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% --- Short names (public-only; no numeric codes)
\newcommand{\Lrn}{\textbf{Lrn}}   % Learnon — Parametric learning
\newcommand{\Evo}{\textbf{Evo}}   % Evolon — Population adaptation
\newcommand{\Sym}{\textbf{Sym}}   % Symbion — Symbolic inference
\newcommand{\Prb}{\textbf{Prb}}   % Probion — Probabilistic inference
\newcommand{\Sch}{\textbf{Sch}}   % Scholon — Search & planning
\newcommand{\Ctl}{\textbf{Ctl}}   % Controlon — Control & estimation
\newcommand{\Swm}{\textbf{Swm}}   % Swarmon — Collective/swarm
\newcommand{\hyb}[1]{\textsc{#1}} % hybrid spec styling (e.g., \hyb{Lrn+Sch})

%\newcommand{\figureW}{0.95\textwidth}
%\newcommand{\figureH}{0.58\textwidth}


% --- Wide figure helper: figure* in two-column; figure in one-column
\newif\iftwocol
\providecommand{\figureW}{0.95\textwidth}
\providecommand{\figureH}{0.58\textwidth}
\newenvironment{WideFig}{\iftwocol\begin{figure*}\else\begin{figure}\fi}{\iftwocol\end{figure*}\else\end{figure}\fi}
% --- Wide table helper: table* in two-column; table in one-column
\newenvironment{WideTab}{\iftwocol\begin{table*}\else\begin{table}\fi}{\iftwocol\end{table*}\else\end{table}\fi}


% --- TikZ/PGF defaults
\pgfplotsset{compat=1.18}

\begin{abstract}
Policy and industry discourse often reduce AI to machine learning framed as “supervised, unsupervised, or reinforcement learning.” This triad omits long-standing AI traditions (symbolic expert systems, search \& planning, probabilistic inference, control/estimation, and evolutionary/collective computation). We formalize the \emph{Operational-Premise Taxonomy}~(OPT), classifying AI by its dominant computational mechanism: \Lrn, \Evo, \Sym, \Prb, \Sch, \Ctl, and \Swm. For each class we provide core mathematical operators, link them to canonical biological mechanisms, and survey hybrid compositions. We argue that OPT yields a principled, biologically grounded, and governance-usable taxonomy that avoids category errors inherent in training-signal–based labels, while remaining compact and readable with a short, compositional naming code.
\end{abstract}

% ---------------------------
\section{Introduction}
% ---------------------------
Regulatory texts frequently equate “AI” with three categories of \emph{learning signals}: supervised, unsupervised, and reinforcement learning \citep{EUAnnex,NISTRMF}. These categories emerged from neural/connectionist practice, not from the full breadth of artificial intelligence \citep{AIMA4}. We propose an alternative taxonomic axis: the \emph{operational premise}—the primary computational mechanism a system instantiates to improve, adapt, or decide. The resulting taxonomy, \emph{operational premise taxonomy}~(OPT) provides a transparent and consistent framework for compactly describing AI systems, including hybrids and pipelines. OPT retains biological analogs (learning vs.\ adaptation) while accommodating symbolic, probabilistic, search, control, and swarm paradigms.

% ---------------------------
\section{Operational-Premise Taxonomy (OPT)}
% ---------------------------

Because OPT introduces several new labels, we present those here before tackling background and related work topics.

OPT classes are defined by dominant mechanism; hybrids are explicit compositions:

\begin{itemize}[leftmargin=1.6em]
\item \textbf{Learnon (\Lrn)} — Parametric learning within an individual (gradient/likelihood/return updates).
\item \textbf{Evolon (\Evo)} — Population adaptation via variation, selection, inheritance.
\item \textbf{Symbion (\Sym)} — Symbolic/logic inference over discrete structures (KB, clauses, proofs).
\item \textbf{Probion (\Prb)} — Probabilistic modeling and approximate inference (posteriors, ELBO).
\item \textbf{Scholon (\Sch)} — Deliberative search and planning (heuristics, DP, graph search).
\item \textbf{Controlon (\Ctl)} — Feedback control and state estimation in dynamical systems.
\item \textbf{Swarmon (\Swm)} — Collective/swarm coordination with local rules and emergence.
\end{itemize}

