Neuroscience Companion Paper¶

Jean-Paul Niko · February 2026

\begin{center} {\LARGE\bfseries\color{sectionblue} A Geometric Framework for Multi-Type Intelligence:
Filter Operators, Attention Dynamics, and Predictions [3pt] for Neuroimaging}

{\large Jean-Paul Niko} [4pt] {} [2pt] {\smallniko@triptomean.com}

{\small February 2026} \end{center}

Abstract

We present a mathematical framework in which cognitive capacity is represented not by a scalar (such as $g$) but by an intelligence vector $\bI = (I_{\mathrm{ling}}, I_{\mathrm{symb}}, I_{\mathrm{spat}}, I_{\mathrm{kin}}, I_{\mathrm{aud}}, I_{\mathrm{soc}}, I_{\mathrm{intra}}, I_{\mathrm{nat}}) \in \\mathbb{R}^{n(e)}_{\geq 0}$, whose components correspond to distinguishable neural circuit families. Interactions between intelligence types are governed by a symmetric compatibility matrix $\bK \in \R^{8\times 8}$, interpretable as a functional connectivity prediction: $K_{ij} > 1$ predicts positive coupling between circuits $i$ and $j$; $K_{ij} < 1$ predicts competitive inhibition. Attentional allocation evolves on the 7-simplex $\Delta^7$ via replicator dynamics---the same equations governing evolutionary population genetics---and we prove that KL divergence from equilibrium is a Lyapunov function, guaranteeing convergence. Five species of filter operator $\Phi_{\mathrm{env}} \circ \Phi_{\mathrm{dev}} \circ \Phi_{\mathrm{cog}} \circ \Phi_{\mathrm{soc}} \circ \Phi_{\mathrm{cult}}$ transform raw capacity into effective intelligence; each has a characteristic neural timescale from evolutionary ($10^6$ yr) to attentional (ms). We derive a cognitive thermodynamics whose Second Law predicts task-switching metabolic cost, connect the framework to Global Workspace Theory via spectral decomposition of the compatibility matrix, and catalog twelve quantitative predictions testable with existing neuroimaging equipment (fMRI, EEG/MEG, PET).

Keywords: multi-type intelligence, functional connectivity, replicator dynamics, attention simplex, cognitive filters, neuroimaging predictions

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Introduction} %% ═══════════════════════════════════════════════════════════════════════════════

The dominant quantitative tradition in intelligence research relies on a single latent factor---Spearman's $g$---extracted from covariance matrices of cognitive test batteries [spearman1904,carroll1993]. While the positive manifold is a robust empirical phenomenon, collapsing an individual's cognitive profile to one number discards the rich structure that neuroimaging reveals. Functional connectivity analyses show that language, spatial, social, and executive circuits form distinguishable networks with characteristic coupling patterns [yeo2011,bassett2017], yet no algebraic framework maps these networks to a vector-valued intelligence measure whose components can be independently manipulated and whose interactions are formally specified.

This paper introduces such a framework. We define the intelligence vector $\bI \in \\mathbb{R}^{n(e)}_{\geq 0}$ (Section ref:sec:vector), derive the compatibility matrix $\bK$ governing cross-type interactions (Section ref:sec:kmatrix), model attentional dynamics as replicator flow on the simplex (Section ref:sec:attention), introduce filter operators that transform raw capacity into effective intelligence (Section ref:sec:filters), develop a cognitive thermodynamics that predicts metabolic cost (Section ref:sec:thermo), connect the hypervisor construct to Global Workspace Theory (Section ref:sec:gwt), and catalog twelve testable neuroimaging predictions (Section ref:sec:predictions).

Throughout, we mark each result with an epistemic tier: \tA{} for results that are proved or definitional, \tB{} for well-supported models with formal structure, and \tC{} for conjectural extensions.

