Capacity Architecture: Independent Processing Channels and Their Predictive Power

Scope and Evidence Status

This synthesis consolidates findings from two formula-verification studies conducted on the Icosa personality model’s capacity architecture. Both studies used computationally generated profiles (N = 1,000 each) scored through the complete Icosa engine pipeline. The evidence is entirely synthetic: the studies characterize the behavior of the model’s scoring arithmetic, not human personality outcomes. No human participants were assessed, no clinical samples were tested, and no diagnostic or treatment claims follow from this work.

The two studies together produced 12 hypothesis tests, all of which reached final reportable significance with large effect sizes after Holm-Bonferroni correction. Two of the 12 carry explicit circularity governance flags (disposition: expected_formula_check) and are reported as implementation fidelity checks rather than independent discoveries. Zero nulls, zero below-threshold findings, zero exploratory-only positives, and zero not-evaluable results were observed across the combined program. That uniformity is itself a datum that requires interpretation: in synthetic benchmarking, universal confirmation may reflect either genuine architectural coherence or insufficient adversarial coverage of the profile space.

The synthesis that follows is organized around four questions: Does the engine faithfully transmit capacity-level and domain-level health into its Coherence? Do the four capacity rows produce distinct variance signatures beyond what the formula guarantees? Do row-level and column-level health indices co-vary, and if so, through what structural mechanism? And what does the complete absence of null findings mean for the benchmark’s coverage?

Study Inventory and Design

Study 1: Capacity and Domain Health as Predictors of Coherence (study ID: capacity-health). This study tested whether the Icosa engine’s Coherence faithfully reflects capacity-row and domain-column health aggregates, and whether individual capacity rows produce emergent variance effects on trap vulnerability and gateway bonus. Eight hypotheses were tested: two formula-verification regressions (Capacity Health and Domain Health predicting Coherence) and six Spearman rank correlations examining variance and domain-specific health effects on trap count and gateway bonus. Evidence type: formula verification. Circularity audit: two findings flagged as expected_formula_check (H1 and H5), both resolved with no action required. Signal profile: 8 reportable, 0 null, 0 below threshold.

Study 2: Cross-Axis Health Interactions (study ID: capacity-interaction). This study tested whether Capacity Health values co-vary across rows and Domain Health values co-vary across columns. Four Pearson correlations examined selected pairings: Open-Focus (capacity axis), Physical-Emotional, Physical-Mental, and Emotional-Relational (domain axis). Evidence type: formula verification. Circularity audit: no flags. Signal profile: 4 reportable, 0 null, 0 below threshold.

Both studies used fixed random seeds for reproducibility and applied Holm-Bonferroni correction within their respective hypothesis families. All 12 results also survived program-level FDR correction across a broader family of 436 tests.

Formula Fidelity: Governed Overlap Checks

Two analyses carry explicit circularity governance and must be reported as implementation checks rather than independent findings.

Capacity Health to Coherence (H1, Study 1). Multiple regression of Coherence on the four Capacity Health scores (Open, Focus, Bond, Move) was significant, F(4, 995) = 167.33, p < .001, R^2 = .402. Together, the four capacity rows accounted for 40.2% of Coherence variance. This is a governed overlap: Capacity Health aggregates are explicit inputs to the Coherence computation. Confirming this relationship establishes that the engine’s aggregation pipeline transmits capacity-level health information into the Coherence without silent distortion, saturation, or dropout.

Domain Health to Coherence (H5, Study 1). Multiple regression of Coherence on the five Domain Health scores (Physical, Emotional, Mental, Relational, Spiritual) was significant, F(5, 994) = 151.37, p < .001, R^2 = .432. Domain Health explained 43.2% of Coherence variance, slightly exceeding the capacity model. This is also a governed overlap check with the same interpretive constraint.

The fact that both models explain roughly 40% of Coherence rather than approaching 100% is architecturally informative. The remaining variance is attributable to non-health components of the Coherence formula: asymmetric penalties for over- versus under-engagement, Gateway State contributions, and cross-center interaction terms. A scoring system whose integration metric reduced to a weighted average of axis health would be trivially predictable from these inputs. The moderate R^2 values confirm that the Coherence computation integrates health with structurally more complex features, as designed.

The regression coefficients provide a secondary diagnostic. In the capacity model, Bond Health carried the largest coefficient (0.424), followed by Focus (0.331), Open (0.290), and Move (0.225). In the domain model, coefficients were more uniform: Physical (0.280), Relational (0.267), Emotional (0.263), Spiritual (0.261), Mental (0.233). The capacity model’s steeper coefficient gradient indicates that Bond Health exerts disproportionate marginal influence on Coherence relative to the other rows, a property worth monitoring across engine versions for unintended drift.