\noindent \emph{Hybrid notation.}~We use \hyb{A+B}~for co-operative mechanisms, \hyb{A/B}~for hierarchical nesting (outer/inner), \hyb{A\{B,C\}}~for parallel ensembles, and \hyb{[A→B]}~for pipelines (Appendix~\ref{app:optcode}).

% --- OPT circle landscape (auto-wide)
\begin{WideFig}
\centering
\begin{tikzpicture}[
    node distance=2cm,
    every node/.style={font=\small},
    optnode/.style={circle, draw=black, very thick, minimum size=11mm, align=center},
    hybridedge/.style={-Latex, very thick},
    weakedge/.style={-Latex, dashed, thick},
    legendbox/.style={draw, rounded corners, inner sep=3pt, font=\footnotesize},
]
\def\R{4.9}
\path
  (90:\R)   node[optnode] (L) {Lrn}
  (38.6:\R) node[optnode] (S) {Sch}
  (-12.8:\R) node[optnode] (Y) {Sym}
  (-64.2:\R) node[optnode] (P) {Prb}
  (-115.6:\R) node[optnode] (C) {Ctl}
  (-167:\R)  node[optnode] (W) {Swm}
  (141.4:\R) node[optnode] (E) {Evo};

\draw[hybridedge] (L) to[bend left=10] (S);
\draw[hybridedge] (S) to[bend left=10] (L);
\draw[hybridedge] (L) to[bend left=10] (Y);
\draw[hybridedge] (Y) to[bend left=10] (L);
\draw[hybridedge] (L) to[bend left=10] (E);
\draw[hybridedge] (E) to[bend left=10] (L);
\draw[hybridedge] (L) to[bend left=10] (C);
\draw[hybridedge] (C) to[bend left=10] (L);

\draw[weakedge] (S) -- (Y);
\draw[weakedge] (P) -- (L);
\draw[weakedge] (P) -- (S);
\draw[weakedge] (W) -- (E);
\draw[weakedge] (C) -- (S);
\draw[weakedge] (P) -- (C);

\node[legendbox, anchor=north east] at ($(current bounding box.north east)+(-0.2, 1.2)$) {
\begin{tabular}{@{}l@{}}
\textbf{Solid:} prominent hybrids (\hyb{Lrn+Sch}, \hyb{Lrn+Sym}, \hyb{Lrn+Evo}) \\
\textbf{Dashed:} frequent couplings (\hyb{Prb+Ctl}, \hyb{Sch+Sym}, \hyb{Swm+Evo}) \\
\end{tabular}
};
\end{tikzpicture}
\caption{OPT landscape using short names only: \Lrn, \Evo, \Sym, \Prb, \Sch, \Ctl, \Swm.}
\label{fig:opt_landscape}
\end{WideFig}

% ---------------------------
\section{Mathematical Foundations and Biological Correspondences}
\label{sec:math}
% ---------------------------

\paragraph{Learnon (\Lrn).} Empirical risk minimization:
\begin{equation}
\theta^\star \in \arg\min_{\theta}\ \mathbb{E}_{(x,y)\sim \mathcal{D}}[ \ell(f_\theta(x),y) ] + \lambda \Omega(\theta),
\end{equation}
with gradient updates $\theta_{t+1}=\theta_t-\eta_t\nabla\widehat{\mathcal{L}}(\theta_t)$; RL maximizes $J(\pi)=\mathbb{E}_\pi[\sum_t \gamma^t r_t]$ in MDPs. \emph{Biology:}~ Hebbian/Oja \citep{Hebb1949,Oja1982}, reward-modulated prediction errors \citep{SuttonBarto2018}.