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The Intelligence Vector} %% ═══════════════════════════════════════════════════════════════════════════════

Intelligence Vector

\tA{} The intelligence vector of an agent $a$ is

\[ \bI(a) = \bigl(I_{\mathrm{ling}},\; I_{\mathrm{symb}},\; I_{\mathrm{spat}},\; I_{\mathrm{kin}},\; I_{\mathrm{aud}},\; I_{\mathrm{soc}},\; I_{\mathrm{intra}},\; I_{\mathrm{nat}}\bigr) \in \\mathbb{R}^{n(e)}_{\geq 0}. \]

Each component $I_t$ is a non-negative real number measured in cognitive units (cog), defined as the capacity to sustain one standard deviation of performance in type-$t$ tasks per unit time.

\[\begin{keyeq} **Key Equation.**\quad $\bI \in \\mathbb{R}^{n(e)}_{\geq 0}$, \quad with components measured in cog units and calibrated via ELO-style pairwise tournaments within each type. \end{keyeq}\]

The eight types are not arbitrary. Each maps to an identifiable neural circuit family:

\begin{center}

[Table — see PDF for formatted version]

\end{center}

\[\begin{intuition} **Neural grounding.**\quad The vector representation predicts that selectively lesioning circuit family $t$ should reduce $I_t$ while leaving other components largely intact---consistent with classical double-dissociation findings [poldrack2006] and the multiple-demand (MD) network literature [duncan2010]. \end{intuition}\]

Relation to CHC and Gardner

\tB{} The eight types subsume the broad abilities of Cattell--Horn--Carroll theory [carroll1993,mcgrew2009] and formalize Gardner's multiple intelligences [gardner1983] by adding algebraic structure: the $\bK$ matrix (Section ref:sec:kmatrix) specifies interactions that neither factor-analytic models nor Gardner's framework provides.

The scalar $\|\bI\| = \sqrt{\sum_t I_t^2}$ recovers an analogue of $g$, but the full vector is strictly more informative. Two agents with identical $\|\bI\|$ may have radically different cognitive profiles---and different neuroimaging signatures.

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The Compatibility Matrix} %% ═══════════════════════════════════════════════════════════════════════════════

Compatibility Matrix

\tA{} The compatibility matrix is a symmetric, positive semi-definite matrix $\bK \in \R^{8 \times 8}$ with entries $K_{ij} \geq 0$, where: [nosep] - $K_{ii} = 1$ (self-compatibility is the identity). - $K_{ij} > 1$: types $i$ and $j$ exhibit synergy---engaging both simultaneously yields superadditive performance. - $K_{ij} < 1$: types $i$ and $j$ exhibit interference---engaging both simultaneously yields subadditive performance. - $K_{ij} = 1$: independence.

\[\begin{keyeq} **Key Equation.**\quad The *effective intelligence* for a task requiring types $i$ and $j$ simultaneously is $I_{\mathrm{eff}}^{(ij)} = K_{ij}\,\sqrt{I_i\, I_j}$. \end{keyeq}\]

Functional Connectivity Interpretation¶

The matrix $\bK$ is directly interpretable as a prediction about functional connectivity. Given the neural circuit assignments in Section ref:sec:vector:

\begin{prediction}[Functional Connectivity from $\bK$] \tB{} Let circuits $C_i$ and $C_j$ be the primary neural substrates for types $i$ and $j$ respectively. Then the resting-state functional connectivity $\mathrm{FC}(C_i, C_j)$ measured by fMRI should correlate positively with $K_{ij}$. Specifically: [nosep] - $K_{\mathrm{spat,symb}} > 1$ predicts positive coupling between dorsal parietal and lateral intraparietal circuits (spatial--algebraic synergy, consistent with mental rotation studies [fox2007]). - $K_{\mathrm{soc,intra}} > 1$ predicts positive coupling between the TPJ and the default mode network (social--reflective synergy). - $K_{\mathrm{ling,kin}} < 1$ predicts weak or negative coupling between Broca's area and motor cortex during dual-task paradigms (speech--motor interference).

\end{prediction}

Synergy and Assembly¶

When multiple intelligence types are engaged simultaneously, the total output of a cognitive assembly is governed by the synergy formula:

Synergy

\tA{} For an assembly $A = \{t_1, \ldots, t_k\} \subseteq \{1,\ldots,8\}$, the synergy is

\[ \Syn(A) = \frac{\sum_{i<j \in A} K_{ij}(I_i I_j)^{1/2}} {\sum_{i \in A} I_i}. \]

An assembly is superadditive if $\Syn(A) > 1$ and subadditive if $\Syn(A) < 1$.