Because both analyses are governed overlap checks, they cannot be cited as evidence that capacity or domain health “predicts” Coherence in any discovery sense. They verify implementation fidelity: the engine does what its formula specifies.

Emergent Variance Signatures: Capacity Rows as Distinct Risk Channels

Six hypothesis tests in Study 1 examined relationships that are not guaranteed by the Coherence formula. These are the synthesis’s primary contribution, because they reveal emergent structural properties of the engine’s trap and gateway architecture.

Open variance and trap vulnerability. Open Capacity variance (the spread of health across the five Open centers: Sensitivity, Empathy, Curiosity, Intimacy, Surrender) positively predicted Trap Count, r_s(998) = .59, p < .001. Profiles with uneven receptivity across domains activated more traps. The mechanism, as characterized in the study’s discussion, runs through the Open row’s gateway infrastructure: when receptivity is high in some domains but suppressed in others (e.g., high Empathy but low Sensitivity), the engine generates feedback loops like Empathic Overwhelm and Sensory Shutdown that lock opposing Open centers into dysfunctional states.

Bond variance and trap vulnerability. Bond Capacity variance similarly predicted Trap Count, r_s(998) = .55, p < .001. Uneven connective expression across domains (e.g., strong Belonging but fragmented Identity) produced traps spanning the Bond row. The effect was slightly smaller than Open’s, consistent with the structural expectation that Bond operates at the integration stage rather than the intake stage.

Move variance and gateway bonus. Move Capacity variance was negatively associated with gateway bonus, r_s(998) = -.60, p < .001. This was the study’s most directionally informative finding. More uniform Move expression across domains facilitated greater gateway bonus accrual, while domain-specialized peaks in expressive capacity reduced it. The mechanism aligns with the model’s geometry: Gateways sit at specific Capacity x Domain intersections, and uneven Move expression pushes some gateway-relevant centers past their optimal range while leaving others underpowered. Balanced expression, not peak expression, optimizes gateway access.

Physical Domain Health and trap count. Physical Domain Health was negatively associated with Trap Count, r_s(998) = -.61, p < .001. This is consistent with the Physical column’s anchoring role in the grid: the Body Gate (Open x Physical) serves as the escape route for 12 of the 50 traps, more than any other gateway. When the Physical Domain degrades, this critical escape pathway narrows and trap activation escalates.

Relational Domain Health and trap count. Relational Domain Health showed the strongest negative association with Trap Count among the domain-axis tests, r_s(998) = -.66, p < .001. The Relational column houses four centers (Intimacy, Attunement, Belonging, Voice) that collectively gate interpersonal feedback loops. Degraded relational health constrains the Belonging Gate and Voice Gate simultaneously, closing escape routes for traps distributed across the Bond and Move rows.

Spiritual Domain Health and gateway bonus. Spiritual Domain Health positively predicted gateway bonus, r_s(998) = .70, p < .001 — the largest single effect across both studies. The Spiritual column sits at the culmination of the Domain progression from Physical through Meaning. Healthy Spiritual scores indicate that the system’s meaning-making architecture is functioning, which in the Icosa model enables the higher-order integration patterns that unlock multiple gateways simultaneously.

Taken together, these six findings establish that within the engine’s computational logic, capacity rows are not interchangeable risk channels. Open and Bond variance predict trap vulnerability through structurally different pathway families. Move variance predicts gateway access through a balance mechanism rather than a magnitude mechanism. And along the domain axis, Physical and Relational columns anchor trap-escape infrastructure while the Spiritual column anchors gateway-bonus accrual. Each row and column contributes a structurally distinct variance signature to system-level outcomes.

Cross-Axis Coupling: Shared Variance Without Shared Formulas

Study 2 established that the Icosa engine’s row-level and column-level health indices co-vary substantially despite being defined as orthogonal organizing principles. All four tested pairings produced large correlations:

The Open-Focus coupling was the strongest. These two capacities occupy the first half of the processing sequence (receive, then discern) and share more gateway infrastructure than any other capacity pair. The Body Gate (Open x Physical) serves as the escape route for 12 traps, most falling in the Open and Focus rows. The Choice Gate (Focus x Mental) anchors 15 trap escape routes spanning all four capacities. When Open Capacity is healthy, the Body Gate tends toward an open state, which in turn releases Focus-row traps. This creates a structural conduit: Open health facilitates Focus health not through any direct formula dependency, but through the gateway-trap architecture that links them. The correlation is an emergent property of the model’s geometry rather than a hardcoded parameter.

