Applications of the Primitives

From the documentation of the field

The six primitives have been applied across several domains, each in a separate published paper. This page lists those papers. Each entry gives the title, version, year, DOI and a short description of what the paper does. The author page lists the artefacts behind the primary paper.

The primary paper

Ismail's Primitives: A Unified Functional Theory of Necessity, Independence, and Sequential Dependence in Adaptive Decision Systems, V6.2, published 2026-10-01. DOI 10.5281/zenodo.23080967.

Proves that sublinear regret across the environment class C requires six functional properties, that the properties are mutually independent, and that they compose into a directed informational chain that closes back on itself. Every theorem is checked in the Lean 4 proof assistant against Mathlib.

Economics

Ismail's Primitives: Lean-verified Economic Adaptation Theory, V2.0, published 2026-07-10. DOI 10.5281/zenodo.21289756.

Relabels the environment, algorithm and reward term for term as economy, coordination mechanism and welfare, and defines the economic Class C as the union of economies with at least one of six structural properties. Walrasian equilibrium is recovered as the case in which the environment is not in the class. Parts I and II rest on the Lean theorems of the primary paper by citation, the Part III instantiation is hand-checked and flagged as such, and the 2008 financial crisis is analysed as a structural diagnostic.

Human development

Ismail's Primitives and Human Development: A Functional Isomorphism Between a Lean-Verified Computational Theory and Developmental Psychology, V3, dated 2026-07-08. DOI 10.5281/zenodo.21257553.

Argues for a functional isomorphism between the six primitives and the sequences in psychological stage theories, mapping them onto Erikson's psychosocial stages, Maslow's motivational hierarchy and Bowlby's attachment phases. It presents the convergence of the three traditions as consilience evidence for the isomorphism. The abstract states that machine verification establishes the mathematical necessity and mutual irreplaceability of the six primitives, and that it does not by itself establish that human development instantiates them, which the paper argues on separate grounds.

Emotional adaptation in therapy

Ismail's Primitives: An Emotional Adaptation Theory Discovered through Functional Isomorphism, V2, dated 2026-07-10. DOI 10.5281/zenodo.21289914.

Argues that the environment of human emotional life is a Class C environment under all six properties, and derives from that six forms of adaptive failure, each requiring its own therapeutic function. It argues that each function has been discovered independently by at least two major therapeutic traditions, and it states falsification criteria.

The SPEA protocol

Ismail's Primitives: The SPEA Protocol for Clinical Psychology, V1, dated 2026-07-11. DOI 10.5281/zenodo.21311895.

The clinical operationalisation of the derivation in the emotional adaptation paper. It presents a six-step clinical sequence, each step operationalising the function required by one of the six conditions, together with a treatment trajectory, a self-application framework, a proposed assessment battery, contraindications, a therapist competency framework and a research programme built on the protocol's falsifiable claims. The abstract states that whether human emotional life instantiates the class remains a clinical and conceptual argument and not a formal one.