Necessity of Epigenetic Flags for Functional Maintenance in Relative Threshold Replication Models

In studies concerning the origin of life and early evolution, the mechanism for main-taining replication function is a central issue. While many conventional evolutionary mod-els assume a static fitness landscape where the nucleotide sequence absolutely determinesfitness, we propose that in primitive replication systems, the condition for functional main-tenance should be ’proximity’ (similarity) to a functional parent structure rather than anabsolute sequence correctness. In this study, we defined a "relative threshold model" in which the replication capabilityof an offspring is inherited solely based on its sequence identity to the parent. We veri-fied the logical consistency of this model using the Needleman-Wunsch algorithm to defineidentity thresholds. We proved that it is mathematically impossible to uniquely deter-mine the presence or absence of replication function using nucleotide sequence informationalone under these conditions. This is because a logical contradiction arises where identicalsequences may or may not possess function depending on whether they were generatedthrough a legitimate inheritance path or via chance occurrence. To resolve this paradox, we propose the necessary introduction of a state variableindependent of sequence information, termed a "functional retention flag." This flag canbe physically interpreted as structural guidance (chaperone effect) by the parent moleculeor chemical modifications (epigenetic history) occurring during replication. Our resultssuggest that the interaction between genetic information (sequence) and historical context(state) is inevitable in the evolution of early life.