Geometry of Seeing: series consistency + accuracy pass

[moiseevigor]

Summary

A consistency + accuracy pass over the Geometry of Seeing series (Parts 1–2 and appendices A1–A5), so the prose, the math, and the computed JS figures all agree.

Note on scope: the working tree already contained substantial uncommitted edits to the series before this pass (sn→cn fixes in A5, Python corrections, and edits across A1/A2/A3/Part 1/the project index). Those are included here since they can't be cleanly separated and form one coherent cleanup. The list below is the review-pass portion; the base already carried the rest. Happy to split them if you'd prefer.

Review-pass corrections

Cross-article inconsistencies / math errors

• Figure-eight / first-Maxwell modulus — set to k ≈ 0.909 (the root of 2E(k²)=K(k²)), which is exactly what the figure generator uses (v1_geodesics.js, sr_geodesics_v1.py). Was 0.71 in Part 2 and 0.84/0.85 in A5. Verified by integration: only k=0.909 closes the inflectional elastica to the origin (0.71 lands 3.36 away, 0.84→1.57, 0.85→1.39).
• Abnormality constant ν — Part 2 now uses ν∈{0,1}, normal ν=1, matching the PMP derivation in appendix A3 (was ν∈{0,½}).
• A5 non-inflectional period — corrected to 2K(m) (was 2√m·K(m), which is the pendulum-time rotation period, not the elastica's arc-length period). Now agrees with Part 2. Verified: m→0 gives a circle of circumference π = 2K(0), while 2√m·K → 0.

Figure fixes in A5

• Fig A5.2 (σ-pair) — caption + JS now state/compute the first Maxwell time as 4K(k²) for all k (matching the boxed result), since y_A = 2k(1−cn) ≥ 0 returns to zero only at s = 4K(k²). The old JS looked for a sign change of y_A, but y_A only touches zero, so it could report "no coincidence"; replaced with the analytic value.
• Fig A5.3 (wavefront) — reference modulus corrected to 0.909; cusp onset attributed to 2π = 4K(0) (the smallest period in the swept family) rather than the numerically-wrong "4K(k_c²) ≈ 6.5–7".

Minor

• A4: asymptotic-period comment 16 → 32 to match the code (T ~ 2 log(32/(1−E))).

Verified correct during the review (no change needed)

elliptic-core.js (AGM K(m), descending-Landen ellipj, integrateElastica, the three κ-profiles); the full PMP → Lie–Poisson → pendulum reduction and Casimir C=h₁²+h₃²; both κ=2k·cn and κ=2·dn solving the elastica Duffing equation; closed forms x(s)=2E(am)−s, y(s)=2k(1−cn), θ=θ₀+2·arcsin(k·sn); the A2 contact form α∧dα=−dx∧dy∧dθ; the A1 SE(2) matrix exponential and the E-basis/X-frame index bookkeeping; A4's Legendre relation, K/E table, and T=4K((E+1)/2).

Checks

• All inline <script> blocks pass node --check.
• Key numeric claims re-verified with scipy (figure-eight modulus, non-inflectional closure).

🤖 Generated with Claude Code