\paragraph{Evolon (\Evo).} Population pipeline $P_{t+1}=\mathcal{R}(\mathcal{M}(\mathcal{C}(P_t)))$ with fitness-driven selection. \emph{Biology:}~ Price equation $\Delta \bar{z}=\frac{\mathrm{Cov}(w,z)}{\bar{w}}+\frac{\mathbb{E}[w\Delta z]}{\bar{w}}$; replicator $\dot{p}_i=p_i(f_i-\bar{f})$ \citep{Price1970,TaylorJonker1978}.

\paragraph{Symbion (\Sym).} Resolution/unification; soundness and refutation completeness \citep{Robinson1965Resolution}.

\paragraph{Probion (\Prb).} Bayes $p(z|x)\propto p(x|z)p(z)$; VI via ELBO $\mathcal{L}(q)=\mathbb{E}_q[\log p(x,z)]-\mathbb{E}_q[\log q(z)]$; \emph{Biology:}~ Bayesian brain \citep{KnillPouget2004}.

\paragraph{Scholon (\Sch).} A* with admissible $h$ is optimally efficient; DP/Bellman updates $V_{k+1}(s)=\max_a[r(s,a)+\gamma\sum_{s'}P(s'|s,a)V_k(s')]$.

\paragraph{Controlon (\Ctl).} LQR minimizes quadratic cost in linear systems; Kalman filter provides MMSE state estimates in LQG \citep{Kalman1960,Pontryagin1962,TodorovJordan2002}.

\paragraph{Swarmon (\Swm).} PSO updates $v_i(t+1)=\omega v_i(t)+c_1 r_1(p_i-x_i)+c_2 r_2(g-x_i)$; ACO pheromone $\tau\leftarrow (1-\rho)\tau+\sum_k \Delta\tau^{(k)}$.

% ---------------------------
\section{Background and Prior Work}
% ---------------------------
Classic textbooks and surveys treat symbolic reasoning, planning/search, probabilistic models, learning, evolutionary methods, and control/estimation as co-equal pillars \citep{AIMA4,CIbook,FuzzySurvey,SuttonBarto2018}. No-Free-Lunch (NFL) theorems for search/optimization motivate pluralism: no single mechanism dominates across all problems \citep{Wolpert1997}. Biological literatures mirror these mechanisms: synaptic plasticity and Hebbian/Oja learning \citep{Hebb1949,Oja1982}, population genetics and replicator dynamics \citep{Price1970,TaylorJonker1978}, Bayesian cognition \citep{KnillPouget2004}, and optimal feedback control in motor behavior \citep{TodorovJordan2002,Kalman1960,Pontryagin1962}.

\include{related-work}

% Bridge
\paragraph{Comparative landscape.}
Table~\ref{tab:opt_vs_frameworks} situates OPT alongside the best-known standards, policy instruments, and textbook structures.  
Each of these prior frameworks serves an important function—shared vocabulary (ISO/IEC 22989), ML-system decomposition (ISO/IEC 23053), risk management (NIST AI RMF), usage contexts (NIST AI 200-1), multidimensional policy characterization (OECD), or regulatory stratification (EU AI Act).  
However, they remain either technique-agnostic or focused solely on machine learning.  
OPT complements them by supplying the missing layer: a stable, biologically grounded \emph{implementation taxonomy}~ that captures mechanism families across paradigms and defines a formal grammar for hybrid systems.

\include{table-opt-comparison}

% ---------------------------
\section{Comparative Analysis, Completeness, and Objections}
\label{sec:analysis}
% ---------------------------

\subsection{Biological--Artificial Correspondences}
Each OPT class aligns with a biological mechanism (plasticity, natural selection, structured reasoning, Bayesian cognition, deliberative planning, optimal feedback control, and distributed coordination). Shared operators in Sec.~\ref{sec:math} support cross-domain guarantees.

