Incoprea Research

Original Theories Volume XVI · science index

92 retained entries from the original 99. Original entry numbers are preserved. These are working hypotheses, not findings or proofs.

Competing Rates

• Theory 32 · Planetesimals Balance Growth and Loss
  Whether a planetesimal grows into a planet is set by the ratio of accretion to collisional erosion in its feeding zone.
• Theory 23 · Aggregation Is Clearance Against Growth
  Whether a protein aggregates in vivo is set by the ratio of clearance rate to aggregation rate rather than by intrinsic aggregation propensity.
• Theory 24 · Catalyst Efficiency Is Diffusion Against Reaction
  The apparent activity of a porous catalyst is set by the ratio of diffusion rate to intrinsic reaction rate, so a faster intrinsic catalyst can appear slower.
• Theory 27 · Defect Density Balances Two Processes
  The equilibrium defect density in a growing crystal is set by the ratio of defect generation to annealing, so a slower growth can be more perfect than a faster one.
• Theory 25 · Coastlines Balance Two Rates
  Whether a coastline advances or retreats is set by the ratio of sediment supply to accommodation space creation, not by either term alone.
• Theory 30 · Lake Level Is a Balance
  Lake level responds to the ratio of evaporation to inflow rather than to rainfall alone, so a wetter basin with more evaporation can fall.
• Theory 31 · Technology Turns Over on a Ratio
  Whether a technology spreads is set by the ratio of its improvement rate to the obsolescence rate of the incumbent, not by its absolute performance.
• Theory 28 · Retention Is Learning Against Forgetting
  Retention after training is set by the ratio of consolidation rate to interference rate rather than by training amount.
• Theory 33 · Nitrogen Retention Is a Balance
  Whether an ecosystem retains nitrogen is set by the ratio of biological uptake to microbial loss rather than by nitrogen input.
• Theory 26 · Peak Viral Load Is a Race
  Peak viral load is set by the ratio of replication rate to clearance rate in the first days, so a slower virus with much slower clearance can peak higher.
• Theory 29 · Mountain Height Is a Ratio
  The steady-state height of a mountain range is set by the ratio of uplift to erosion rate rather than by uplift alone.

Geometry & Scale

• Theory 44 · Deposition Follows the Bifurcation
  Where inhaled particles deposit is set by the ratio of particle stopping distance to airway branch radius, not by particle size alone.
• Theory 36 · Biofilms Follow the Pipe
  Biofilm thickness in pipes is set by the ratio of pipe diameter to the mass-transfer boundary layer, so narrow pipes support thinner biofilms at the same flow.
• Theory 43 · Bone Strength Is Geometry
  Bone strength is set by cross-sectional geometry rather than by mass, so two bones of equal mass can differ several-fold in bending strength.
• Theory 40 · Tall Buildings Scale Badly
  Wind loads on a building rise with height faster than mass does, so structural material per floor rises with height rather than staying constant.
• Theory 34 · Body Size Is a Heat Leak
  A body's heat loss per unit mass is set by its surface-to-volume ratio, so small animals in cold climates are limited by geometry before they are limited by insulation.
• Theory 38 · Islands Scale With Area
  Species richness on islands follows a power of area whose exponent is set by the ratio of immigration to extinction rates, not by area alone.
• Theory 42 · Meanders Scale With the Valley
  The wavelength of river meanders is set by the ratio of valley width to channel width rather than by discharge, so confined rivers meander differently.
• Theory 41 · Small Particles Are Surface
  Catalytic activity per unit mass peaks at an intermediate particle size because surface-to-volume rises as size falls while surface energy rises faster.
• Theory 35 · Trophic Transfer Needs a Size Gap
  Trophic transfer efficiency is set by the ratio of predator to prey body size, so food chains are limited by size geometry rather than by productivity.
• Theory 37 · Water Retention Follows Grain Size
  Soil water retention is set by the ratio of grain size to pore-throat size rather than by total porosity, so two soils with equal porosity can hold very different water.
• Theory 39 · Trees Stop at a Hydraulic Limit
  Maximum tree height is set by the ratio of water potential gradient to path length, so taller trees need disproportionately safer xylem.

