#!/usr/bin/env julia
include(joinpath(@__DIR__,"..","src","OmegaNaughtProofs.jl"))
using .OmegaNaughtProofs

d=big(32767)
record=encode(Q,S,23,d)
restored=decode_checked(Q,S,record.terminal,record.remainders)
println("Seed: ",d,"; terminal: ",record.terminal,"; decoded seed: ",restored)
println("First remainder: ",first(record.remainders))
println("Seed from first remainder: ",seed_from_remainder(first(record.remainders)))

# A retained rational grid scale, center, and isometric frame realize the data.
placement=ExactPlacement([2,-3,5],[3//5 0;4//5 0;0 1])
shape=reconstruct_outline(1//8,placement,record.terminal,record.remainders)
println("Reconstructed radius: ",shape.radius)
println("Center: ",shape.center)
println("Frame: ",shape.frame)
println("Circle rule: ",shape.circle_rule)
println("Major interval / pi: ",shape.major_angle_pi)
println("All six marks remain exact symbolic polynomials:")
foreach(println,shape.marks)

println("\nGeneric signed example (A=-2, B=3, seed=-17):")
generic=encode(-2,3,5,-17)
println(generic)
println("Decoded: ",decode_checked(-2,3,generic.terminal,generic.remainders))
println("\nRead the universal ordered-reconstruction proof with PROOFS[\"P09\"].")