Domain Health correlations follow a parallel logic along the column axis. The Physical-Emotional pairing (r = .57) likely reflects the density of basins spanning both domains (e.g., Affective Shutdown involves centers in both columns). The slightly weaker Physical-Mental (r = .55) and Emotional-Relational (r = .53) correlations are consistent with fewer shared basins and gateways between those domain pairs.

The coupling pattern — shared but not redundant, with 28-37% shared variance leaving 63-72% unique to each axis — is consistent with what network approaches to personality would predict for a system with densely interconnected nodes. Rather than positing a general health factor causing all axes to co-vary, the Icosa model treats the gateway system and basin architecture as structural channels through which dysfunction or wellness propagates. This is network-mediated coupling, not latent-factor saturation, and the distinction carries implications for path planning algorithms that assume row-level interventions have row-local effects.

Null and Below-Threshold Findings

None. Across 12 hypothesis tests spanning two studies, every result reached final reportable significance with large effect sizes. No hypotheses were reclassified during multiple-comparison correction. No findings fell below the practical significance threshold (r >= .10 or R^2 >= .10).

The complete absence of null findings warrants explicit discussion rather than silent celebration. In synthetic benchmarking of a deterministic computational model, universal confirmation can arise for at least three reasons: (1) the engine’s architecture reliably produces the tested relationships across the full profile space, (2) the hypothesis set was conservative and only tested relationships likely to hold, or (3) the random-uniform profile distribution does not adequately stress the scoring system’s edge cases. All three likely contribute here. The studies tested structurally motivated hypotheses about a system whose trap and gateway mechanics create strong dependencies between health, variance, and integration metrics. The uniform profile distribution covers the score space broadly but does not concentrate on boundary regions (e.g., profiles where all centers cluster near 50, or profiles with extreme within-row divergence) where null results might emerge.

This is a gap in adversarial coverage, not a flaw in the studies. It means the current benchmark establishes that the engine behaves as expected across the broad middle of its profile space, but it has not yet probed the regions where the architecture might fail, saturate, or behave unexpectedly.

Architectural Implications

Three architectural properties emerge from the combined findings.

Property 1: Coherence is multi-component, not axis-reducible. The 40-43% R^2 from axis health alone confirms that Coherence integrates health with gateway states, asymmetric penalties, and interaction terms. This validates the formula’s multi-component design but also means that Coherence changes cannot be attributed to any single axis without decomposing the remaining 57-60% of variance. Future engine modifications that increase the weight of any one component (e.g., amplifying gateway contributions) will shift the axis-health R^2 proportionally, and the current 40-43% serves as a baseline for detecting such drift.

Property 2: Within-row variance is an independent risk dimension. The variance-trap findings (Open r_s = .59, Bond r_s = .55) and the variance-gateway finding (Move r_s = -.60) establish that row-level variance carries information about trap vulnerability and gateway access that is not captured by row-level health alone. A profile with adequate Open health but high Open variance can be trap-vulnerable in ways that a health-only assessment would miss. This has direct implications for the Centering Path algorithm: variance reduction should be a distinct optimization target alongside health improvement, and the two targets may sometimes conflict (e.g., raising the weakest center in a row reduces variance but may not maximize overall row health if the marginal gain is small).

Property 3: Cross-axis coupling is gateway-mediated and non-uniform. The Open-Focus coupling (r = .61) is substantially stronger than any domain-axis pairing (r = .53-.57), suggesting that the capacity axis has tighter structural interdependence than the domain axis. This is consistent with the gateway architecture: the Body Gate and Choice Gate bridge Open and Focus through shared trap-escape infrastructure, creating a propagation channel that has no equally dense counterpart on the domain axis. Centering Path algorithms that target one capacity row should model the spillover to adjacent rows, particularly the Open-Focus pair, where intervening on one row is likely to produce measurable movement in the other.

Circularity Governance Summary

Two of the 12 findings (H1 and H5 in Study 1) are governed by circularity audits with disposition expected_formula_check. Both involve regressing Coherence on axis health aggregates that are explicit inputs to the Coherence formula. These results verify implementation fidelity — confirming that the pipeline transmits what it claims to transmit — but they cannot serve as evidence of independent predictive validity. The remaining 10 findings have no circularity flags and represent emergent properties of the engine’s trap, gateway, and basin architecture that are not guaranteed by any single formula.

No findings in either study received a shared_anchor_benchmark or disallowed circularity disposition. The audit infrastructure detected the two expected overlaps and correctly classified them, and no unresolved circularity issues remain.

Limitations

Four limitations constrain interpretation.

Synthetic data only. All 1,000 profiles per study were computationally generated. The observed relationships characterize the Icosa engine’s scoring behavior, not human personality structure. Whether the variance-trap relationships, the Spiritual Domain gateway effect, or the cross-axis coupling patterns replicate in human samples is an open empirical question.

