spectra-fourier: add Polar codes mode (channel polarization, SC / SC-list / CA-SCL)

[kkd16]

What

Adds a twentieth mode — Polar — to the existing spectra-fourier-7k9d DSP lab, completing its forward-error-correction pillar with its third and most modern paradigm: Arıkan's channel polarization. Polar codes are the first family proven to achieve the symmetric capacity of any binary-input channel with an explicit, low-complexity construction, and they carry the 5G-NR control channels. Everything is from scratch — no coding libraries.

The change is entirely inside projects/spectra-fourier-7k9d/ (Golden Rule ✓).

New engine — src/lib/polar.ts (~640 lines)

• Transform / encoder — u·F^⊗n as an in-place GF(2) butterfly that is its own inverse; transformStages snapshots each stage for the encoder animation.
• Two frozen-set constructions — the Bhattacharyya recursion on the erasure channel (z⁻=2z−z², z⁺=z²) and the Gaussian approximation of density evolution on BI-AWGN (mean LLR through the Chung–Richardson–Urbanke φ-function with a bisection inverse). channelCapacities maps both onto one [0,1] capacity axis.
• SC decoder — the recursive f (exact stable box-plus or min-sum) / g message schedule.
• SC-list decoder (Tal–Vardy) — the L best paths carried through the same f/g recursion, ranked by the LLR path metric PM += softplus(−(1−2û)·L), pruned to L via a survivor-map that each recursion frame applies to remap its own state.
• CRC-aided SC-list — bit-wise CRC-6/8/11; returns the lowest-metric survivor whose info bits check (the 5G decoder).
• Yardsticks — BI-AWGN capacity + binary Shannon limit by adaptive Simpson/bisection, and an adaptive-budget BPSK/AWGN Monte-Carlo waterfall.

New UI — src/modes/Polar.tsx (four deep-linkable tabs)

• Polarization — the capacity staircase sorting every synthetic channel toward 0/1, the self-similar frozen-set map, Σcapacity ≈ N·C shown conserved.
• Encoder — the F^⊗n XOR butterfly with a live message flowing through the stages.
• Decode — one noisy word decoded three ways (greedy SC vs best-metric SCL vs CA-SCL), with the ranked survivor list, path-metric bars and CRC flags.
• Waterfall — SC · SCL L=2/8 · CA-SCL L=8 racing uncoded BPSK toward the Shannon line.

Wired into src/App.tsx nav; styles added to src/index.css.

Verification

• 8 new self-tests (119 → 127, all green) in src/lib/selftest.ts: the transform is an involution; SC recovers a clean word; SCL(L=1) ≡ SC bit-for-bit; the CRC self-verifies and catches a flip; BLER SC ≥ SCL(8) ≥ CA-SCL(8) at a fixed SNR; BLER monotone in SNR; BI-AWGN rate-½ Shannon limit ≈ 0.19 dB; the GA φ is a decreasing bijection.
• Standalone engine bundle: 17 assertions pass, e.g. N=128 K=64 @2 dB BLER SC=0.128 → SCL8=0.059 → CA-SCL8=0.041.
• CI gate (scope + conformance + lint + build) ✓ — 85 modules.
• Full self-test suite 127/127 in ~19 s.
• Drove every Polar tab in headless Chromium (DevTools protocol): all four render, tabs switch, canvases paint, reroll works, zero console/runtime errors.

JOURNAL.md and project.json updated (v16 plan + shipped checklist + session log; card copy bumped to twenty modes with polar tags).

🤖 Generated with Claude Code

https://claude.ai/code/session_011n7XWZKS8M3TYCgMT6y4KV

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Generated by Claude Code

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✅ Scope + lint + build passed.