"""Boundary and seeded-error checks for Chapters 5, 10, 18, 22 and 24.

Run from the repository root:

    uv run python content/examples/math/tool-chapters/ch05_10_18_22_24_checks.py

Illustrative checks. They are not claim-bound EvidenceResults.
"""

from sympy import Rational, simplify, sqrt, symbols
import z3

print("sympy", __import__("sympy").__version__, "z3", z3.get_version_string())

# --- Chapter 5: seeded SymPy witness ---------------------------------------
t, x, v = symbols("t x v", real=True)
shear = t**2 - (x + v * t) ** 2
original = t**2 - x**2
assignment = {t: Rational(0), x: Rational(0), v: Rational(1, 2)}
residual_value = simplify((shear - original).subs(assignment))
original_value = simplify(original.subs(assignment))
transformed_value = simplify(shear.subs(assignment))
valid = residual_value != 0 and transformed_value != original_value
print("ch05 seeded residual:", residual_value)
print("ch05 seeded witness valid:", valid)

# --- Chapter 10: seeded weakened gamma hypothesis --------------------------
T, X, V, G = z3.Reals("t x v gamma")
goal_negation = (G * (T - V * X)) ** 2 - (G * (X - V * T)) ** 2 != T * T - X * X

seeded = z3.Solver()
seeded.add(G * G * (1 - V * V) >= 1)
seeded.add(goal_negation)
outcome = seeded.check()
print("ch10 weakened hypothesis negation:", outcome)
if outcome == z3.sat:
    print("ch10 weakened model:", seeded.model())

# --- Chapter 18: sign-slip check ------------------------------------------
gamma = 1 / sqrt(1 - v**2)
normal_t = gamma * (t - v * x)
normal_x = gamma * (x - v * t)
slip_t = gamma * (t - v * x)
slip_x = gamma * (x + v * t)
point = {t: Rational(5), x: Rational(3), v: Rational(3, 5)}
print("ch18 normal interval at (5,3):", simplify((normal_t**2 - normal_x**2).subs(point)))
print("ch18 sign-slip interval at (5,3):", simplify((slip_t**2 - slip_x**2).subs(point)))
print("ch18 normal factors at (5,3):",
      simplify((normal_t - normal_x).subs(point)),
      simplify((normal_t + normal_x).subs(point)))
print("ch18 sign-slip factors at (5,3):",
      simplify((slip_t - slip_x).subs(point)),
      simplify((slip_t + slip_x).subs(point)))

# --- Chapter 22: timelike boundary and seeded velocity bound --------------
valid_boundary = z3.Solver()
valid_boundary.add(V > -1, V < 1, T > 0)
valid_boundary.add(X >= -T, X <= T, T - V * X <= 0)
print("ch22 valid boundary negation:", valid_boundary.check())

seeded_boundary = z3.Solver()
seeded_boundary.add(V >= -1, V <= 1, T > 0)
seeded_boundary.add(X >= -T, X <= T, T - V * X <= 0)
outcome = seeded_boundary.check()
print("ch22 seeded |v|<=1 negation:", outcome)
if outcome == z3.sat:
    print("ch22 seeded model:", seeded_boundary.model())

# --- Chapter 24: v=0 deletion boundary -------------------------------------
gamma_rel = G * G * (1 - V * V) == 1
with_gamma = z3.Solver()
with_gamma.add(V == 0, gamma_rel, goal_negation)
print("ch24 v=0 with gamma relation:", with_gamma.check())

without_gamma = z3.Solver()
without_gamma.add(V == 0, goal_negation)
outcome = without_gamma.check()
print("ch24 v=0 without gamma relation:", outcome)
if outcome == z3.sat:
    print("ch24 v=0 model:", without_gamma.model())