SilverSight/julia/SilverSight/silversight_engine.jl

"""
    SilverSight Engine — Julia Port

Mirrors `python/silversight_engine.py` and `rust/src/silversight/mod.rs`.
All formulas verified by 3 independent agents.

References:
    * `formal/CoreFormalism/BraidEigensolid.lean` — eigensolid convergence theorem
    * `formal/SilverSight/PIST/FisherRigidity.lean` — Fisher rigidity
"""
module SilverSightEngine

using Random

export normalize, byte_class, F, tau, Phi,
       d_F, d_Phi,
       C, geodesic_step, chaos_game,
       corkscrew_index,
       Concept, SilverSight

# ── Constants ─────────────────────────────────────────────────────────

const PHI = (1 + sqrt(5.0)) / 2.0
const PSI = 2.0 * pi / (PHI^2)

# ── R1: Token Normalization ──────────────────────────────────────────

function normalize(s::AbstractString)::String
    lower = lowercase(s)
    out = IOBuffer()
    i = 1
    while i <= length(lower)
        c = lower[i]
        if isdigit(c)
            write(out, 'N')
            while i <= length(lower) && isdigit(lower[i]); i += 1; end
        elseif isletter(c)
            write(out, 'V')
            while i <= length(lower) && isletter(lower[i]); i += 1; end
        else
            write(out, c)
            i += 1
        end
    end
    String(take!(out))
end

# ── Byte Classification ──────────────────────────────────────────────

function byte_class(c::Char)::Int
    asc = Int(c)
    asc <= 31 && return 0
    asc <= 47 && return 1
    asc <= 57 && return 2
    asc <= 64 && return 3
    asc <= 90 && return 4
    asc <= 96 && return 5
    asc <= 122 && return 6
    return 7
end

# ── Feature Extraction ───────────────────────────────────────────────

function F(s::AbstractString)::Vector{Float64}
    norm = normalize(s)
    counts = zeros(Int, 8)
    for c in norm
        counts[byte_class(c) + 1] += 1
    end
    total = sum(counts)
    total == 0 && return zeros(8)
    return Float64.(counts) ./ total
end

function parse_tree_depth(expr::AbstractString)::Vector{Tuple{Char, Int}}
    ops = Tuple{Char, Int}[]
    depth = 0
    for c in expr
        if c == '('
            depth += 1
        elseif c == ')'
            depth -= 1
        elseif c in "+-*/="
            push!(ops, (c, depth))
        end
    end
    ops
end

function tau(s::AbstractString)::Vector{Float64}
    op_depths = parse_tree_depth(s)
    weights = zeros(6)
    for (op, d) in op_depths
        w = 2.0^(-d)
        if op == '+'; weights[2] += w
        elseif op == '='; weights[3] += w
        elseif op == '/'; weights[4] += w
        elseif op == '*'; weights[5] += w
        elseif op == '-'; weights[6] += w
        end
    end
    total = sum(weights)
    if total > 0
        weights ./= total
    end
    weights
end

function Phi(s::AbstractString)::Vector{Float64}
    vcat(F(s), tau(s))
end

# ── Fisher Distance ──────────────────────────────────────────────────

function d_F(p::Vector{Float64}, q::Vector{Float64})::Float64
    s = sum(sqrt.(max.(p .* q, 0.0)))
    s = clamp(s, -1.0, 1.0)
    2.0 * acos(s)
end

function d_Phi(phi1::Vector{Float64}, phi2::Vector{Float64})::Float64
    f1, t1 = phi1[1:8], phi1[9:14]
    f2, t2 = phi2[1:8], phi2[9:14]
    sqrt(d_F(f1, f2)^2 + d_F(t1, t2)^2)
end

# ── Coarse-Graining / Eigensolid ────────────────────────────────────

function C(phi::Vector{Float64})::Vector{Float64}
    result = copy(phi)
    for k in 0:3
        avg = (phi[2k+1] + phi[2k+2]) / 2.0
        result[2k+1] = avg
        result[2k+2] = avg
    end
    for k in 0:2
        avg = (phi[9+2k] + phi[10+2k]) / 2.0
        result[9+2k] = avg
        result[10+2k] = avg
    end
    result
end

function geodesic_step(phi1::Vector{Float64}, phi2::Vector{Float64}; eps::Float64=0.5)::Vector{Float64}
    f1, t1 = phi1[1:8], phi1[9:14]
    f2, t2 = phi2[1:8], phi2[9:14]

    sf1 = sqrt.(clamp.(f1, 0.0, 1.0))
    sf2 = sqrt.(clamp.(f2, 0.0, 1.0))
    interp_f = (1.0 - eps) .* sf1 .+ eps .* sf2
    interp_f_sq = interp_f.^2
    sum_f = sum(interp_f_sq)
    if sum_f > 0; interp_f_sq ./= sum_f; end

    st1 = sqrt.(clamp.(t1, 0.0, 1.0))
    st2 = sqrt.(clamp.(t2, 0.0, 1.0))
    interp_t = (1.0 - eps) .* st1 .+ eps .* st2
    interp_t_sq = interp_t.^2
    sum_t = sum(interp_t_sq)
    if sum_t > 0; interp_t_sq ./= sum_t; end

    vcat(interp_f_sq, interp_t_sq)
end

# ── Chaos Game ────────────────────────────────────────────────────────

function chaos_game(start::Vector{Float64}, references::Dict{String, Vector{Float64}};
                    steps::Int=30, eps::Float64=0.5, seed::Int=42)::Vector{Float64}
    rng = MersenneTwister(seed)
    refs = collect(values(references))
    x = copy(start)
    for _ in 1:steps
        dists = [d_Phi(x, r) for r in refs]
        nearest = refs[argmin(dists)]
        x = geodesic_step(x, nearest; eps=eps)
    end
    x
end

