Vocabulary across the sequence
Each entry gives the shared definition, the book and chapters that supply its canonical treatment, and the refinement carried into the rest of the sequence.
A
A separate accept, reject, or abstain judgment under a named certificate and evidence contract.
Across the sequence. Infinitesimal Creativity refines admission into an explicit epistemic status for proposed theory extensions.
A
The visual-language system that compiles scene declarations into structural diagnosis, localized repair, and independent checking.
Across the sequence. ARTISTIC repair supplies assurance infrastructure; it is not by itself transformational creativity.
C
Learning a compositional world from a presentation up to a declared class of observationally meaningful equivalences.
Across the sequence. ORACLE generalizes identification in the limit from languages or state machines to categories, presentations, doctrines, and tangent structure.
C
A collection of objects and composable morphisms with associative composition and identity morphisms.
Across the sequence. The later books use categories as languages of learning systems and maintained theories.
C
Boden's distinction among new combinations, exploration under current rules, and changes to the rules or conceptual space itself.
Across the sequence. DIAL-X must name which mode it targets rather than treating every adaptation as creative.
C
A typed failure of a declared factorization, path agreement, or designated universal property.
Across the sequence. Diagrammatic curvature is one scalar observation of such a failure, not its general definition.
D
Double Involution ALgebroid: the proposed interaction of two typed infinitesimal repair directions with an interchange comparison and bridge obligations to classical double Lie theory.
Across the sequence. DIAL is a proposed formal architecture, not an established theorem or a synonym for creativity.
D
A domain specialization of DIAL that declares its target, two repair semantics, mixed witness, finite-realization gate, proposal language, admission contract, and persistence record.
Across the sequence. The hyphen preserves the identity and semantics of the underlying domain method X.
D
Double Involution Learning for Artistic Theory Extension, aimed at constructing reusable operations over generative dynamics rather than repairing one image.
Across the sequence. Current results provide local paintbrush and routing evidence; a genuinely new admitted artistic generator remains open.
D
A declared categorical theory specifying the kinds of structure, models, morphisms, and universal constructions admitted in a hypothesis class.
Across the sequence. The fourth volume recasts core knowledge, learning formalisms, and scientific theories as doctrinal priors rather than neutral data representations.
E
Compatibility of an observed result with a bounded claim under stated controls and within a registered environment.
Across the sequence. Support does not imply formal proof, external validity, or unrestricted generalization.
F
A declared mathematical or empirical test of whether an infinitesimal candidate composes into a coherent finite path, rollout, continuation, or action.
Across the sequence. A meaningful local direction is not an executable repair until it passes the relevant finite gate.
F
A consequence derived from stated assumptions in a specified formal system.
Across the sequence. A proof establishes neither empirical adequacy nor the novelty and value of the surrounding theory.
F
A mapping between categories that preserves identities and composition.
Across the sequence. Later books use functors to separate formal declarations from their models and to transport structure across revisions.
I
The tangent response of a typed compositional obstruction under an admitted probe.
Across the sequence. INC is not merely a gradient magnitude and does not by itself authorize a repair.
K
A universal way to extend a functor along another functor, using colimit-like left or limit-like right constructions.
Across the sequence. LINCS uses direct-versus-extended routes as structural obligations and Infinitesimal Creativity studies transport across theory extension.
L
A declaration of generators, path equations, designated limit cones, and designated colimit cocones for a learning system.
Across the sequence. Infinitesimal Creativity treats finite sketch extension as a candidate creative artifact.
L
Restriction of surviving obstruction data to a declared cover or family of substructures with the required overlap comparisons.
Across the sequence. Localization identifies where a promise fails; it does not prove identifiability, effectivity, or global repairability.
N
A coherent family of morphisms between two functors, compatible with every morphism in their common source category.
Across the sequence. It supplies one model of coherent componentwise change, but an arbitrary family of edits is not automatically natural.
O
A declared map that turns a typed obstruction into evidence available to a learner, controller, or admission procedure.
Across the sequence. Observability is an assumption to justify, not a free consequence of declaring a sketch.
O
Online Rational Agent for Categorical LEarning: the program of discovering compositional worlds and their governing doctrines from interaction.
Across the sequence. ORACLE supplies the meta-learning setting in which UOCL discovers categorical worlds and UODL specializes discovery to decisions.
P
A local, statistically evaluated categorical search process whose admissible mutations improve performance without conditioning updates on individual examples.
Across the sequence. The construction categorifies Valiant's evolvability while preserving explicit mutation neighborhoods, tolerance, representation bounds, and categorical discrepancy.
P
Probably Approximately Categorically Correct learning, where success is measured probabilistically through a categorical discrepancy or query semantics rather than literal equality of hypotheses.
Across the sequence. It extends PAC learning to structured hypotheses while making the chosen observer, sampling law, equivalence, and compositional error explicit.
R
A typed proposed edit selected from a registered repair language, with an explicit target and preservation obligations.
Across the sequence. A structural repair becomes a causal intervention only when explicit mechanism and intervention semantics support that reading.
S
A task-dependent numerical measurement or ranking applied after the structural type and semantics of an obstruction have been declared.
Across the sequence. A scalarization may be useful for optimization without becoming the definition of non-compositionality.
S
A compact presentation of a categorical theory by generators, equations, and designated universal constructions.
Across the sequence. Categories for AGI supplies the diagrammatic language; LINCS operationalizes sketches; Infinitesimal Creativity studies their acquisition and extension.
T
A category equipped with a tangent endofunctor and coherent projection, zero, addition, lift, and canonical-flip structure.
Across the sequence. The structure abstracts differentiation without requiring the category of ordinary smooth manifolds to be Cartesian closed.
T
A typed map from a maintained presentation to an augmented one, together with semantics for new generators and transport of the old theory.
Across the sequence. A theory extension is proposed finitely and admitted independently; it is not identical to an infinitesimal probe.
U
A characterization of an object by its canonical maps to or from all relevant objects, typically determining it up to canonical isomorphism.
Across the sequence. LINCS treats failure to realize designated universal properties as typed structural obstruction.
U
Universal Online Categorical Learning: incremental identification of an unknown categorical world from a growing interaction presentation.
Across the sequence. UOCL contains familiar model learning—automata, predictive-state, causal, language, and MDP learning—as doctrine-restricted cases.
U
Universal Online Decision Learning: the decision-making specialization of UOCL under progressively revealed information and declared online/offline comparison observers.
Across the sequence. Classical online convex optimization, regularized action, bandits, and decentralized decisions arise under different clock and information doctrines.