PrimeVisuals

An instrument for seeing structure in the primes — and for hunting structure that current theory doesn't explain.

The default scene is Riemann's explicit formula: the prime staircase ψ(x) assembling out of zeta-zero waves as you raise the zero count. From there: drag math ops onto any axis (transform chips), subtract the best-known prediction (RESIDUAL), compare against Cramér pseudoprimes (TWIN), check persistence and holdout at growing range (×2×4×8), and run the anomaly scanner — a worker that sweeps residue classes, exponential-sum angles, and gap correlations, then re-scores every candidate on an unseen range of primes. Every view is a shareable URL; pinned finds live in the notebook with OEIS lookup links.

The ATLAS mode is the repo-wide theory map: primes sit at the center, surrounded by operations, mathematical frameworks, proved results, open conjectures, project programs, and named proof obstructions. Search and status lenses expose typed connections, while dashed “open bridge” edges state the missing lemma or comparison theorem instead of treating visual proximity as evidence.

User guide

See HOW_TO_USE.md for a practical guide to the controls, presets, and what each dot represents. ROADMAP.md tracks what is built and what comes next. THEORY_MAP.md defines how the Atlas evolves without mixing mathematical truth status with the lifecycle of this project’s experiments.

MACHINE_HOW_TO_USE.md documents the headless interface for AI coding agents: scripts/explore.mjs evaluates any pipeline without a browser, scores its shape (linearity, flatness, oscillation), and emits shareable links — so you can hand your IDE a goal like "find another straight line by a different route" and open whatever it finds.

Run locally

npm install
npm run dev

Then open http://localhost:5173/.

Tests

npm test

Unit tests cover the number-theory kernel (sieves, Möbius, ζ on the critical line, the explicit formula), the expression engine, the statistics battery, and the anomaly scanner, plus jsdom interaction tests of the UI. scripts/verify.mjs drives a headless Chromium through the main flows (requires npx playwright install chromium and a running dev server). scripts/genzeros.mjs regenerates the bundled zeta-zero table.

Crack atlas

The systematic prime crack-hunt runner is available as npm scripts:

npm run crack:quick   # smoke-test the full plan/run/audit/pack loop
npm run crack:plan    # freeze the cycle manifest
npm run crack:run     # discovery sweep
npm run crack:audit   # holdout and hostile controls
npm run crack:pack    # evidence pack

Artifacts are written to logs/crack-atlas/.

FrontierLab

The residual-first Chowla/Liouville atlas is available as:

npm run frontier:liouville

It builds C_h(N)=sum_{n<=N} lambda(n)lambda(n+h) across shifts and dyadic ranges, compares against random completely multiplicative and shuffled nulls, calibrates against F_2[t] and F_3[t], and writes JSON, Markdown, and SVG evidence packs to logs/frontierlab-artifacts/.

Build for production

npm run build
npm run preview

The production build is written to dist/.

Deploy

Use a static hosting target. The usual settings are:

• Build command: npm run build
• Output directory: dist
• Install command: npm install

Vercel, Netlify, Cloudflare Pages, GitHub Pages, S3, and similar static hosts can serve the built dist/ folder.