Checkpoint the party/runtime stack before share-program and malicious-mode work.

Ship the TLS mesh, composer, Beaver/Yao/leaf MPC, prep/online paths, apps, and docs so the tree is pushable before elevating share_expr, security_mode, and prep resume.

Co-authored-by: Cursor <cursoragent@cursor.com>

examples/grotto/jet_and_ring.cpp

@@ -0,0 +1,98 @@
+#include <cstdint>
+#include <iostream>
+#include <vector>
+
+#include "grotto.hpp"
+
+/// Binomial jet readouts and an exact ring switch from one public offset.
+int main()
+{
+    //! [jet-and-ring]
+    // --- Binomial jet -------------------------------------------------------
+    // After eta opens, the jet is the binomial basis at the wrapped
+    // center+kappa. Degree 3 leaves room for a degree-2 hockey-stick prefix.
+    const std::uint8_t center = 12;
+    const std::uint8_t eta = 3;
+    const std::uint8_t point = static_cast<std::uint8_t>(center + eta);  // 15
+    const std::size_t degree = 3;
+    auto jet_keys = grotto::make_offset_jet_keys<std::uint8_t>(center, degree);
+    // f(t) = 4 + 2 C(t,1) + C(t,2)  (padded to degree 3).
+    const std::vector<std::uint64_t> poly{4, 2, 1};
+    std::vector<std::uint64_t> coeff = poly;
+    coeff.push_back(0);
+    const std::vector<std::uint8_t> knots{0};
+
+    const auto j0 = grotto::offset_jet_shares<0>(jet_keys, knots, eta);
+    const auto j1 = grotto::offset_jet_shares<1>(jet_keys, knots, eta);
+    std::vector<std::uint64_t> jet(degree + 1);
+    for (std::size_t k = 0; k <= degree; ++k)
+        jet[k] = j0[k] + j1[k];
+
+    const std::uint64_t value = grotto::offset_jet_dot(coeff, jet);
+    const std::uint64_t diff = grotto::offset_jet_dot(
+        grotto::offset_jet_difference_coeff(coeff), jet);
+    const std::uint64_t prefix = grotto::offset_jet_dot(
+        grotto::offset_jet_prefix_coeff(poly), jet);
+
+    // Padé / Newton are public dots against the same jet, then one reciprocal
+    // after the shares are opened. For a seed p(t)/p'(t):
+    //   auto num = offset_jet_dot(coeff, jet);
+    //   auto den = offset_jet_dot(offset_jet_difference_coeff(coeff), jet);
+    //   // open num, den; one masked reciprocal; Newton: t - num/den.
+
+    // --- Exact ring switch --------------------------------------------------
+    // Same public-offset pattern: eta = x - r, then x lands in the residue.
+    const std::uint8_t r = 200;
+    const std::uint8_t x = 44;
+    const std::uint8_t ring_eta = static_cast<std::uint8_t>(x - r);  // 100, wraps
+    using Z = grotto::zn64<1009>;
+    auto ring = grotto::make_ring_switch_keys<Z>(r);
+    const Z x_mod = grotto::ring_switch_eval<0>(ring, ring_eta)
+        + grotto::ring_switch_eval<1>(ring, ring_eta);
+
+    auto field = grotto::make_ring_switch_keys<dpf::field128>(r);
+    const dpf::field128 x_field = grotto::ring_switch_eval<0>(field, ring_eta)
+        + grotto::ring_switch_eval<1>(field, ring_eta);
+    //! [jet-and-ring]
+
+    auto c = [](std::uint64_t t, unsigned k) {
+        return grotto::offset_jet_binom(t, k);
+    };
+    const std::uint64_t expect_v =
+        4 + 2 * c(point, 1) + c(point, 2);
+    if (value != expect_v)
+    {
+        std::cerr << "jet value\n";
+        return 1;
+    }
+    const std::uint64_t expect_fx1 =
+        4 + 2 * c(static_cast<std::uint8_t>(point + 1), 1)
+          + c(static_cast<std::uint8_t>(point + 1), 2);
+    if (diff != expect_fx1 - expect_v)
+    {
+        std::cerr << "jet difference\n";
+        return 1;
+    }
+    std::uint64_t expect_p = 0;
+    for (std::uint8_t i = 0; i < point; ++i)
+        expect_p += 4 + 2 * c(i, 1) + c(i, 2);
+    if (prefix != expect_p)
+    {
+        std::cerr << "jet prefix\n";
+        return 1;
+    }
+    if (x_mod.raw() != static_cast<std::uint64_t>(x) % 1009)
+    {
+        std::cerr << "ring zn64\n";
+        return 1;
+    }
+    if (x_field != dpf::field128{x})
+    {
+        std::cerr << "ring field128\n";
+        return 1;
+    }
+
+    std::cout << value << " " << diff << " " << prefix << " "
+              << x_mod.raw() << "\n";
+    return 0;
+}