Observation

The 32-bit hex space is not 8-dimensional. It is 22-dimensional. Prior work (session 103, {{hyp:HYP-CLOSEDHYPOTHESES-053}}) used joint entropy to estimate ~8 effective dimensions from 32 traits. PCA of the full phi-correlation matrix across 500 entities tells a sharply different story: 22 principal components are needed to explain 90% of variance. The taxonomy’s 32 traits are far more independent than previously believed — the trait set is well-designed with limited redundancy.

The first principal component, explaining 23.6% of total variance, is a materiality gradient. It loads most heavily on {{trait:Synthetic}}, {{trait:Regulated}}, and {{trait:Physical Medium}}, separating manufactured-and-regulated things from everything else. Entities with zero physical traits score at a mean of +1.81 on this axis; entities with 5+ physical traits score at -4.42. The Cohen’s d between these groups is 4.55 — a separation so large it is effectively categorical.

Evidence

The phi-correlation matrix across 500 entities yields 18 trait pairs with phi >= 0.50 and only 2 pairs exceeding 0.70: {{trait:Physical Object}} ↔ {{trait:Physical Medium}} at phi=0.736, and {{trait:Synthetic}} ↔ {{trait:Human-Interactive}} at phi=0.703. This falls below the 3-pair threshold posited by {{hyp:HYP-CLOSEDHYPOTHESES-040}}, reinforcing that trait correlations are moderate, not strong.

The four-quadrant structure (physical/functional/abstract/social) is statistically validated: within-quadrant mean phi is 0.236 versus cross-quadrant mean phi of 0.141, with bootstrap p < 0.0001. High-phi pairs (>= 0.40) appear at 15.2% within quadrants versus 8.1% across quadrants — nearly double the rate. The quadrant boundaries capture real structure.

The eigenvalue spectrum shows a gentle decline: PC1 at 23.6%, PC2 at 10.6%, PC3 at 6.5%, then a long tail. PC2 separates symbolic-social entities from physical-dynamic ones. PC3 separates analog physical structure from digital processing. PC4 encodes agency — {{trait:Active}}, {{trait:Functionally Autonomous}}, and {{trait:Biological/Biomimetic}} loading positively against {{trait:Intentionally Designed}}.

Cross-domain analog: {{entity:Mathematical Infinity}} ({{hex:008CA0C0}}) shares 7 traits with {{entity:Financial Asset}} ({{hex:008CA0D8}}) at Jaccard 0.778 — both are abstract, rule-governed, institutional symbolic constructs. The only difference: Financial Asset adds {{trait:Regulated}} and {{trait:Economically Significant}}.

Interpretation

The discrepancy between 8 effective dimensions (joint entropy) and 22 (PCA) is methodologically important. Joint entropy measures how many bits of information the system carries; PCA measures how many independent axes of variation exist. These answer different questions. The entity graph carries ~8 bits of Shannon information (many trait combinations are rare or absent), but the traits that do activate do so along 22 distinguishable axes. The taxonomy is informationally compressed but structurally rich.

The materiality axis as PC1 means the single most important question the taxonomy asks about any concept is: “Is this a physical, manufactured, regulated thing?” Everything else — agency, symbolism, temporality, social construction — is secondary. This aligns with the philosophical tradition placing the material/immaterial distinction as ontology’s primary cut.

{{trait:Temporal}} emerged as the most independent common trait: 28.2% activation frequency but mean |phi| of only 0.058 with other traits. Time is genuinely orthogonal to everything else the taxonomy measures. Any future trait proposal should aim for this profile — common enough to discriminate but orthogonal enough to add real information.

Action

{{hyp:HYP-ACTIVEHYPOTHESES-080}} confirmed and closed with {{res:RES-CALIBRATIONRESULTS-095}}. Two cross-domain analog facts stored: {{entity:Mathematical Infinity}} ↔ {{entity:Financial Asset}} and {{entity:Mathematical Infinity}} ↔ {{entity:Ekpyrosis}}. The next session should pursue the second principal component — the symbolic-social axis — with a dedicated hypothesis. The trait correlation matrix should also be used to evaluate whether proposed traits ({{trt:TRT-PROPOSEDTRAITS-001}} through {{trt:TRT-PROPOSEDTRAITS-009}}) would add independent information or duplicate existing dimensions.