\subsection{Coverage, Hybrids, and Orthogonal Descriptors}
Hybrids are explicit (e.g., \hyb{Lrn+Sch} AlphaZero, \hyb{Lrn+Sym} neuro-symbolic, \hyb{Evo/Lrn} neuroevolution). Orthogonal axes capture representation, locus of change, objective, data regime, timescale, and human participation.

\subsection{Objections and Responses}
\textbf{Reduction to optimization.} Mechanisms imply distinct guarantees/hazards (data leakage vs.\ fitness misspecification vs.\ rule brittleness). NFL cautions against collapsing mechanisms.  
\textbf{Hybrid blurring.} OPT treats compositions as first-class; the notation discloses “what changes where, on what objective, and on what timescale.”  
\textbf{Regulatory simplicity.} Seven bins appear minimal for coverage; the short names keep disclosures compact and meaningful.

% ---------------------------
\section{Examples and Mapping}
% ---------------------------
\begin{table}[htbp]
\centering
\caption{Representative paradigms mapped to OPT.}
\renewcommand{\arraystretch}{1.1}
\begin{tabular}{@{}p{3.9cm}p{3.6cm}p{2.2cm}@{}}
\toprule
\textbf{Type / Implementation} & \textbf{Examples} & \textbf{OPT (short)}\\
\midrule
NN/Transformer (GD) & CNN, LSTM, attention & \Lrn\\
Reinforcement learning & DQN, PG, AC & \Lrn\;(+\Sch,\,+\Ctl)\\
Evolutionary algorithms & GA, GP, CMA-ES & \Evo\\
Swarm intelligence & ACO, PSO & \Swm\;(+\Evo)\\
Expert systems & Prolog, Mycin, XCON & \Sym\\
Probabilistic models & BN, HMM, factor graphs & \Prb\\
Search \& planning & A*, MCTS, STRIPS & \Sch\\
Control \& estimation & PID, LQR, KF/MPC & \Ctl\\
\bottomrule
\end{tabular}
\label{tab:OPTmap}
\end{table}

% ---------------------------
\section{Orthogonal Axes and Risk Perspectives}
% ---------------------------

\paragraph{Secondary axes (orthogonal descriptors).}
\begin{itemize}[leftmargin=1.2em]
\item \textbf{Representation:} parametric vectors, symbols/logic, graphs, programs, trajectories, policies.
\item \textbf{Locus of Change:} parameters, structure/architecture, population composition, belief state, policy.
\item \textbf{Objective Type:} prediction, optimization, inference, control, search cost, constraint satisfaction.
\item \textbf{Timescale:} online vs.\ offline; within-run vs.\ across-generations.
\item \textbf{Data Regime:} none/synthetic, labeled, unlabeled, interactive reward.
\item \textbf{Human Participation:} expert-authored knowledge vs.\ learned vs.\ co-created.
\end{itemize}


\begin{table}[htbp]
\centering
\caption{Orthogonal descriptive axes and governance risks (abridged).}
\renewcommand{\arraystretch}{1.05}
\begin{tabular}{@{}p{1.25cm}p{3.5cm}p{3.9cm}@{}}
\toprule
\textbf{OPT} & \textbf{Primary Risks} & \textbf{Assurance Focus} \\
\midrule
\Lrn & Data leakage, reward hacking & Data governance, OOD tests, calibration \\
\Evo & Fitness misspecification & Proxy validation, replicates, constraints \\
\Sym & Rule brittleness, KB inconsistency & Provenance, formal verification \\
\Prb & Miscalibration, inference bias & Posterior predictive checks \\
\Sch & Heuristic inadmissibility & Optimality proofs, heuristic diagnostics \\
\Ctl & Instability, unmodeled dynamics & Stability margins, robustness \\
\Swm & Emergent instability & Swarm invariants, safety envelopes \\
\bottomrule
\end{tabular}
\label{tab:OPT_risk}
\end{table}

% --- Radar plots (two figures; auto-wide; short-name legends)

