Mathematical Criteria of Life and Sense: A Relational Information-Theoretic Framework for Observerhood, Agency and Human–AI Super-Agents

Three practical questions this paper answers: 1. What architectural criterion separates an AI system that processes information from one that qualifies as a genuine observer or agent — independently of behavioural impression? 2. When does AI assistance amplify human agency, and when does it quietly replace it while the human remains formally “in the loop”? 3. Does ordinary mind-uploading — copying memories, weights, neural measurements or behavioural traces — actually continue a person, or only produce an external recording of one? A single structural criterion connects all three questions. A subsystem qualifies as an observer when its own past states causally rewrite the rule governing its future — not merely when it stores information, behaves in complex ways or produces convincing outputs. This separates self-accumulated memory (Pₛelf) from externally written memory (Pₑxt) and yields an operational test that is independent of substrate, scale or biological origin. Concrete contributions: – Three formal conditions for observerhood: non-Markovian effective dynamics, self-accumulated history and feedback integration of novelty. These are stated as testable structural conditions rather than philosophical commitments. – An architectural diagnosis of frozen-weights AI: current inference systems fail the criterion not because they are artificial, but because generated tokens do not rewrite the rule generating future tokens. The paper also specifies what an artificial observer would have to do differently: online self-modification, closed causal feedback and continuity of self-history. – A formal account of human–AI coupling using two coefficients: ρ, measuring whether AI alignment amplifies or suppresses human novelty in the joint causal record; and α, measuring the fraction of human physical novelty that actually enters shared action, decision and history. Together they define a measurable signature of pseudo-crystallisation — the regime in which humans remain biologically creative but cease to be authors of the composite system. – A treatment of mind uploading as Pₑxt transfer rather than Pₛelf continuation. Behavioural similarity does not imply causal identity of self-history; the paper states what a continuity-preserving procedure would have to satisfy. – A phase-transition hierarchy of observerhood — inert object → replicator → living cell → nervous animal → emotional animal → rational human → human–AI Super-Agent — defined by the closure of specific causal loops rather than by a smooth scale of consciousness. – Weak and strong Anti-Crystal principles. The weak form follows from the One-Neuron Oracle Barrier: while at least one living causally active subsystem exists, no internal physical computer can become its exact oracle. The strong form is conjectural and is grounded in locality, finite temperature, quantum-thermodynamic openness and no-cloning. – Eight falsifiable predictions, including measurable drops in α under AI over-reliance and detectable phase-transition signatures when new causal loops close. Intended audiences: – AI researchers and alignment theorists: an architectural criterion for artificial Others and α / ρ diagnostics for human–AI coupling. – Transhumanism and longevity research: a formal account of why ordinary mind-uploading is copying rather than continuation, and what would have to change for it to be otherwise. – Philosophy of mind: a minimal structural threshold that does not conflate life, agency, observerhood and phenomenal consciousness. – Theoretical biology and origin-of-life research: abiogenesis as the onset of rule-coupling between a region’s history and its update rule. – Cognitive science and HCI: operational language for diagnosing when intelligent tools convert authors into operators. The framework is substrate-neutral and falsifiable. It excludes no technology in principle and endorses none by default. Author InformationJulian Zoria (Independent Researcher) ORCID: 0009-0002-2424-5291Email: julian. zoria@proton. me