Thresholds & Tipping

• Theory 04 · Synergy Tips at a Ratio
  Combination synergy appears only within a range of dose ratios, so the same pair of drugs can be synergistic, additive or antagonistic depending on proportion.
• Theory 09 · Exacerbations Tip on Two Exposures
  Asthma exacerbation occurs when viral load and allergen exposure together cross a threshold, so either alone can be tolerated while the pair triggers.
• Theory 08 · Avalanches Release on a Ratio
  Slab avalanche release occurs when the ratio of load to weak-layer strength exceeds a threshold, so a thin slab on a weak layer can release before a thick slab on a strong one.
• Theory 07 · Cooperativity Has an Onset
  Enzymes show cooperative kinetics only above a threshold in substrate occupancy, so the same enzyme responds hyperbolically at low substrate and sigmoidally at high.
• Theory 10 · Eutrophication Is a Switch
  A lake switches to algal dominance above a phosphorus threshold rather than degrading gradually, and the switch is not reversed by returning to the same concentration.
• Theory 03 · Fire Needs Fuel Connectivity
  Fire spread stops when fuel connectivity falls below a threshold, so removing a small fraction of fuel in the right pattern can halt a front.
• Theory 11 · Marine Ice Sheets Have a Cliff
  Marine-based ice sheets become unstable above a threshold in bed slope and grounding-line depth, so retreat accelerates without any warming change.
• Theory 02 · Phosphorus Tips on pH
  Plant-available phosphorus rises abruptly above a soil pH threshold because iron and aluminium binding collapses, so liming can release phosphorus without adding any.
• Theory 01 · Recruitment Tipping on Patch Size
  Reef fish recruitment collapses below a critical habitat patch size, not in proportion to area lost.
• Theory 05 · Sleep Onset Is a Crossover
  Sleep onset occurs when homeostatic pressure crosses the circadian wake signal, so the same sleep debt can leave a person alert at one hour and asleep at another.
• Theory 06 · Outbreaks Tip on Superspreading
  Whether an outbreak becomes an epidemic is set by the fraction of transmission from superspreading events rather than by the reproduction number alone.

Networks & Connectivity

• Theory 61 · Internet Resilience Is Degree
  The resilience of the internet at the autonomous-system level is set by the ratio of peer links to transit links, not by node count.
• Theory 66 · Outbreak Size Follows Clustering
  Final outbreak size is set by the ratio of clustering to mean degree, so a highly clustered network can produce smaller outbreaks at the same R.
• Theory 57 · Cascades Follow Topology
  The size of a cascading failure is set by the ratio of load to spare capacity at the most loaded cut-set, not by the size of the initial fault.
• Theory 60 · Hub Proteins Are Essential
  The probability that a protein is essential is set by the ratio of its interaction degree to the redundancy of its partners, not by degree alone.
• Theory 56 · Persistence Needs Connectivity
  Metapopulation persistence is set by the ratio of colonisation to extinction rate, which is governed by connectivity, not by patch count.
• Theory 58 · Hub Damage Costs More
  Cognitive deficit after network damage is set by the ratio of lost hub degree to redundant pathways, so lesions of equal size differ by location.
• Theory 64 · Nestedness Buffers Loss
  The robustness of a pollination network to species loss is set by its nestedness relative to its connectance, not by species richness.
• Theory 59 · Sediment Follows Branching
  Sediment yield from a catchment is set by the ratio of branching order to slope, so two catchments of equal area can export very different loads.
• Theory 65 · Accessibility Is Connectivity
  Accessibility in a city is set by the ratio of network connectivity to detour, not by road length.
• Theory 62 · Roots Hold Soil by Network
  Erosion resistance is set by the ratio of root network connectivity to root mass, so a sparse connected network resists more than a dense disconnected one.

