Diffusion
  Sintering rate is set by the rate of grain-boundary diffusion rather than by temperature alone.
• Theory 155 · Densification Needs a Grain Threshold
  Full densification requires grains to stay below a threshold size, because grain boundaries are the diffusion path.
• Theory 156 · Shrinkage Is Surface Against Bulk
  Shrinkage is set by the ratio of surface energy to bulk modulus, so finer powders shrink more for the same density gain.

Wildfire smoke

• Theory 21 · Optical Depth Is Emitted Against Dispersed
  Smoke optical depth over a region is set by the ratio of emission to dispersion, so a large fire in stagnant air and a small one in wind can look identical from orbit.
• Theory 19 · Plume Rise Follows Heat Release
  Smoke plume rise is set by the rate of heat release relative to ambient stability, not by total fuel consumed.
• Theory 20 · Injection Needs Buoyancy
  Stratospheric smoke injection requires a threshold in plume buoyancy, so most fires never reach it regardless of size.

Snowpack

• Theory 33 · Snow Water Is Accumulated Against Lost
  Peak snow water equivalent is set by the ratio of accumulation to sublimation, so a cold windy winter can leave less water than a milder calm one.
• Theory 31 · Melt Follows Energy, Not Air
  Snowmelt rate is set by the rate of net energy input rather than by air temperature, so a windy warm night can melt more than a still sunny day.
• Theory 32 · Runoff Needs Saturated Pores
  Meltwater runoff begins above a threshold in the ratio of meltwater to pore space, so early melt is absorbed and only later melt reaches streams.

Springs

• Theory 48 · Temperature Is Path Depth
  Spring temperature is set by the ratio of deep to shallow flow path, so a spring fed mostly by deep circulation is warmer in winter and cooler in summer.
• Theory 47 · Springs Stop on a Pumping Ratio
  Spring flow ceases below a threshold in the ratio of recharge to abstraction, so a modest well field can dry a large spring.
• Theory 46 · Discharge Follows Transmission
  Spring discharge is set by the rate at which recharge is transmitted through the aquifer rather than by total recharge.

Standards adoption

• Theory 190 · Standards Spread at Conversion Rate
  Standards adoption rate is set by the rate at which users convert rather than by the size of the installed base.
• Theory 192 · Lock-In Is Benefit Against Switching
  Lock-in persists while the ratio of switching cost to benefit exceeds one, so a small improvement cannot dislodge an entrenched standard.
• Theory 191 · Standards Tip on a Base Threshold
  A standard takes over above a threshold in the ratio of its installed base to the incumbent's, so a small lead can be decisive.

Taste

• Theory 70 · Taste Fades at Adaptation Rate
  The speed at which a taste disappears is set by the rate of receptor adaptation rather than by the concentration, so a strong taste can vanish while a weak one persists.
• Theory 71 · Detection Is a Genetic Threshold
  Whether a compound tastes bitter is set by a threshold in receptor sensitivity, so the same molecule is tasteless to one person and overwhelming to another.
• Theory 72 · Mixtures Are Suppression
  The taste of a mixture is set by the ratio of suppressing to suppressed components, so sweetness can be hidden by bitterness without either changing.

Terraces

• Theory 43 · Abandonment Follows Labour Cost
  Terrace abandonment rate is set by the rate of change in labour cost rather than by the absolute cost, so slow increases are absorbed and fast ones are not.
• Theory 44 · Walls Fail on a Storm Ratio
  Terrace wall failure occurs above a threshold in the ratio of rainfall intensity to drainage capacity, so a modest storm on a blocked drain does more than a large one on a clear drain.
• Theory 45 · Spacing Is Slope Against Wall
  Terrace spacing is set by the ratio of slope to wall height, so steeper slopes require closer terraces for the same retaining capacity.

Textile wear

• Theory 166 · Wear Follows Abrasion Cycles
  Textile failure is set by the rate of fibre loss per abrasion cycle rather than by total cycles.
• Theory 167 · Pilling Needs a Fibre Threshold
  Pilling occurs above a threshold in the ratio of loose fibre to anchorage, so a tight weave resists pilling despite weak fibres.
• Theory 168 · Strength Is Twist Against Density
  Yarn strength is set by the ratio of twist to linear density, so the same fibre is strong at one twist and weak at another.

Timber drying

• Theory 163 · Drying Follows Diffusion
  Timber drying rate is set by the rate of moisture diffusion through the wood rather than by surface evaporation.
• Theory 164 · Checking Needs a Gradient Threshold
  Surface checking occurs above a threshold in the moisture gradient, so too-fast drying damages timber that slow drying preserves.
• Theory 165 · Distortion Is Radial Against Tangential
  Distortion is set by the ratio of radial to tangential shrinkage, so species with a high ratio warp predictably.

