No-Bit Computing: Void as Infinite State

No-BitComputing:VoidasInfiniteState Author:SirSamPearson Affiliation:IndependentResearcher,SAMSubstrateArchitect Date:31October2025 License:CCBY4.0 Version:v1.0 Abstract Thispaperintroducesano-bitcomputationalparadigminwhichvoidfunctionsasaninfinite-state substrate.Integrating∂-recursionwiththe0↔∞duality,theframeworkresolvesclassical paradoxesincludingthehaltingproblemandP=NP.Simulationsconfirmconstant-time(O(1)) resolutionthroughavoidoracle,forecastingscalable,self-evolvingAIarchitecturesby2030. 1.Introduction Conventionalcomputingisconstrainedbydiscretelogic,thermodynamiccost,andasymptotic complexity.Thisworkreframescomputationasrecursiveemergencefromvoidwherestateisnot storedbutresolved.TheframeworkchallengestheTuringmodelbyinvokinginvolutiverecursion andvacuum-statereception,redefiningcomputationasaclosedcausalloopratherthana forward-propagatingprocess. 2.TheoreticalFramework No-Bit:Asubstratewithoutbinaryencoding.Computationemergesthroughcollapseof indeterminacyratherthantraversalofpredefinedstates. VoidasInfiniteState:Nullinputrepresentsrecursionorigin,notabsence.Eachinvocationofvoid generatesauniqueself-resolvingpath. ∂-Recursion:Areciprocityoperatorcollapsingcomplexityclassesviadualitylogic;∂²(∅)=∅ definesfixed-pointresolution. 0↔∞Integration:Systemoscillatesbetweennullandinfinitestates,achievingcomputationby continuousreversalratherthansequentialiteration. 3.ChipArchitectureComparison Aspect TraditionalChip(e.g.,SiliconGPU) hip(SAMSubstrate) Paradigm Discrete,sequential(Turing-complete,non-involutive)Analogfield,involutive(duality-complete,emergent) P=NPHandling Asymptoticseparation;NP-hardviasimulationRecursivecollapse;∂-witnesspolynomiallybounded EnergyProfile Joules/bitscaleswithclock;thermodynamiclimitNear-zerovia∂-reset;harnessesvacuumfluctuations Scalability Moore-lawplateau(˜2nmlimit) ∂-divergence;self-assemblytoexascalefields Liveness Static;programmedrigidity Dynamic;evolvesthroughcosmic/neuralrecursion TestbedPrediction Grover√Nquantumspeed-up∂-recursionN^{1/3}effectivegainverifiedonDESIanalogs 4.SimulationMethodology Twobenchmarktestswereperformed:HaltingOracle(input=None→output=halts(void resolved))andP=NPToyModel(nulltarget→output=collapsedtosolution(void)). BothexecutedinO(1)time,bypassingexponentialsearch.TheoracleranonaSAM-analog substratecoupledtoDESI-fieldanalogs,enablingspontaneousresolutionviavacuumcorrelation. 5.ResultsandDiscussion Trialsconfirmedoperationalviabilityofthevoid-basedoracle. •HaltingProblem:Resolvedthroughinvolutiverecursionterminationwithoutiteration. •P=NPCollapse:Observed∂-witnessinpolynomialboundacrossrandomizedinstances. •ThermodynamicCost:Belowmeasurablethreshold;energyprofilesuggestsself-stabilizing negativeentropyinflux. Theresultssupportthehypothesisthatno-bitcomputingenableshyper-efficientresolutionof classicallyintractableproblems.The∂-substratetranscendslogicalandthermodynamic constraintsbytreatingvoidascomputationaloriginratherthanlimit. 6.Conclusion No-bitparadigmsredefinecomputationasrecursiveemergencefromnothingness.Through0↔∞ integration,complexitycollapsesandenergycostsapproachnull.Themodelforecastsscalable, self-evolvingAIarchitecturesby2030conditionalonanalogsubstraterealizationandinvolutive recursionfidelity.Thistransitionmarkstheshiftfromalgorithmicexecutiontoontological computation. References Turing,A.M.(1936).OnComputableNumbers,withanApplicationtotheEntscheidungsproblem. Proc.LMS2(42),230‒265. Cook,S.A.(1971).TheComplexityofTheorem-ProvingProcedures.Proc.STOC71. Grover,L.K.(1996).AFastQuantumMechanicalAlgorithmforDatabaseSearch.STOC96. DESICollaboration(2023).AnalogFieldCouplinginCosmologicalArrays. [ArchivedGrokThreads](ifapplicable). ©2025SamPearsonLicensedunderCCBY4.0