# ── Corkscrew Index ──────────────────────────────────────────────────

function corkscrew_index(phi::Vector{Float64})::Int
    coeffs = floor.(Int, phi[1:9] .* 256)
    spiral = 0
    for (i, c) in enumerate(coeffs)
        spiral += c * (8^(i - 1))
    end
    abs(spiral)
end

# ── Concept Data Structure ───────────────────────────────────────────

mutable struct Concept
    name::String
    prototype::Vector{Float64}
    attractor::Vector{Float64}
    corkscrew_index::Int
    operator_type::String
    members::Vector{Tuple{String, Vector{Float64}}}
end

function Concept(name::String, prototype::Vector{Float64}, attractor::Vector{Float64},
                  corkscrew_idx::Int, op_type::String)
    Concept(name, prototype, attractor, corkscrew_idx, op_type, Tuple{String, Vector{Float64}}[])
end

# ── SilverSight Engine ───────────────────────────────────────────────

mutable struct SilverSight
    concepts::Vector{Concept}
    references::Dict{String, Vector{Float64}}
    basin_map::Dict{NTuple{14, Int}, Int}
end

SilverSight() = SilverSight(Concept[], Dict{String, Vector{Float64}}(), Dict{NTuple{14, Int}, Int}())

function detect_operator(s::AbstractString)::String
    norm = normalize(s)
    for (op, name) in [('+', "addition"), ('/', "division"), ('*', "multiplication"),
                       ('-', "subtraction"), ('=', "equality")]
        if occursin(op, norm)
            return name
        end
    end
    "literal"
end

function learn(ss::SilverSight, equation::AbstractString)::Int
    phi = Phi(equation)
    ss.references[equation] = phi

    limit = chaos_game(phi, ss.references; steps=30, eps=0.5)
    eigensolid = C(limit)
    idx = corkscrew_index(eigensolid)

    attractor_key = Tuple(round.(Int, limit .* 1e8))

    if haskey(ss.basin_map, attractor_key)
        cid = ss.basin_map[attractor_key]
        push!(ss.concepts[cid].members, (equation, phi))
        return cid
    end

    op_type = detect_operator(equation)
    cid = length(ss.concepts) + 1
    concept = Concept("concept_$(cid - 1)", eigensolid, limit, idx, op_type)
    push!(concept.members, (equation, phi))
    push!(ss.concepts, concept)
    ss.basin_map[attractor_key] = cid
    cid
end

function classify(ss::SilverSight, equation::AbstractString)::Tuple{Union{Concept, Nothing}, Float64}
    isempty(ss.concepts) && return (nothing, Inf)
    phi = Phi(equation)
    best = nothing
    best_dist = Inf
    for concept in ss.concepts
        d = d_Phi(phi, concept.attractor)
        if d < best_dist
            best_dist = d
            best = concept
        end
    end
    (best, best_dist)
end

function is_novel(ss::SilverSight, equation::AbstractString)::Tuple{Bool, Float64}
    if length(ss.concepts) < 2
        return (isempty(ss.concepts), Inf)
    end

    inter_dists = Float64[]
    for i in 1:length(ss.concepts)
        for j in (i+1):length(ss.concepts)
            push!(inter_dists, d_Phi(ss.concepts[i].attractor, ss.concepts[j].attractor))
        end
    end
    threshold = isempty(inter_dists) ? 0.5 : minimum(inter_dists) / 2.0

    _, dist = classify(ss, equation)
    (dist > threshold, dist)
end

function summary(ss::SilverSight)
    println("SilverSight: $(length(ss.concepts)) concepts, $(length(ss.references)) references")
    for (i, c) in enumerate(ss.concepts)
        members = join([m[1] for m in c.members], ", ")
        println("  [$(i-1)] $(rpad(c.operator_type, 15)) idx=$(lpad(c.corkscrew_index, 12)) members: $members")
    end
end

# ── Demo ──────────────────────────────────────────────────────────────

function demo()
    ss = SilverSight()
    equations = [
        "a+b=c", "x+y=z",
        "p/q=r", "a/b=c",
        "a*b=c",
        "a-b=c",
        "hello",
        "(a+b)*c=d",
    ]
    for eq in equations
        learn(ss, eq)
    end
    summary(ss)

    println("\nClassification:")
    for eq in ["a+b=c", "m+n=p", "p/q=r", "foo", "a+b+c=d"]
        concept, dist = classify(ss, eq)
        n, _ = is_novel(ss, eq)
        status = n ? "NOVEL" : "known"
        cname = concept === nothing ? "none" : concept.operator_type
        println("  $(rpad(eq, 15)) -> [$(findfirst(==(concept), ss.concepts) !== nothing ? findfirst(==(concept), ss.concepts) - 1 : "?")] $(rpad(cname, 15)) d=$(round(dist, digits=6)) [$status]")
    end
end

end # module

if abspath(PROGRAM_FILE) == @__FILE__
    using .SilverSightEngine
    SilverSightEngine.demo()
end