Selection & Bias

• Theory 96 · Ascertainment Distorts Heritability
  Heritability estimates from ascertained samples are biased in proportion to the ratio of ascertainment strength to trait heritability.
• Theory 99 · Hospital Controls Are Not Population
  Hospital-based case-control studies produce spurious associations because both cases and controls are selected on admission, which depends on both exposure and disease.
• Theory 94 · Conditioning Creates Associations
  Controlling for a common effect of two variables induces a spurious association between them, so adjusting for the wrong variable can create a relationship that does not exist.
• Theory 98 · Time Before Treatment Counts
  Classifying participants by treatment received after follow-up begins creates immortal time, biasing survival in favour of the treated group.
• Theory 90 · Effect Sizes Inflate
  Meta-analytic effect sizes are inflated in proportion to the ratio of publication bias to study precision, so a field of small studies overstates its effect.
• Theory 97 · Recall Follows the Diagnosis
  Recall of exposure is biased by the diagnosis itself, so cases report exposures differently from controls even when true exposure is equal.
• Theory 92 · Hospital Cohorts Are Selected
  Associations observed in hospital cohorts are biased by referral, so a factor that increases admission can appear protective or harmful without affecting disease.
• Theory 91 · Screening Detects on a Schedule
  Screening programmes detect preferentially the cases that pass through the test window at the right time, so incidence in screened groups is artificially raised.
• Theory 89 · Failures Are Selected Out
  Analyses of failures are biased toward components that survived long enough to fail visibly, so the riskiest designs can appear the safest.

Energy Limits

• Theory 82 · Energy Density Is a Chemistry Ceiling
  Battery energy density is capped by the ratio of cell voltage to the mass of the redox couple, so chemistry sets the ceiling and engineering only approaches it.
• Theory 84 · Catalysts Have an Activity Floor
  A catalyst's rate is bounded by the ratio of activation energy to the Sabatier optimum, so binding too strongly is as limiting as binding too weakly.
• Theory 83 · Evaporative Cooling Has a Limit
  Evaporative cooling cannot go below the wet-bulb temperature, and the approach to that limit sets the size and cost of the system.
• Theory 79 · Desalination Has a Floor
  The energy needed to separate salt from water is bounded below by the ratio of osmotic pressure to recovery, so higher recovery costs disproportionately more.
• Theory 87 · Exchangers Pay for Approach
  Heat exchanger area is set by the reciprocal of the approach temperature, so halving the approach doubles the area and roughly doubles the cost.
• Theory 81 · Muscle Has an Efficiency Ceiling
  Muscle mechanical efficiency is capped by the ratio of cross-bridge work to ATP hydrolysis, so faster contraction lowers efficiency even at higher power.
• Theory 85 · Fixing Nitrogen Is Expensive
  Biological nitrogen fixation costs a fixed fraction of photosynthetic energy, so its occurrence is set by the ratio of nitrogen need to carbon surplus.
• Theory 78 · Photosynthesis Has a Ceiling
  Photosynthetic efficiency is capped by the ratio of usable to absorbed photons, and the cap is set by the spectrum rather than by the enzyme.
• Theory 80 · Solar Cells Have a Band-Gap Limit
  Single-junction solar efficiency is capped by the ratio of band gap to photon energy, producing an optimum gap rather than a monotonic improvement with absorption.
• Theory 86 · Transmission Has a Per-Bit Floor
  The energy per bit of a communication link is bounded below by the ratio of noise to bandwidth, so widening bandwidth lowers the floor but raises total power.
• Theory 88 · Turbines Are Temperature Limited
  Turbine efficiency is capped by the ratio of firing temperature to compressor discharge temperature, which materials and cooling set together.

Hysteresis & Memory

• Theory 15 · Voltage Hysteresis Tracks the Path
  Voltage hysteresis in conversion-type electrodes is set by the size of the phase boundary formed on the last cycle, so capacity depends on cycling history rather than on state of charge.
• Theory 22 · Polymorphs Remember Their Route
  Which polymorph crystallises depends on the pathway taken rather than on the final conditions, so the same solution can yield different forms at the same supersaturation.
• Theory 12 · Enzymes Remember Substrate
  Enzymes retain a conformational memory of their last substrate, so turnover rate depends on the order in which substrates are presented, not only on the current one.
• Theory 16 · Gene Switches Hold Their State
  Bistable genetic switches require a larger inducer concentration to flip than to hold, so the switching threshold depends on the direction of approach.
• Theory 19 · Regrounding Is Harder Than Ungrounding
  A glacier that has ungrounded does not reground at the same conditions, because the geometry that supported contact has been altered.
• Theory 20 · Exhaustion Outlasts the Signal
  T cell exhaustion persists after antigen clearance, so the response to a later challenge is set by the history of chronic stimulation rather than by current antigen.
• Theory 14 · Kelp Forests Have Two States
  Kelp forests exist in two stable states, and the return from urchin barrens requires a larger reduction in grazing than the increase that caused the shift.
• Theory 13 · Compaction Does Not Reverse
  Soil compaction follows a hysteresis loop, so reloading to a stress previously experienced produces almost no further strain, and unloading does not restore structure.
• Theory 17 · Cities Store Heat
  Urban heat follows a hysteresis loop between day and night, so the same air temperature produces different surface temperatures depending on whether the city is heating or cooling.
• Theory 18 · Withdrawal Is the Mirror
  Withdrawal severity is set by the magnitude of the adaptation built during exposure, not by the dose removed, so tapering to a low dose can still produce severe symptoms.