Uniform profile distribution. Random-uniform sampling provides broad coverage of the score space but does not reflect population prevalence of specific configurations. Clinically common profiles (e.g., depression-like patterns with concentrated low scores in the Emotional and Relational columns) may be underrepresented, and the engine’s behavior in those regions may differ from what uniform sampling reveals.

Incomplete cross-axis mapping. Study 2 tested 4 of the 16 possible pairings (6 capacity pairs + 10 domain pairs). The full correlation matrix remains uncharacterized. Pairs not yet tested — particularly Bond-Move on the capacity axis and Mental-Spiritual on the domain axis — may show weaker or stronger coupling than the tested pairs, and the current synthesis cannot generalize to the full topology.

No stratification by integration level. Neither study stratified results by Coherence Band (Severe, Burdened, Strained, Steady, Thriving). Cross-axis coupling might tighten under severe dysfunction (where basin entrainment dominates) and loosen in high-Coherence profiles (where open gateways no longer constrain propagation). Without stratification, the reported correlations are averages across all integration levels and may mask regime-dependent variation.

Research Priorities

The following priorities are ordered by their expected yield for the Icosa research program.

Priority 1: Hierarchical Coherence decomposition. A hierarchical regression entering health, variance, gateway, and penalty terms sequentially would decompose the Coherence formula’s relative weighting of each component and identify redundancies that could simplify the formula without sacrificing fidelity. The current 40-43% R^2 for axis health leaves 57-60% unexplained, and knowing how much of that residual belongs to gateways versus penalties versus interaction terms would inform both engine optimization and narrative report generation.

Priority 2: Coherence Band stratification. Rerunning the cross-axis coupling analyses (Study 2) stratified by Coherence Band would test whether the coupling documented here is a stable engine property or a regime-dependent phenomenon. If coupling tightens in the Severe band, it would indicate that basin entrainment creates a “everything degrades together” dynamic that has implications for Centering Path sequencing at low integration levels.

Priority 3: Complete cross-axis correlation matrix. Extending Study 2 to all 6 capacity pairs and all 10 domain pairs would map the full topology of structural coupling in the engine. Specific predictions can be tested: the Bond-Move pairing should show weaker coupling than Open-Focus if fewer gateways bridge those rows, and the Mental-Spiritual pairing should show distinctive coupling if the meaning-making architecture creates a unique propagation channel.

Priority 4: Center-pair resolution within rows. Study 1 collapsed within-row variance into a single statistic. Examining which specific center pairs drive the variance-trap relationship (e.g., does Open variance matter most when Empathy and Sensitivity diverge, or when Curiosity and Surrender diverge?) would map the trap-vulnerability landscape at finer resolution and directly inform Centering Path center-selection heuristics.

Priority 5: Persona-based replication. Both studies used random profiles. Replicating the key findings with persona-based profiles — where center scores cluster around clinically meaningful configurations — would test whether the emergent relationships hold, strengthen, or attenuate when the profile space is constrained to psychologically coherent patterns. This is the necessary bridge between synthetic benchmarking and eventual human-data validation.

Priority 6: Adversarial edge-case profiling. The absence of null findings across 12 tests suggests insufficient adversarial coverage. Targeted profile sets designed to stress the engine’s boundary conditions — flat profiles (all centers at 50), maximally polarized profiles (alternating 0 and 100 within rows), and single-row-degraded profiles — would probe regions where the current benchmark has not reached and are more likely to surface nulls, saturation effects, or unexpected nonlinearities.

Conclusion

The two capacity-architecture studies establish three things within the Icosa engine’s synthetic benchmark. First, the engine faithfully transmits capacity-level and domain-level health into its Coherence, with axis health accounting for 40-43% of Coherence variance and the remainder attributable to gateways, penalties, and cross-center interactions. These are governed overlap checks that verify implementation fidelity. Second, capacity rows produce structurally distinct emergent signatures: Open and Bond variance predict trap vulnerability through different pathway families, Move variance predicts gateway access through a balance mechanism, and the Physical, Relational, and Spiritual columns each anchor different system-level outcomes. These findings are not formula-guaranteed and represent the synthesis’s primary contribution. Third, the engine’s row and column health indices are coupled through gateway and basin architecture rather than through explicit cross-axis formulas, with the Open-Focus pair sharing 37% of variance — a coupling that Centering Path algorithms should model rather than ignore.

No null findings were observed. That result is consistent with the studies’ structurally motivated hypothesis sets and the broad-middle coverage of uniform random profiling, but it also marks a gap in adversarial stress testing that the next research wave should close. The capacity architecture behaves as designed across the profile space that has been tested. The open question is whether it continues to do so at the boundaries.