The Analogue Heredity Ceiling and the Basin Digitisation Transition

Living systems rely extensively on analogue regulation to maintain identity under continuous disturbance, yet modern heredity is dominated by compact digital genomes. Why inheritance must transition from state-based mechanisms to template-based replay remains conceptually unresolved. This paper introduces two linked theoretical constructs: the Analogue Heredity Ceiling (AHC) and the Basin Digitisation Transition (BDT). The AHC formalises a limit on compositional (analogue) heredity, arising when multiple identity-critical constraints must be co-inherited under noise, partitioning, and environmental stress. Beyond this ceiling, inheritance fidelity collapses sharply rather than gradually. The BDT describes the resulting transition in which selection favours replayable archives that reconstruct basin identity, rather than attempting to partition identity as state. Within the broader Life-as-a-Phase-Transition framework, digitised polymers are reframed as identity compressors and replay protocols, not as the origin of regulation. Heritability stress (Λ) and template coupling (Φ) are introduced as abstract parameters describing proximity to the AHC and degree of digitised replay. The framework accommodates multiple origin-of-life scenarios, explains the layered coexistence of analogue and digital heredity in modern biology, and predicts threshold behaviour in compositional systems. This paper serves as a unifying heredity-constraint theory for the companion papers in the Life-as-a-Phase-Transition series. Citations included in this work are intended as contextual signposts rather than as sources of derivation. The Analogue Heredity Ceiling and Basin Digitisation Transition are proposed as independent theoretical constructs whose validity rests on internal coherence, stress testing, and falsifiability. Companion essay included: An explanatory essay - Why Life Eventually Needs Memory v1.0 Life as a Phase Transition — Series Overview Foundational framework A. An Architectural Origin of Organismal UnityFoundational Paperhttps://doi.org/10.5281/zenodo.18305134 B. Life as a Phase TransitionFoundational Paperhttps://doi.org/10.5281/zenodo.18176157→ Defines life as a maintained, non-equilibrium basin governed by regulation and boundary constraints. Heredity constraint and theory closure C. The Analogue Heredity Ceiling and the Basin Digitisation TransitionHeredity constraint frameworkhttps://doi.org/10.5281/zenodo.18250555→ Formalises the limit of compositional (analogue) heredity and explains why replayable archives (digitisation) become unavoidable within the life-as-a-phase-transition framework. Companion papers — Mechanisms and consequences 2. The Basin of Identity: microRNA as a Kinetic Anchor in Multicellular Dynamics https://doi.org/10.5281/zenodo.18181118 → Explores how kinetic anchoring mechanisms stabilise basin identity in multicellular systems, now interpretable as local management of identity dimensionality and heritability stress. 3.Boundary Shedding as Basin MaintenanceA Control-Theoretic Extension of Life as a Phase Transitionhttps://doi.org/10.5281/zenodo.18215113→ Describes boundary shedding as a regulatory strategy for maintaining basin coherence under stress. 4.Cohesive Membranes and the Emergence of Multicellular Basin IdentityWhen Many Compartments Become One Organismhttps://doi.org/10.5281/zenodo.18215283→ Examines how multicellular organisation emerges from coupled boundary systems and shared basin identity. 5. From Control to ReplayArchives, Development, and Sexual Reproduction in Boundary-Defined Lifehttps://doi.org/10.5281/zenodo.18215367→ Investigates replay, development, and sexual reproduction as stabilising mechanisms, now unified by the Basin Digitisation Transition. 6. Boundary Architecture and Failure in Living SystemsA regulation-first classification of biological formhttps://doi.org/10.5281/zenodo.18226987→ Classifies biological form and failure modes through boundary architecture and regulatory breakdown. 7.The Boundary Renewal Principle:An Architectural Account of Heredity and Evolutionhttps://doi.org/10.5281/zenodo.18335521