feat(american-option): closed-form terminal step + documented boundary-split negative result

[0xC000005]

Summary

Two Dynamic Chebyshev American-put options behind default-off flags, plus a case-study note explaining the boundary Gamma. Companion to the W1 docs in #226 (kink theory + Chebfun ↔ AutoKnots).

W2 — ClosedFormTerminalStep (a real, modest win)

Seed the terminal backward step with the exact one-period European Black–Scholes value instead of quadrature against the kinked payoff. Removes the strike-corner quadrature distortion at the worst-fitted step.

Measured vs the QLNet FD oracle (flag is default-off; these are the variant numbers):

spot	oracle P	quadrature P-err	closed-form P-err
100 (ATM)	6.08824	0.004631	0.003490
105	4.30275	0.002788	0.001561
110	2.98523	0.001428	0.000207

Greeks essentially unchanged (the terminal kink is a strike-corner effect, not the boundary Gamma).

W3 — BoundarySplit (a documented negative result)

Root-find the exercise boundary B0 ≈ 81.86 (Math.NET Brent) and build the first continuation as a 2-piece ChebyshevSpline knotted there. A multi-agent investigation showed this does not help; it is kept default-off purely as a reproducible artifact:

• The kink lives in the price max(payoff, C) (applied exactly outside the interpolant), not in the continuation C, which is a Gauss–Hermite (Gaussian) convolution and therefore smooth at B0.
• Splitting a smooth C resolves no singularity; it only relocates the spot-82 Gamma query onto the clustered Chebyshev piece edge, where the second-derivative differentiation matrix has a measured ~4000× amplification → a non-physical negative Gamma one tick above the knot.
• Refinement destabilizes both paths (the wide-S Gauss–Hermite quadrature loses finite values at high n).

The correct cure is a front-fixing (Landau) transform, pursued as a follow-up (a log-spot variant first).

Docs

New case-study subsection "Why the boundary Gamma is weak, and why splitting there does not help" — smooth-pasting V_SS jump, the measured negative result, W2's win, and front-fixing as the cure.

Tests / gates

EuropeanPutPrice vs BS analytic; closed-form terminal accuracy profile; boundary finder; boundary-split Gamma profile (the negative-result artifact). Full suite 1801 passed, dotnet format clean, docfx 0 warnings / 0 errors.

Notes

• Default behaviour is unchanged (both flags default-off; the OFF path is bit-identical to before).
• Touches the case study, which docs: kink theory + Chebfun↔AutoKnots bridge (W1 of kink/boundary work) #226 also edits — sequence docs: kink theory + Chebfun↔AutoKnots bridge (W1 of kink/boundary work) #226 first, then rebase if there is overlap.

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Codecov Report

❌ Patch coverage is 91.01124% with 8 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...AmericanOptionDynamicChebyshev/DynamicChebyshev.cs	91.01%	5 Missing and 3 partials ⚠️

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