Synergy Well-Definedness

\tA{} Synergy is invariant under permutation of the engine indices within an assembly: $\Syn(\sigma(A)) = \Syn(A)$ for any permutation $\sigma$.

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Attention Dynamics on the Simplex} %% ═══════════════════════════════════════════════════════════════════════════════

An agent does not deploy all eight types simultaneously at full capacity. Attention is allocated across types, and this allocation evolves in time.

Attention Simplex

\tA{} The attention vector is $\lambda = (\lambda_1, \ldots, \lambda_8) \in \Delta^7$, where $\Delta^7 = \{\lambda \in \\mathbb{R}^{n(e)}_{\geq 0} : \sum_t \lambda_t = 1\}$ is the 7-simplex. The effective intelligence under attention allocation $\lambda$ is $\bI_{\mathrm{eff}} = \mathrm{diag}(\lambda)\,\bI$.

Replicator Dynamics

\tA{} Given a task demand vector $\bR \in \\mathbb{R}^{n(e)}_{\geq 0}$ (encoding the task's requirements in each intelligence type), the attention vector evolves according to the replicator equation:

\[ \dot{\lambda}_t = \lambda_t\bigl(f_t(\lambda) - \bar{f}(\lambda)\bigr), \qquad f_t(\lambda) = (\bK\,\bR)_t, \qquad \bar{f}(\lambda) = \sum_t \lambda_t\, f_t(\lambda). \]

\[\begin{keyeq} **Key Equation.**\quad $\dot{\lambda}_t = \lambda_t\bigl(f_t - \bar{f}\bigr)$ on $\Delta^7$. This is the *same* equation governing allele frequency dynamics in evolutionary biology, now governing attentional allocation. \end{keyeq}\]

Lyapunov Convergence

\tA{} The KL divergence $D_{\KL}(\lambda^* \| \lambda(t))$ from the Nash equilibrium $\lambda^*$ is a Lyapunov function: $\frac{d}{dt} D_{\KL}(\lambda^* \| \lambda) \leq 0$, with equality if and only if $\lambda = \lambda^*$.

\[\begin{intuition} **Neural interpretation.**\quad The replicator dynamics on the attention simplex predict that task-switching is not instantaneous: the trajectory from one attentional equilibrium to another follows a geodesic on the simplex (under the Fisher--Shahshahani metric), and the transit time is measurable. EEG/MEG temporal resolution ($\sim$1 ms) should reveal the switching trajectory as a sequence of spectral power shifts across frequency bands associated with different intelligence types. \end{intuition}\]

Bifurcation and Decision¶

Decision as Symmetry Breaking

\tB{} When a task demand changes continuously through a critical value $\mu_c$, the stable attentional equilibrium undergoes a pitchfork bifurcation. Near criticality, the time to resolve the decision scales as:

\[ \tau \sim |\mu - \mu_c|^{-1/2}. \]

This result connects to the well-documented speed--accuracy tradeoff in psychophysics: near-threshold decisions are slow because the dynamical system is near a bifurcation point where the restoring force toward the new equilibrium vanishes.

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Filter Operators} %% ═══════════════════════════════════════════════════════════════════════════════

Raw intelligence is never fully expressed. A cascade of filters transforms $\bI_{\mathrm{raw}}$ into the effective intelligence $\bI_{\mathrm{eff}}$ that actually drives behavior.

Filter Species

\tA{} A filter is a diagonal contraction $\Phi: \\mathbb{R}^{n(e)}_{\geq 0} \to \\mathbb{R}^{n(e)}_{\geq 0}$ of the form $\Phi(\bI) = \mathrm{diag}(\phi_1, \ldots, \phi_8)\,\bI$, where each $\phi_t \in [0,1]$. There are five canonical species, ordered by characteristic timescale: \begin{center}

[Table — see PDF for formatted version]

\end{center}

\[\begin{keyeq} **Key Equation.**\quad The effective intelligence is the pipeline composition: \[ \bI_{\mathrm{eff}} = (\Phi_{\mathrm{env}} \circ \Phi_{\mathrm{dev}} \circ \Phi_{\mathrm{cog}} \circ \Phi_{\mathrm{soc}} \circ \Phi_{\mathrm{cult}}) (\bI_{\mathrm{raw}}). \] \end{keyeq}\]

Filter Composition

\tA{} The composition of any two filters is a filter. Explicitly: $\Phi_2 \circ \Phi_1 = \mathrm{diag}(\phi_1^{(1)}\phi_1^{(2)}, \ldots, \phi_8^{(1)}\phi_8^{(2)})$, and since each $\phi_t^{(1)}\phi_t^{(2)} \in [0,1]$, the result is again a filter.