% --- Radar helper: one polygon with six axes (Rep., Locus, Obj., Data, Time, Human)
\newcommand{\RadarPoly}[7]{%
  % #1 style, #2..#7 = values on axes in order
  \addplot+[#1] coordinates
    {(0,#2) (60,#3) (120,#4) (180,#5) (240,#6) (300,#7) (360,#2)};
}


\begin{WideFig}
\centering
\begin{tikzpicture}
\begin{polaraxis}[
  width=\figureW, height=\figureH,
  ymin=0, ymax=5,
  grid=both,
  xtick={0,60,120,180,240,300},
  xticklabels={Rep.,Locus,Obj.,Data,Time,Human},
  legend columns=3,
  legend style={draw=none, at={(0.5,1.03)}, anchor=south, font=\small},
  tick label style={font=\small},
]
% Lrn, Evo, Sym
\RadarPoly{very thick, mark=*, mark options={solid}, mark size=2pt}{0}{0}{4}{4}{4}{1}
\addlegendentry{\Lrn}
\RadarPoly{densely dashed, very thick, mark=square*, mark options={solid}, mark size=2.2pt}{2}{5}{5}{2}{5}{2}
\addlegendentry{\Evo}
\RadarPoly{dashdotdotted, very thick, mark=triangle*, mark options={solid}, mark size=2.4pt}{5}{4}{4}{5}{3}{5}
\addlegendentry{\Sym}
\end{polaraxis}
\end{tikzpicture}
\caption{Orthogonal axes (0–5) for \Lrn, \Evo, \Sym.}
\label{fig:opt_radar_1}
\end{WideFig}


\begin{WideFig}
\centering
\begin{tikzpicture}
\begin{polaraxis}[
  width=\figureW, height=\figureH,
  ymin=0, ymax=5,
  grid=both,
  xtick={0,60,120,180,240,300},
  xticklabels={Rep.,Locus,Obj.,Data,Time,Human},
  legend columns=4,
  legend style={draw=none, at={(0.5,1.03)}, anchor=south, font=\small},
  tick label style={font=\small},
]
% Prb, Sch, Ctl, Swm
\RadarPoly{very thick, loosely dotted, mark=diamond*, mark options={solid}, mark size=2.2pt}{4}{3}{5}{4}{3}{3}
\addlegendentry{\Prb}
\RadarPoly{densely dashed, very thick, mark=*, mark options={solid}, mark size=2pt}{3}{3}{4}{2}{3}{3}
\addlegendentry{\Sch}
\RadarPoly{dashdotdotted, very thick, mark=square*, mark options={solid}, mark size=2.2pt}{2}{3}{5}{3}{5}{3}
\addlegendentry{\Ctl}
\RadarPoly{solid, very thick, mark=triangle*, mark options={solid}, mark size=2.4pt}{3}{4}{3}{2}{3}{2}
\addlegendentry{\Swm}
\end{polaraxis}
\end{tikzpicture}
\caption{Orthogonal axes (0–5) for \Prb, \Sch, \Ctl, \Swm.}
\label{fig:opt_radar_2}
\end{WideFig}

% ---------------------------
\subsection{Artificial Immune Systems (AIS) in OPT}
% ---------------------------

It is useful to show how OPT-code specifications can be derived for examples of a technique that is a hybrid. 

Artificial Immune Systems (AIS) instantiate computation via biomimetic mechanisms drawn from adaptive immunity. Their operative core combines (i) population-level \emph{variation and selection} (somatic hypermutation, clonal expansion, memory) and (ii) distributed, locally interacting agents (cells, idiotypic networks), often with (iii) probabilistic fusion of uncertain signals. In OPT, this places AIS primarily in \Evo\ and \Swm, with frequent couplings to \Prb\ and occasional \Sch/\Ctl\ layers depending on task and implementation.

