artifact: add nearly-orthogonal - #172
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Claim: high-dimensional near-orthogonality / concentration of measure — the geometry behind DiFR's random orthogonal projection fingerprints.
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…scene) A three.js scene visualizing concentration of measure: each point is a random unit vector in R^d placed on a sphere by its exact cosine-to-reference distribution (Var = 1/d). Slide d from 3 to 8192 and the cloud collapses onto the equator orthogonal to a fixed reference — the Johnson-Lindenstrauss geometry behind DiFR's random-projection activation fingerprints. - scene archetype (underrepresented); createScene + attachOrbit, dt-based, disposes all - readout shows measured cosine spread vs exact theory 1/sqrt(d) (they match) - no data.json: exact mathematics generated live, no fabricated/sourced numbers Embeds in the merged article 'The Committed Sample' at its Johnson-Lindenstrauss section (updatedDate + artifacts frontmatter + regenerated index).
blokzdev
marked this pull request as ready for review
July 15, 2026 09:22
blokzdev
enabled auto-merge (squash)
July 15, 2026 09:22
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Artifact:
nearly-orthogonal(three / scene)What it shows. In high dimensions two random vectors are almost always near-orthogonal — the geometric reason DiFR's random orthogonal projection activation fingerprints work (Johnson–Lindenstrauss). Each point is a random unit vector in ℝ^d, placed on a sphere by its exact cosine-to-reference distribution (density ∝ (1−c²)^((d−3)/2), so Var(cos) = 1/d). Slide dimension d (3 → 8192) and the cloud collapses from covering the whole sphere onto the thin equatorial band orthogonal to a fixed reference vector.
attachOrbit), dimension slider (keyboard-accessible native range input), tap to mark the orthogonal plane.Archetype
scene— underrepresented in the catalog (3/137) and the natural fit: the spatial structure (angles on a sphere) is the concept.Data
No
data.json. The quantities are exact mathematics generated live (cosine density / std = 1/√d) — no measured or sourced numbers, so nothing is fabricated. Small-d cosines use exact χ²(d−1); large-d uses the normal approximation (error negligible, and the readout displays measured-vs-theory so honesty is visible).Pairs with (merged)
The Committed Sample: Activation Fingerprints for Verifiable LLM Inference — embedded at its Johnson–Lindenstrauss section (
updatedDate+artifacts:frontmatter + regenerated index). That article's existing artifactthe-activation-receiptshows that fingerprints diverge under quantization; this scene shows why a random orthogonal projection can separate models at all. Complementary, not a duplicate.Verification
npm run check(validate + astro check): 0 errors.npm run build: green (962 pages, pagefind indexed).createScene()+attachOrbit(), all animation dt-based, cleanup disposes every geometry/material/listener/observer.Duplicate check
Scanned all 137 artifacts, open PR #169 (prediction-market fragmentation — unrelated), and open
commission-artifactissues (none). No existing artifact covers high-dimensional geometry / concentration of measure / random projections.Generated by Claude Code