Kernel Composition

\tA{} $\ker(\Phi_2 \circ \Phi_1) \supseteq \ker(\Phi_1)$. Information loss accumulates monotonically through the filter pipeline.

Pharmacological Filter Predictions¶

The cognitive/state filter $\Phi_{\mathrm{cog}}$ is directly modulated by neuroactive substances. Each substance has a filter signature:

\begin{prediction}[Pharmacological Filter Signatures] \tB{} [nosep] - Caffeine: amplifies $\phi_{\mathrm{symb}}$ and $\phi_{\mathrm{ling}}$ (enhanced symbolic processing and verbal fluency), attenuates $\phi_{\mathrm{kin}}$ (fine motor tremor). The filter is $\Phi_{\mathrm{caff}} \approx \mathrm{diag}(1.05, 1.08, 1.0, 0.95, 1.0, 1.0, 0.98, 1.0)$. - Cortisol (acute stress): amplifies $\phi_{\mathrm{spat}}$ and $\phi_{\mathrm{kin}}$ (fight-or-flight), attenuates $\phi_{\mathrm{symb}}$ and $\phi_{\mathrm{soc}}$ (narrowed executive and social processing). - SSRIs (chronic): modulates $\phi_{\mathrm{soc}}$ and $\phi_{\mathrm{intra}}$ upward (enhanced social engagement and emotional regulation), minimal effect on $\phi_{\mathrm{symb}}$.

Each of these signatures is testable by administering the substance and measuring performance across type-specific cognitive batteries. \end{prediction}

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Cognitive Thermodynamics} %% ═══════════════════════════════════════════════════════════════════════════════

The attention simplex admits a thermodynamic structure that yields metabolic predictions.

Cognitive Entropy and Temperature

\tA{} The cognitive entropy is $S(\lambda) = -\sum_t \lambda_t \ln \lambda_t$. The cognitive temperature is $T_{\mathrm{cog}} = \mathrm{Var}[\lambda \cdot f] / \bar{f}$, measuring the variance of fitness-weighted attention fluctuations. The cognitive free energy is $F_{\mathrm{cog}} = E - T_{\mathrm{cog}}\,S$, where $E = \bar{f}(\lambda)$ is the mean fitness.

Boltzmann Equilibrium on the Simplex

\tA{} The equilibrium attention distribution maximizing entropy subject to a mean-energy constraint is the Boltzmann distribution on the simplex:

\[ \lambda_t^* \propto \exp\!\bigl(f_t / T_{\mathrm{cog}}\bigr). \]

This coincides with the fixed point of the stochastic replicator dynamics at temperature $T_{\mathrm{cog}}$.

\[\begin{keyeq} **Key Equation.**\quad The cognitive *Second Law*: for any spontaneous attentional reallocation, $\Delta S_{\mathrm{cog}} \geq 0$. Task-switching from a low-entropy (focused) state to a high-entropy (diffuse) state is thermodynamically favored; the reverse requires metabolic work. \end{keyeq}\]

Friction Tensor

\tB{} The friction tensor $\bF \in \R^{8\times 8}_{>0}$ encodes the metabolic cost of reallocating attention between types:

\[ W_{\mathrm{switch}} = \sum_{s,t} F_{st}\, |\Delta\lambda_s|\,|\Delta\lambda_t|. \]

High $F_{st}$ means switching between types $s$ and $t$ is metabolically expensive; low $F_{st}$ means cheap.

\[\begin{prediction}[Task-Switching Metabolic Cost] \tB{} The friction tensor predicts that task-switching cost (measured by BOLD signal in fMRI) is *not uniform* across type pairs. Specifically: $F_{\mathrm{ling,spat}} > F_{\mathrm{ling,symb}}$---switching from language to spatial reasoning is more costly than switching from language to symbolic reasoning (because linguistic and symbolic circuits share prefrontal infrastructure while spatial circuits are posterior). This prediction is testable in a block-design fMRI paradigm with calibrated switch points. \end{prediction}\]