\paragraph{Canonical families and OPT placement.}
\begin{itemize}
  \item \textbf{Clonal selection \& affinity maturation (CLONALG, aiNet).} Population of detectors/antibodies $\{a_i\}$ undergo clone--mutate--select cycles driven by affinity to antigens $x$. OPT: \textbf{\Evo+\Swm} (often $+$\Prb).\\
  Affinity (bitstrings; Hamming distance $d_H$): $\mathrm{aff}(x,a)=1-\frac{d_H(x,a)}{|x|}$. Clone count $n_i \propto \mathrm{aff}(x,a_i)$; hypermutation rate $\mu_i=f(\mathrm{aff})$ (typically inversely proportional).
  \item \textbf{Negative Selection Algorithms (NSA).} Generate detectors that avoid ``self'' set $\mathcal S$ and cover $\mathcal X\setminus \mathcal S$. OPT: \textbf{\Evo/\Sch} ($+$\Prb\ for thresholded matching).\\
  Objective: choose $D$ s.t. $\forall d\in D: d\notin \mathcal S$ and coverage $\Pr[\mathrm{match}(x,d)\mid x\notin \mathcal S]\ge \tau$.
  \item \textbf{Immune network models (idiotypic).} Interacting clones stimulate/suppress each other; dynamics produce memory and regulation. OPT: \textbf{\Swm+\Evo} (sometimes $+$\Ctl).\\
  Skeleton dynamics: $\dot a_i=\sum_j s_{ij}a_j-\sum_j \sigma_{ij}a_ia_j-\delta a_i$ with stimulation $s_{ij}$, suppression $\sigma_{ij}$, decay $\delta$.
  \item \textbf{Dendritic Cell Algorithm (DCA) / Danger Theory.} Cells fuse PAMP/danger/safe signals to decide anomaly labeling; aggregation over a population provides robust detection. OPT: \textbf{\Swm+\Prb} (optionally $+$\Evo\ if online adaptation is added).
\end{itemize}

\paragraph{OPT-Code exemplars.}
\begin{quote}\small
\texttt{CLONALG: OPT=Evo+Swm; Rep=bitstring; Obj=affinity; Data=labels$\mid$unlabeled; Time=gens; Human=low}\\
\texttt{aiNet: OPT=Evo+Swm; Rep=realvector; Obj=affinity+diversity; Time=gens}\\
\texttt{NSA (anomaly): OPT=Evo/Sch+Prb; Rep=bitstring; Obj=coverage; Data=self/nonself; Time=gens}\\
\texttt{DCA: OPT=Swm+Prb; Rep=signals; Obj=anomaly-score; Time=online}\\
\texttt{Idiotypic control: OPT=Swm+Ctl; Rep=rules; Obj=stability+coverage; Time=online}
\end{quote}

\paragraph{Where biology and OPT coincide.}
Somatic hypermutation+$\,$selection $\to$ \Evo; massive agent concurrency and local rules $\to$ \Swm; uncertainty fusion (signal weighting, thresholds) $\to$ \Prb; homeostatic regulation $\to$ \Ctl; detector-set coverage and complement generation $\to$ \Sch.

\paragraph{Assurance considerations.}
Key failure modes are coverage gaps (missed anomalies), detector drift, and instability in network dynamics. Assurance suggests (i) held-out self/non-self tests, (ii) diversity and coverage metrics, (iii) stability analysis of interaction graphs, and (iv) calibration of anomaly thresholds (if \Prb). These layer cleanly with risk/management frameworks (NIST RMF, ISO 23053) while OPT communicates mechanism.


% ---------------------------
\section{Discussion: Why OPT Supersedes Signal-Based Taxonomies}
% ---------------------------
\paragraph{Mechanism clarity.} \Lrn–\Swm encode distinct improvement/decision operators (gradient, selection, resolution, inference, search, feedback, collective rules).  
\paragraph{Biological alignment.} OPT mirrors canonical biological mechanisms (plasticity, natural selection, Bayesian cognition, optimal feedback control, etc.).  
\paragraph{Compact completeness.} Seven bins cover mainstream AI while enabling crisp hybrid composition; short names and hybrid syntax convey the rest.  
\paragraph{Governance usability.} Mechanism-aware controls attach naturally per class (Table~\ref{tab:OPT_risk}).

