SilverSight/julia/hachimoji_encode.jl

#!/usr/bin/env julia

using Printf

const LETTER_NAMES = ["\u03A6", "\u039B", "\u03A1", "\u039A", "\u03A9", "\u03A3", "\u03A0", "\u0396"]

function sigma3(n::Integer)
    n == 0 && return zero(n)
    s = zero(n)
    d = one(n)
    while d * d <= n
        if n % d == 0
            s += d * d * d
            other = n ÷ d
            if other != d
                s += other * other * other
            end
        end
        d += 1
    end
    return s
end

function hachimoji_letter(sigma3_value::Integer)
    return UInt8(sigma3_value % 8)
end

function cartan_weight(a::Integer, b::Integer)
    if a == b
        return UInt64(273)
    elseif a ÷ 2 == b ÷ 2
        return UInt64(256)
    else
        return UInt64(0)
    end
end

function angrysphinx_gate(elements::Vector{UInt64})
    sum_counts = Dict{UInt64, Int}()
    n = length(elements)
    for i in 1:n
        for j in i:n
            s = elements[i] + elements[j]
            sum_counts[s] = get(sum_counts, s, 0) + 1
        end
    end
    collisions = 0
    for (_, count) in sum_counts
        if count > 1
            collisions += count - 1
        end
    end
    raw = 273 + 17 * collisions - 256 * collisions
    energy_remaining = max(0, raw)
    return (passed=collisions <= 1, collisions=collisions, energy_remaining=UInt64(energy_remaining))
end

function hachimoji_encode(n::Integer)
    s3 = sigma3(UInt64(n))
    letter = hachimoji_letter(s3)
    return (sigma3_value=s3, hachimoji_letter=letter, letter_name=LETTER_NAMES[letter + 1])
end

function main()
    println("=== Hachimoji Encoder + AngrySphinx Gate (Julia) ===")
    println()

    test_numbers = UInt64[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    expected_sigma3 = UInt64[1, 9, 28, 73, 126, 252, 344, 585, 757, 1134]

    println("--- Sigma3 Verification ---")
    all_sigma3_ok = true
    for (i, n) in enumerate(test_numbers)
        s3 = sigma3(n)
        ok = s3 == expected_sigma3[i]
        if !ok
            all_sigma3_ok = false
        end
        status = ok ? "OK" : "FAIL"
        @printf("  n=%2d: sigma3=%5d  expected=%5d  %s\n", n, s3, expected_sigma3[i], status)
    end
    @assert all_sigma3_ok "sigma3 verification failed"
    println("  Sigma3: PASS")
    println()

    println("--- Hachimoji Encoding ---")
    for n in test_numbers
        r = hachimoji_encode(n)
        @printf("  n=%2d: sigma3=%5d  letter=%s (index=%d)\n",
                n, r.sigma3_value, r.letter_name, r.hachimoji_letter)
    end
    println()

    println("--- Cartan Weight ---")
    @printf("  cartan_weight(0, 0) = %d (self)\n", cartan_weight(0, 0))
    @printf("  cartan_weight(0, 1) = %d (same pair, opposite sign)\n", cartan_weight(0, 1))
    @printf("  cartan_weight(0, 2) = %d (different pairs)\n", cartan_weight(0, 2))
    println()

    println("--- AngrySphinx Gate Tests ---")

    r = angrysphinx_gate(UInt64[1, 2])
    @assert r.passed == true
    @assert r.collisions == 0
    @assert r.energy_remaining == 273
    @printf("  elements=[1,2]   -> passed=%s, collisions=%d, energy=%d  OK\n",
            r.passed, r.collisions, r.energy_remaining)

    r = angrysphinx_gate(UInt64[1, 2, 3])
    @assert r.passed == true
    @assert r.collisions == 1
    @assert r.energy_remaining == 34
    @printf("  elements=[1,2,3] -> passed=%s, collisions=%d, energy=%d  OK\n",
            r.passed, r.collisions, r.energy_remaining)

    r = angrysphinx_gate(UInt64[1, 2, 3, 4])
    @assert r.passed == false
    @assert r.collisions == 3
    @assert r.energy_remaining == 0
    @printf("  elements=[1,2,3,4] -> passed=%s, collisions=%d, energy=%d  OK\n",
            r.passed, r.collisions, r.energy_remaining)
    println("  AngrySphinx: PASS")
    println()

    println("--- E8LevelSet Tests ---")

    r = angrysphinx_gate(UInt64[1, 2, 3])
    @assert r.passed "E8LevelSet(32) gate should be OPEN"
    @assert r.collisions == 1
    @printf("  E8LevelSet(32):  elements=[1,2,3]     -> gate OPEN   (%d collision)\n", r.collisions)

    r = angrysphinx_gate(UInt64[1, 2, 3])
    @assert r.passed "E8LevelSet(64) gate should be OPEN"
    @assert r.collisions == 1
    @printf("  E8LevelSet(64):  elements=[1,2,3]     -> gate OPEN   (%d collision)\n", r.collisions)

    r = angrysphinx_gate(UInt64[1, 2, 3, 4, 5])
    @assert !r.passed "E8LevelSet(128) gate should be CLOSED"
    @assert r.collisions == 6
    @printf("  E8LevelSet(128): elements=[1,2,3,4,5] -> gate CLOSED (%d collisions)\n", r.collisions)
    println("  E8LevelSet: PASS")
    println()

    println("=== All tests passed ===")
end

if !isinteractive()
    main()
end