Four Laws of Cognitive Thermodynamics¶

By structural analogy with physical thermodynamics (noting these are mathematical analogies, not metaphysical claims):

[nosep] - Zeroth Law: If two cognitive subsystems are each in equilibrium with a third, they are in equilibrium with each other (transitivity of $T_{\mathrm{cog}}$ equalization). - First Law: $dE = \delta W + \delta Q$---changes in cognitive energy equal work done (task performance) plus heat (metabolic dissipation). - Second Law: $\Delta S_{\mathrm{cog}} \geq 0$ for spontaneous processes---attention diffuses unless work is applied to concentrate it. - Third Law: The zero-entropy state ($\lambda = e_t$ for some $t$, complete focus on one type) requires infinite work to maintain---perfect concentration is an asymptotic limit.

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Global Workspace Connection} %% ═══════════════════════════════════════════════════════════════════════════════

Baars' Global Workspace Theory (GWT) [baars1988] posits that conscious access corresponds to information being broadcast to a global workspace. Dehaene and colleagues [dehaene2014] grounded this in the ignition of prefrontal--parietal networks.

In the present framework, the hypervisor is the spectral decomposition of the compatibility matrix:

Hypervisor

\tB{} Let $\bK = \sum_{n=1}^{8} \mu_n\, \mathbf{v}_n\, \mathbf{v}_n^\top$ be the spectral decomposition of the compatibility matrix. A cognitive content enters conscious access when its projection onto the principal eigenvector $\mathbf{v}_1$ exceeds a threshold:

\[ \text{content } c \text{ is conscious} \iff |\langle c, \mathbf{v}_1 \rangle| > \delta. \]

The eigenvectors $\mathbf{v}_1, \ldots, \mathbf{v}_8$ define the modes of cognitive integration, and $\mu_1 / \mu_8$ measures the spectral gap---the dominance of the principal mode.

\[\begin{intuition} **GWT correspondence.**\quad The principal eigenvector $\mathbf{v}_1$ corresponds to the global workspace broadcast mode. Resting-state networks [yeo2011] can be interpreted as the spatial distribution of the principal eigenvectors of $\bK$. The spectral gap $\mu_1 / \mu_2$ predicts the clarity of conscious access: a large gap means one dominant mode (focused awareness); a small gap means competing modes (distractibility or creative diffuse states). \end{intuition}\]

\[\begin{prediction}[Resting-State Eigenmodes] \tC{} The 7 canonical resting-state networks identified by Yeo et al.\ [yeo2011] should correspond approximately to the 8 eigenvectors of $\bK$, with the visual network split between $I_{\mathrm{spat}}$ and $I_{\mathrm{nat}}$ modes. This predicts that individual differences in $\bK$ eigenstructure will correlate with individual differences in resting-state network topology. \end{prediction}\]

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Evolutionary Context} %% ═══════════════════════════════════════════════════════════════════════════════

The human intelligence vector is not given a priori---it is the product of evolutionary selection. Two major findings from comparative cognition ground the evolutionary trajectory:

The social brain hypothesis [dunbar1998] establishes that primate neocortex ratio correlates with social group size, predicting that $I_{\mathrm{soc}}$ was a primary driver of hominid encephalization. In the IAG framework, this means the $K_{\mathrm{soc},*}$ row of the compatibility matrix was under particularly strong selection. Tomasello's shared intentionality framework [tomasello2005] adds that the capacity for joint attention and shared goals---formalized as alignment of $\bR$ vectors across agents---is uniquely elaborated in humans, predicting that human $K_{\mathrm{soc,symb}}$ is unusually high compared to other great apes.

\[\begin{prediction}[Hominid $\bK$ Evolution] \tC{} Comparative analysis of primate functional connectivity should reveal a monotonic increase in $K_{\mathrm{soc,symb}}$ from macaques to chimpanzees to humans, reflecting the co-evolution of social and symbolic intelligence that underlies language, culture, and institutional complexity. \end{prediction}\]

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Twelve Testable Predictions} %% ═══════════════════════════════════════════════════════════════════════════════