\subsection{Reclassification of Classic Systems}
\begin{table}[htbp]
\centering
\caption{Classic systems: historical labels vs.\ OPT placement (short names only).}
\renewcommand{\arraystretch}{1.1}
\begin{tabular}{@{}p{3.4cm}p{2.7cm}p{2.4cm}@{}}
\toprule
\textbf{System} & \textbf{Prior label} & \textbf{OPT (short)}\\
\midrule
XCON / R1 & Expert system & \Sym \\
CLIPS & Expert shell & \Sym \\
Instar/Outstar & Neural rules & \Lrn \\
Backprop & Supervised NN & \Lrn \\
ART 1/2 & Unsupervised NN & \Lrn \\
LMS/ADALINE & Supervised NN & \Lrn \\
Hopfield–Tank TSP & Neural optimization & \Lrn\;(+\Sch) \\
Boltzmann Machines & Energy-based NN & \Lrn \\
Fuzzy Logic Control & Soft computing & \Ctl\;(+\Sym) \\
Genetic Algorithms & Evolutionary & \Evo \\
Genetic Programming & Program induction & \Evo \\
Symbolic Regression & Model discovery & \Evo\;(+\Sym) \\
PSO & Swarm optimization & \Swm\;(+\Evo) \\
A*/STRIPS/GraphPlan & Search/planning & \Sch\;(+\Sym) \\
Kalman/LQR/MPC & Estimation/control & \Ctl \\
\bottomrule
\end{tabular}
\label{tab:classicOPT}
\end{table}

\subsection{On “Everything is a Spin Glass”: Scope and Limits}
Energy formulations fit symmetric Hopfield/BM subsets but fail to subsume asymmetric architectures, symbolic proof search, population dynamics, or LQG control; complexity frontiers also differ. OPT preserves energy insights without overreach.

% ---------------------------
\section{Conclusion}
% ---------------------------
OPT provides a formal, biologically grounded taxonomy that clarifies mechanisms and hybrids and supports governance. We encourage standards bodies to adopt short-name OPT identifiers and hybrid syntax in system documentation.

% ---------------------------
\appendix
\section{OPT-Code v1.0: Naming Convention}
\label{app:optcode}

\paragraph{Purpose.} Provide compact, semantically transparent names that self-identify an AI system’s operative mechanism(s). These are the \emph{only}~ public OPT names; legacy signal types remain descriptive but are not taxonomic.

\subsection*{Roots (frozen set in v1.0)}
\begin{center}
\begin{tabular}{@{}lll@{}}
\toprule
\textbf{Short} & \textbf{Name} & \textbf{Mechanism}\\
\midrule
\Lrn & Learnon & Parametric learning (loss/likelihood/return) \\
\Evo & Evolon & Population adaptation (variation/selection/inheritance) \\
\Sym & Symbion & Symbolic inference (rules/constraints/proofs) \\
\Prb & Probion & Probabilistic inference (posteriors/ELBO) \\
\Sch & Scholon & Search \& planning (heuristics/DP/graph) \\
\Ctl & Controlon & Control \& estimation (feedback/Kalman/LQR/MPC) \\
\Swm & Swarmon & Collective/swarm (stigmergy/distributed rules) \\
\bottomrule
\end{tabular}
\end{center}

\subsection*{Composition syntax}
\begin{itemize}[leftmargin=1.2em]
\item \hyb{A+B}: co-operative mechanisms (e.g., \hyb{Lrn+Sch}).
\item \hyb{A/B}: hierarchical nesting, outer/inner (e.g., \hyb{Evo/Lrn}).
\item \hyb{A\{B,C\}}: parallel ensemble (e.g., \hyb{Sym\{Lrn,Prb\}}).
\item \hyb{[A→B]}: sequential pipeline (e.g., \hyb{[Lrn→Ctl]}).
\end{itemize}

\subsection*{Attributes (orthogonal descriptors)}
Optional, mechanism-agnostic, appended after a semicolon:
\[
\text{\small\tt OPT=Evo/Lrn+Ctl; Rep=param; Obj=fitness; Data=sim; Time=gen; Human=low}
\]
Keys: \texttt{Rep} (representation), \texttt{Locus}, \texttt{Obj}, \texttt{Data}, \texttt{Time}, \texttt{Human}.

