The Convexity Principle: Life as the Invariant Variable

TheConvexityPrinciple:LifeastheInvariantVariable ThePlanetaryConvexitySeriesPaperIII HollisBlack©2025¦CCBY-NC4.0 Abstract Planetarysystemsexhibitcyclicinstabilityyetmaintainapersistentbiastowardthepreservationoflife.This paperformalizesthattendencyastheConvexityPrinciple,whichproposesthatlifefunctionsastheinvariantin planetaryevolution,whilephysical,chemical,andecologicalvariablesoscillatearoundit.Withinthismodel, extinctionevents,climateoscillations,andbiosphericreorganizationsarenotterminalbreakdownsbut curvatureadjustmentsthatpreservetotallifepotential.TheConvexityPrinciplereframesGaia-likehomeostasis notasequilibriummaintenance,butasacontinuousoptimizationtowardsurvivalconvexityabiasthat convertsdisturbanceintorenewedorder.Thismodelpredictsthatplanetarysystemscapableofsustaininglife willdisplayrecursivefeedbacksthatpreventirreversiblecollapse.Thegreaterthedeviationfrom biocompatibility,thestrongerthecorrectiveresponse.Lifethusrepresentstheorganizingconstantofplanetary physics:notanepiphenomenonofchemistry,butanemergentattractorshapingenergyflows,atmospheric composition,andecologicalsuccession. CoreAssertionsandTestablePredictions 1.LifeasanInvariant Assertion:Totalplanetarybiosphericloadremainsapproximatelyconstantacrosslong-termgeologic timescales,despiteextinction-levelevents.Prediction:Netbiomassproductivity(viaisotopicandsedimentary proxies)reboundstopre-collapselevelswithin10⁵‒10⁶yearsfollowingmajorextinctions. 2.Feedback-DrivenConvexity Assertion:Planetarysystemsexhibitfeedbacksthatincreaseinstrengthnearcriticalthresholds,creatingconvex resiliencecurves.Prediction:Paleoclimateandredoxdatashouldrevealacceleratedrecoveryratesimmediately followingmajorperturbations,consistentwithnonlinearfeedbackcompensation. 3.CatastropheasCorrection Assertion:Systemicbreakdowns(massextinctions,glaciations,impactwinters)serveascorrectional realignmentstowardbiosphericsustainability.Prediction:Eachglobalextinctionshouldprecedearisein biologicaldiversityorcomplexityproportionaltothescaleofpriorloss. 4.EnergeticEconomyofLife Assertion:Planetaryenergyflowself-regulatestowardconfigurationsthatmaximizeentropyproduction withoutcompromisingbiocompatibility.Prediction:Post-catastropheecosystemsexhibithigherenergy throughputandtrophicefficiencythantheirprecursors. 5.PlanetaryLawofLifeBias Assertion:Givenidenticalstartingconditions,life-bearingplanetswilltendtoretainbiosphereslongerthan lifelessanalogues.Prediction:Comparativeexoplanetmodelingshouldshowthatoncebiosphericfeedback initiates,climatestabilitywindowslengthenexponentiallyrelativetosterileplanets. License:CCBY-NC4.0 Keywords:PlanetaryConvexity,Gaiatheory,biosphericregulation,catastrophedynamics,feedbackresilience, lifeinvariance,astrobiology Thispaperfollows'ThePrincipleofPlanetaryConvexity'andcompletesthetheoreticaltriadthatbeganwith 'DiachronousOxygenationasaPlanetaryTippingPoint'inthePlanetaryConvexitySeries. PreparedforZenodo.Version1.0•October2025