We collect twelve predictions derived from the framework, organized by measurement modality.

fMRI Predictions¶

[label=P\arabic., nosep] - $\bK$--FC correlation.\quad Off-diagonal entries of $\bK$ correlate with resting-state functional connectivity between corresponding circuit families (Prediction ref:pred:fc*). \tB{}

Friction asymmetry.\quad Task-switching BOLD cost between type pairs is asymmetric: $F_{\mathrm{ling,spat}} \neq F_{\mathrm{spat,ling}}$, and the asymmetry correlates with structural connectivity asymmetry measured by diffusion tensor imaging. \tB{}
Pharmacological filter signatures.\quad Caffeine, cortisol, and SSRIs produce distinct 8-component filter profiles measurable as differential BOLD response across type-specific tasks (Prediction ref:pred:pharma). \tB{}
Second Law metabolic cost.\quad Switching from focused ($S$ low) to diffuse ($S$ high) attention requires less metabolic work than the reverse, measurable as BOLD signal difference in task-switching paradigms. \tB{}

EEG/MEG Predictions¶

[label=P\arabic., nosep, resume] - Replicator trajectory.\quad Task-switching produces a continuous trajectory through the attention simplex $\Delta^7$, observable as a sequence of spectral power shifts with characteristic time constants matching the replicator dynamics equation (ref:eq:replicator*). \tB{}

Bifurcation scaling.\quad Near-threshold decisions exhibit critical slowing with $\tau \sim |\mu - \mu_c|^{-1/2}$ (Theorem ref:thm:bifurcation), measurable via EEG as increased pre-decision variability. \tB{}
Spectral gap and distractibility.\quad Individuals with smaller $\mu_1/\mu_2$ ratios (smaller spectral gap in $\bK$) should show higher P300 amplitude variance and lower sustained attention performance. \tC{}
Eigenmode signatures.\quad EEG source-localized power in canonical frequency bands should cluster along the principal eigenvectors of $\bK$ during resting state. \tC{}

Behavioral and PET Predictions¶

[label=P\arabic., nosep, resume] - Synergy predicts team performance.\quad For dyads with measured $\bI$ vectors, the synergy formula (Definition ref:def:syn*) predicts joint performance better than the sum or maximum of individual scalar scores. \tB{}

Cross-type transfer.\quad Training type $i$ produces transfer to type $j$ in proportion to $K_{ij}$---spatial training improves algebraic reasoning (if $K_{\mathrm{spat,symb}} > 1$) but impairs social tasks (if $K_{\mathrm{spat,soc}} < 1$). \tB{}
Glucose uptake pattern.\quad PET glucose metabolism during type-specific tasks should show differential uptake patterns corresponding to the circuit families in Definition ref:def:ivec, with switching tasks showing elevated uptake in proportion to $F_{st}$. \tB{}
Filter cascade ordering.\quad Longitudinal studies should reveal that developmental filters ($\Phi_{\mathrm{dev}}$) account for more variance in childhood performance than state filters ($\Phi_{\mathrm{cog}}$), with the ratio reversing in adulthood as $\Phi_{\mathrm{dev}}$ stabilizes. \tB{}

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Three-Space Neuroscience}

The three-space ontology (Part XIII) reframes the neural correlates of consciousness as $\PS$-signatures of instantiation rather than generators of consciousness. The brain does not produce consciousness; it provides the $\PS$-substrate through which consciousness ($\CSp$) projects $\QS$-potentiality into definite experience. Neural correlates are the physical traces of this projection, not its cause. Searching for the "neural basis of consciousness" within $\PS$ alone is structurally analogous to searching for quantum gravity within $\QS$ alone: both are ontological type errors that produce apparent intractability (the explanatory gap, the unrenormalisable infinities) because the single-space domain lacks the structure to pose the question correctly.

Memory Architecture in Three-Space¶

The three-space ontology reveals that the five memory subsystems correspond to distinct algebraic structures:

\begin{center}

[Table — see PDF for formatted version]

\end{center}

The $p$-adic (ultrametric) organization of semantic memory predicts that category-level priming should show discrete jumps rather than smooth distance gradients: items within the same branch of the ultrametric tree should be equally accessible, with a sharp transition to items in different branches. This is testable via reaction-time studies with hierarchically organized stimuli.