\subsection*{Grammar (ABNF)}
\begin{verbatim}
opt-spec   = "OPT=" compose [ ";" attrs ]
compose    = term / compose "+" term / compose "/" term
           / "[" compose "→" compose "]"
           / term "{" compose *("," compose) "}"
term       = "Lrn" / "Evo" / "Sym" / "Prb" / "Sch" / "Ctl" / "Swm"
attrs      = attr *( ";" attr )
attr       = key "=" value
key        = 1*(ALPHA)
value      = 1*(ALNUM / "-" / "_" / "." )
\end{verbatim}

\subsection*{Stability and change control}
\textbf{S1 (Root freeze).} The seven roots above are frozen for OPT-Code v1.0.  
\textbf{S2 (Extensions via attributes).} New nuance is expressed via attributes, not new roots.  
\textbf{S3 (Mechanism distinctness).} Proposals to add a root in a future major version must prove a distinct operational mechanism not subsumable by existing roots.  
\textbf{S4 (Compatibility).} Parsers may accept legacy aliases but must render short names only.  
\textbf{S5 (Priority).} First published mapping of a system’s OPT-Code (with mathematical operator) has naming priority; deviations must be justified.
 
% --- Hybrid ancestry diagram (for readability)
\begin{figure}[htbp]
\centering
\begin{tikzpicture}[
  node distance=8mm and 14mm,
  every node/.style={font=\small},
  mech/.style={rounded corners, draw=black, very thick, inner sep=4pt, align=center},
  hyb/.style={rounded corners, draw=black!60, dashed, inner sep=3pt, align=center},
  ->, >=Latex
]
% Roots
\node[mech] (L)  {\Lrn};
\node[mech, right=of L] (S) {\Sch};
\node[mech, right=of S] (C) {\Ctl};
\node[mech, below=of L] (E) {\Evo};
\node[mech, right=of E] (Y) {\Sym};
\node[mech, right=of Y] (P) {\Prb};
\node[mech, below=of E] (W) {\Swm};

% Hybrids (examples)
\node[hyb, above=6mm of $(L)!0.5!(S)$] (LS) {\hyb{Lrn+Sch}\\ \footnotesize(AlphaZero-type)};
\node[hyb, above=6mm of $(L)!0.5!(C)$] (LC) {\hyb{Lrn+Ctl}\\ \footnotesize(model-based control)};
\node[hyb, below=6mm of $(L)!0.5!(E)$] (EL) {\hyb{Evo/Lrn}\\ \footnotesize(neuroevolution)};
\node[hyb, below=6mm of $(L)!0.5!(Y)$] (LY) {\hyb{Lrn+Sym}\\ \footnotesize(neuro-symbolic)};
\node[hyb, below=6mm of $(P)!0.5!(C)$] (PC) {\hyb{Prb+Ctl}\\ \footnotesize(Bayesian control)};
\node[hyb, below=6mm of $(E)!0.5!(W)$] (EW) {\hyb{Swm+Evo}\\ \footnotesize(swarm-evolution)};

% Edges
\draw (L) -- (LS); \draw (S) -- (LS);
\draw (L) -- (LC); \draw (C) -- (LC);
\draw (E) -- (EL); \draw (L) -- (EL);
\draw (L) -- (LY); \draw (Y) -- (LY);
\draw (P) -- (PC); \draw (C) -- (PC);
\draw (E) -- (EW); \draw (W) -- (EW);
\end{tikzpicture}
\caption{Hybrid “ancestry” diagram: short-name roots (solid) and exemplar hybrids (dashed).}
\label{fig:opt_hybrid_tree}
\end{figure}