Timing & Gating

• Theory 67 · Song Needs a Window
  A bird learns song only within a developmental window whose length is set by the ratio of sensitive period to auditory experience, so timing of exposure matters more than amount.
• Theory 70 · Radiosensitivity Is Gated by Phase
  Radiosensitivity is set by the fraction of cells in the sensitive phase at the time of exposure, so fractionation matters more than total dose.
• Theory 68 · Toxicity Is Gated by the Clock
  The toxicity of a drug is set by the phase of administration relative to the target tissue's circadian cycle, not by dose alone.
• Theory 73 · Weathering Needs Cycling
  Frost weathering is set by the rate of freeze-thaw cycling rather than by minimum temperature, so a milder climate with more cycles can weather faster.
• Theory 77 · Bursts Gate Expression
  Whether a gene is expressed at a given moment is set by the ratio of burst frequency to burst duration, not by mean expression level.
• Theory 75 · Organ Size Is Set in a Window
  Final organ size is set by the growth rate within a developmental window rather than by total growth time, so early perturbation cannot be compensated later.
• Theory 71 · Ozone Peaks on a Schedule
  Peak ozone depends on the ratio of precursor emission timing to the photochemical timescale, so the same daily emissions can produce different peaks.
• Theory 76 · Breeding Is Gated by Photoperiod
  The onset of breeding is set by the rate of change of photoperiod rather than by absolute day length, so the same day length signals differently in autumn and spring.
• Theory 69 · Timing Sets Vaccine Response
  Vaccine immunogenicity is set by the ratio of the interval before exposure to the time needed for the response to mature, not by dose or formulation.
• Theory 72 · Larvae Leave on a Tide
  The timing of larval release is set by the ratio of tidal amplitude to predation risk, so populations in high-predation sites release on specific tides.

Precision & Information

• Theory 54 · Interpretability Follows Compression
  A model is interpretable when the ratio of its description length to its input dimension is small, so a large model can be more interpretable than a small one.
• Theory 50 · Coverage Sets Detection
  The ability to detect a variant is set by the ratio of sequencing depth to the variant allele fraction, not by depth alone.
• Theory 48 · Confidence Is Ensemble Spread
  Forecast confidence should be set by the ratio of ensemble spread to the decision threshold, not by the deterministic forecast alone.
• Theory 55 · Learning Follows Precision
  The rate of perceptual learning is set by the ratio of practice precision to task noise, so practice with feedback that is more precise than the task teaches little.
• Theory 53 · Adaptation Timing Follows Precision
  The timing of adaptation investment is set by the ratio of projection precision to the cost of being wrong, so uncertain projections can justify earlier action, not later.
• Theory 51 · Classification Follows Resolution
  Target classification accuracy is set by the ratio of target extent to radar resolution cell, so a large target can be classified at coarse resolution.
• Theory 49 · Resolution Sets Detection
  The smallest detectable lesion is set by the ratio of image resolution to lesion contrast rather than by resolution alone.
• Theory 45 · Control Stability Is Precision
  The stability of a feedback controller is set by the ratio of sensor precision to loop gain, so a higher-gain controller can be less stable with a noisier sensor.
• Theory 46 · Thresholds Follow Test Precision
  The optimal clinical decision threshold is set by the ratio of test precision to the cost of a missed diagnosis, not by the test's sensitivity alone.

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.