Procedural memory is not "stored" in the conventional sense but built into the compatibility matrix $\bK$ through developmental filtering. Learning to ride a bicycle sculpts $K_{\mathrm{spatial,kinesthetic}}$ into a synergistic configuration ($K > 1$) that cannot be "retrieved" as a discrete memory trace because it is the connectivity structure itself.

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Discussion} %% ═══════════════════════════════════════════════════════════════════════════════

The framework presented here differs from existing approaches in three principal ways. First, it replaces scalar intelligence with a vector whose components map to identifiable neural circuits, enabling predictions that no single-factor model can make. Second, it specifies the interaction structure via $\bK$, which is absent from both factor-analytic and multiple-intelligence traditions. Third, the dynamical components (replicator attention, filter pipeline, thermodynamics) yield quantitative predictions about temporal evolution, metabolic cost, and pharmacological response.

Limitations¶

The circuit assignments in Definition ref:def:ivec are coarse: each type spans multiple cortical and subcortical regions, and the one-to-one mapping is a simplification. The diagonal filter assumption (Section ref:sec:filters) excludes cross-type coupling within a single filter; a full treatment would use $8\times 8$ filter matrices, at the cost of greatly expanded parameter space. The pharmacological predictions (Prediction ref:pred:pharma) use illustrative values; empirical calibration requires large-scale dose--response studies.

Relation to Global Workspace and IIT¶

The hypervisor construct (Section ref:sec:gwt) is compatible with GWT [baars1988,dehaene2014] in identifying conscious access with a dominant mode, and with Integrated Information Theory (IIT) [tononi2004] in measuring integration via the spectral structure of $\bK$. The eigenvalue ratio $\mu_1/\mu_8$ is a rough analogue of $\Phi$ (integrated information), though a precise mapping requires further work.

Open Directions¶

Three avenues merit immediate investigation. First, empirical estimation of $\bK$ from large-scale resting-state fMRI datasets [yeo2011] would test whether the eigenstructure predicted by the framework matches observed network topology. Second, combining the filter formalism with computational psychiatry [friston2014] could yield a principled account of how neuromodulatory dysfunction (filter distortion) produces psychiatric symptom profiles. Third, the replicator dynamics (Theorem ref:thm:replicator) make millisecond-resolution predictions testable with MEG, particularly regarding the trajectory of attentional switching and the bifurcation timescale near decision thresholds.

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Conclusion} %% ═══════════════════════════════════════════════════════════════════════════════

We have presented a geometric framework for intelligence in which cognition is characterized by an variable-dimensional vector, cross-type interactions are specified by a compatibility matrix with direct functional connectivity interpretations, attention evolves via replicator dynamics with provable convergence, five species of filter transform raw capacity into effective intelligence, and a cognitive thermodynamics predicts metabolic cost. The framework generates twelve quantitative predictions testable with existing neuroimaging equipment. If even a subset of these predictions survives empirical scrutiny, the vector representation of intelligence would constitute a significant advance over scalar models for neuroscience.

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References¶

See PDF for full bibliography.¶

v2 Integration: Entity Dimensionality & Neural Complexity (TMP-20260217)¶

The entity dimensionality measure maps directly onto neural architecture:

\[\text{dim}(n) = |\{k \in \{1,\ldots,8\} : \mathbf{I}_k(n) \geq \theta_k\}|\]

A single-circuit neuron has dim = 1. A concept like "emotion" spanning somatic, social, linguistic, and temporal circuits has dim ≥ 4 — providing a principled complexity measure grounded in I-vector activation count, not connection count alone.

Document ≅ Mind ≅ Brain (Theorem 6): At the neuronal level, synaptic weights form a relation matrix isomorphic to the RTSG SynergyTensor. Mind, Document, and Brain are isomorphic RTSG graphs at appropriate granularity, connected by structure-preserving functors. The morphism Brain → Mind is the aggregation functor mapping synaptic graphs to concept graphs.

Intelligence fingerprinting: From a sufficiently rich neural activation corpus C(ξ), the intelligence vector I(ξ) is recoverable via IdeaRank analysis — the neural instantiation of the cognitive fingerprinting pipeline.