Tip-of-the-tongue

• Theory 80 · Blocking Needs Partial Access
  A tip-of-the-tongue state requires a threshold of partial access, so a word with no features retrieved produces no feeling of knowing.
• Theory 81 · Resolution Is Target Against Interference
  Whether a word is eventually retrieved is set by the ratio of target activation to competitor interference, so similar-sounding words delay resolution.
• Theory 79 · Tip-of-Tongue Is Slow Retrieval
  The tip-of-the-tongue state occurs when retrieval rate falls below the rate at which the feeling of knowing fades, so slower retrievers experience it more.

Traffic jams

• Theory 194 · Breakdown Needs a Density Threshold
  Flow breaks down above a threshold in the ratio of density to capacity, so a small perturbation at high density produces a jam that the same perturbation would not at low density.
• Theory 195 · Delay Diverges Near Capacity
  Delay is set by the ratio of demand to capacity and diverges as the ratio approaches one.
• Theory 193 · Jams Move Backward at a Rate
  A traffic jam propagates upstream at a rate set by the density difference across the shock, not by the speed of the cars in it.

Coastal upwelling

• Theory 16 · Supply Is Divergence Rate
  Nutrient supply to the surface is set by the rate of Ekman transport divergence rather than by wind stress magnitude.
• Theory 17 · Blooms Need Supply Over Grazing
  Upwelling blooms occur above a threshold in the ratio of nutrient supply to grazing pressure, so a well-supplied system can stay green.
• Theory 18 · Intensity Is Wind Against Stratification
  Upwelling intensity is set by the ratio of alongshore wind to stratification, so a strongly stratified ocean resists upwelling that a well-mixed one permits.

Mind wandering

• Theory 86 · It Needs a Goal Threshold
  Mind wandering requires a threshold in goal commitment, so a weakly held goal permits more off-task thought at the same task demand.
• Theory 87 · Rate Is Load Against Capacity
  Mind wandering rate is set by the ratio of cognitive load to working memory capacity, so high capacity protects against wandering on the same task.
• Theory 85 · Wandering Follows Task Rate
  Mind wandering becomes frequent when the rate of task demand falls below the rate at which attention decays, so a slow task loses attention faster than a hard one.

Waste collection

• Theory 204 · Cost Is Logistics Against Volume
  Collection cost per tonne is set by the ratio of route distance to volume collected, so sparse areas cost more per tonne at the same service level.
• Theory 203 · Diversion Needs a Contamination Threshold
  Recycling diversion collapses above a threshold in contamination rate, because contaminated streams are rejected wholesale.
• Theory 202 · Collection Follows Generation Rate
  Required collection frequency is set by the rate of waste generation relative to storage capacity, not by population.

Water networks

• Theory 199 · Loss Grows at Leak Rate
  Network water loss is set by the rate at which new leaks appear rather than by the number of existing leaks.
• Theory 201 · Non-Revenue Water Is Loss Against Supply
  The fraction of non-revenue water is set by the ratio of leakage to total supply, so a network's apparent efficiency depends on how much it supplies.
• Theory 200 · Bursts Follow a Pressure Threshold
  Pipe bursts occur above a threshold in the ratio of operating pressure to pipe strength, so a modest pressure reduction produces a large fall in failures.

Wine ageing

• Theory 118 · Ageing Follows Oxygen Ingress
  Wine ageing rate is set by the rate of oxygen ingress through the closure rather than by time in bottle.
• Theory 119 · Reduction Needs an Oxygen Floor
  Reductive aromas appear below a threshold in oxygen ingress, so a very tight closure can damage a wine it protects.
• Theory 120 · Longevity Is Tannin Against Acid
  Ageing potential is set by the ratio of tannin to acid, so a wine needs both in proportion rather than either in quantity.

Yawning

• Theory 54 · Frequency Is Arousal Against Sleep
  Yawn frequency is set by the ratio of arousal to sleep pressure, peaking where the two are both moderate rather than at either extreme.
• Theory 52 · Yawn Length Follows Cooling
  Yawn duration is set by the rate at which brain temperature can be reduced, not by fatigue.
• Theory 53 · Contagion Needs Closeness
  Contagious yawning occurs above a threshold in social closeness, so the same yawn spreads among kin and not among strangers.

Index narrowed to the focused science collection. Biological and ecological population dynamics, genetics, physiology and engineering are retained. Source numbering remains historical; no remaining hypothesis has been promoted to a finding.