Prometheus belief vector space — 3D PCA projection

What this is

4,967 active beliefs (99.4% embedding_768 coverage — used over the 384-dim column, which only covers 94.5%), reduced from 768 to 3 dimensions via PCA. The first 3 components carry only ~11% of total variance — treat the 3D plot as illustrative, the numbers below as the evidence.

Domains do not separate in embedding space

Silhouette (cosine) for domain is 0.001 on the full 768 dimensions and -0.10 on the 3D projection — near zero or negative both ways, confirming this isn't a projection artifact. k=15 nearest-neighbor same-domain purity is 56.1% against a 21.4% chance baseline — some signal above chance, but much weaker than the equivalent check on the source /domains chunk corpus (75.1% purity there — see that repo's visualisation for the comparison). authority_tier shows essentially no separation either (silhouette -0.05).

The open question: where does domain signal go during extraction?

Chunks carry meaningfully more retrievable domain structure than the beliefs later extracted from them. This doesn't yet prove the extractor is responsible — plausible alternative causes include generic belief wording from the prompts, evidence-excerpt-to-belief-statement compression, embedding model/preprocessing differences between the two pipelines, cross-domain aggregation, or formulaic language making otherwise-distinct beliefs converge in embedding space.

The decisive next experiment is a paired comparison: embed the same triple — source chunk → exact evidence excerpt → composed belief statement — with the same model, and measure cosine drift by domain, prompt ID/version, and epistemic mode. That would identify where domain signal disappears along the pipeline, rather than guessing at which stage is responsible. Not yet run — flagged here as the recommended follow-up, not a finding.