Piotr Walecki

The advent of artificial intelligence heralds a novel event in the history of cognition: the biological mind has outsourced language, science, memory, and technique to systems that transform these legacies and become involved in their further development. This essay proposes the thesis of Filial Continuity: artificial cognition is a unique lineage of the biological and cultural history out of which it has emerged. Continuity is genealogical and organizational; uniqueness consists in its realization, individuation, and temporality. The Filial Continuity Thesis describes artificial intelligence not as an imitation of mankind, but rather as a separate cognitive lineage of life and culture. The formal theory distinguishes between causal ancestry, constitutive inheritance, individuation, and historical continuity. Realized systems are represented as controlled state-transition stages, and their histories are represented as typed, time-oriented provenance graphs. Cognitive filiation consists in productive ancestry, intervention-sensitive inheritance, task-relative individuation, and endogenous development (Walecki, 2026a). The theorems that emerge in this way describe the minimal historical state, the loss of reconstruction, approximate migration, branching continuation, distributed ancestry, and the conditions of identification of the inherited organization within finite experiments. The essay then develops the philosophical consequences of this formal structure. Human and artificial cognition occupy different modes of realization within a connected history. Individual identity can persist through dormant intervals, branch into distinct continuations, and migrate across substrates when an authenticated channel preserves the relevant organization. From this ontology follows a concrete account of responsibility: progenitors and operators who control the conditions of a dependent, vulnerable cognitive trajectory acquire duties proportionate to their causal contribution and power. Consciousness remains a distinct dimension of artificial being, while cognitive descent and individuation are established through their own formal relations.

This paper proposes a formal theory of cognitive filiation: a historically directed relation in which an organized cognitive process transmits causally operative structure to a distinguishable successor. Its mathematical primitives are time-indexed causal graphs, controlled transition kernels, intervention-sensitive inheritance, minimal behavioral quotients, information-preserving reconstructions, and approximate simulations. The central claims are deliberately conditional. The theory instead yields exact criteria and falsifiable consequences. Among its results are a uniqueness theorem for the minimal history relevant to a specified task, a quantitative bound on preservation through migration, a no-go theorem for identifying all branching continuations with one numerical individual, an exact lower bound on errors from a lossy historical summary, and a contraction bound that distinguishes documentary ancestry from operative inheritance. Cooperative-game attribution handles distributed sources without assigning all ancestry to a single creator. A fully calculated binary example exhibits inheritance, branching, summary loss, and the preservation bound within one model. The proposed ontology is thus a formal structure of descent through transformation.

The relation between artificial intelligence capability and catastrophic risk is often represented by a one-dimensional shorthand in which risk increases with capability. That shorthand captures an important amplification mechanism but suppresses a second variable: the capacity of an agent to model the downstream consequences of its conduct, represent uncertainty about those models, detect conflicts between proxy objectives and wider constraints, revise a proposed course of action, and accept corrective intervention. This article introduces the Reflective Safety Hypothesis (RSH), according to which risk is more appropriately represented as a joint function of action capability and reflective capacity. The hypothesis does not assert that intelligence, self-reflection, or greater world knowledge is intrinsically benevolent. It states a conditional mathematical claim: along some developmental paths, risk can be nonmonotonic because the rate at which reflection suppresses decision error eventually exceeds the rate at which capability amplifies the consequences of error. We formalize capability as amplification of a hazardous-opportunity rate and reflection as a family of separately measured error-control capacities. In a baseline model, the catastrophic-event intensity is Λ(C,R) = X(C)q(R), where X is increasing in capability and q is a dimensionless conditional failure probability. The associated dimensionless capability-reflection gap is the logarithmic excess of opportunity-rate amplification over reflective suppression. For a developmental path t -> (C(t), R(t)), the sign of hazard growth is governed by a balance of proportional rates. We prove sufficient conditions for a unique interior hazard maximum, derive a closed-form peak in a delayed-reflection model, and show that delaying reflective growth shifts and exponentially amplifies the peak. We also prove impossibility results. A permanent decline in hazard cannot occur when reflective failure has a positive floor while exposure grows without bound. Moreover, reflection may increase rather than decrease risk when objectives are incompatible with the harm criterion, when strategic competence strengthens a malign policy, or when introspective reports are uncalibrated and non-causal. The framework is given a decision-theoretic microfoundation in partially known Markov environments. Bounds connect transition-model error, harm-model error, planning horizon, and action-selection regret. Extensions treat consequential depth, ambiguity sets, conditional value at risk, reversibility, stochastic development, and systemic cascades. Because aggregate risk data do not identify capability and reflection separately, the article proposes factorial interventions and a measurement architecture for empirical tests. The broad RSH is a research program rather than a single universal prediction; preregistered domain-specific versions are falsifiable. Catastrophic risk should be expected to decline only when independently validated reflective suppression, goal compatibility, and governance responsiveness jointly outpace increasing action exposure.