The Anti-Barnum threshold

What the threshold is

Every Metryval respondent has a coordinate in the 19-dimension PAREN space (Perception 5, Agency 3, Responsiveness 4, Engagement 4, Navigation 3). The Anti-Barnum gate is two simultaneous conditions, both measured against the calibration distribution for the same instrument version:

• On each of the 19 dimensions, compute the deviation of the respondent’s coordinate from the population mean, expressed in standard-deviation units (a z-score).
• The respondent passes the gate if and only if at least 2 of those 17 z-scores have an absolute value of 1.5 or greater.

A respondent who passes is in a region of the space where their pattern is distinguishable from the population mean on multiple independent dimensions.

A respondent who does not pass is closer to the mean than the gate permits for a specific-pattern artifact to defensibly render.

Why 1.5 SD on 2 dimensions specifically

The rule comes from the same four-criterion framework that governs the launch-set Vectyr ship list (criterion C1, the Anti-Barnum guard, in the cardinality decision documented 2026-04-28). Criterion C1 requires a candidate centroid to deviate by ≥1.5 SD on ≥2 facets from the population mean before the centroid earns a place in the launch registry. The respondent-side gate mirrors the centroid-side gate: a respondent whose coordinate satisfies the same condition is demonstrably in a region of the space where a registered centroid lives, not in the dense central region where the measurement signal is too weak to distinguish patterns from shared baseline variance.

The 2-dimension requirement is the load-bearing piece.

A single-dimension deviation, however extreme, is consistent with a wide range of patterns and does not by itself discriminate between them.

Two independent dimensions deviating in concert reduces the probability of accidental recognition by orders of magnitude relative to single-axis extremes.

What the threshold filters

The centroid-coverage audit on a synthetic calibration sample (N=50,000, distribution calibrated against Big Five / HEXACO / Self-Determination Theory parameters, documented 2026-04-26) estimates that approximately 49% of respondents land in the dense central region the Anti-Barnum gate is designed to exclude from specific-pattern rendering. The exact passage rate depends on instrument version, calibration sample, and the specific Vectyr ship list; the synthetic estimate is directional and will be replaced by an empirical estimate post-pilot at N≥1,500.

The high filter rate is not a bug.

It is the rate at which honest personality measurement should refuse to render a specific-pattern artifact, given that the empirical natural cardinality of personality clustering sits at k=3-4 (Asendorpf 1999; Gerlach 2018 at N=1.5M), well below the launch-set cardinality.

The 49% figure is what the gate is for.

What sub-threshold respondents see instead

A sub-threshold respondent does not receive a specific Vectyr attribution. They receive a methodology-explanation variant that:

• Names the coordinate region they occupy (a tier between established patterns, not a registered pattern itself).
• Surfaces the 3 to 5 nearest reference centroids with their distances, framed as orbital references and not as categorical assignments.
• Explains why a specific-pattern artifact would not be defensible at this coordinate, and what data would change that.

The sub-threshold variant is the dominant user experience for a substantial fraction of respondents.

The product architecture treats it as a first-class delivery, not a degraded fallback — the “richer not poorer” rule from the cohort-discovery and between-patterns Read specifications.

What this excludes

The Anti-Barnum gate operates within the consumer self-reflection scope.

It governs whether a specific personality artifact renders for an individual respondent who chose to take the instrument voluntarily.

It does not authorize the instrument for consequential third-party decisions about that respondent.

Selection contexts (hiring, promotion, performance review, comparative ranking) invert the validity conditions the gate assumes; the gate is necessary but not sufficient in those contexts, and the policy answer is structural exclusion of the use case rather than threshold tuning. See Policy Decisions Ledger entry P-01 for the full B2B-selection exclusion rationale.

Limitations

Pre-pilot, the threshold is calibrated against a synthetic distribution.

The synthetic distribution is constructed from published parameters of Big Five, HEXACO, and Self-Determination Theory measures, projected into the PAREN coordinate system; it is a defensible proxy but is not the empirical pilot distribution.

The threshold value (1.5 SD on 2 dimensions) is held constant pre-pilot and re-evaluated against empirical standard deviations at N≥1,500.

Any revision is documented in the Framework Reception Ledger and dated.

The distance metric is Euclidean at launch.

At N≥500 empirical responses with adequate dimensional coverage, the metric transitions to Mahalanobis, which corrects for inter-dimension correlation and gives a more conservative passage rate in correlated regions.

The transition is documented in advance, not back-fit.

The gate is one of several content rules that operate simultaneously.

It is necessary but not sufficient for a Vectyr-pattern artifact to render; the artifact must independently pass the somatic specificity requirement, the banned-vague-qualifier check, and the reference-centroid language constraint, all documented at Methodology / Language constraints.

Cross-references

• Methodology landing— the coordinate-frame and reference-centroid framing the gate operates inside.
• Framework Reception Ledger — per-framework academic-reception status; the calibration sources behind the synthetic distribution live here.
• Methodology / Language constraints — the banned-vague-qualifier list and somatic specificity requirement that operate alongside the Anti-Barnum gate.
• Policy Decisions Ledger entry P-01 — why the gate is not the answer to B2B selection contexts; structural exclusion is.
• Methodology / Transparency — where in the pipeline LLMs are used, and where they are explicitly not.