SSM-Infinity — Core Engine (Full Source Code)

# ssm_infinity_core.py  — Shunyaya Symbolic Mathematical Infinity (SSM-Infinity)
# v1.0 — Directional infinity with deterministic symbolic classes
#
# Classes returned:
#   ("infinite-class", SymbolicInfinity)
#   ("zero-class", lane)
#   ("finite-class", lane)
#   ("undefined", None)

import math

EPS = 1e-12

def clamp(x, lo, hi):
    return max(lo, min(hi, x))

def merge_align(a1, a2):
    a1_c = clamp(a1, -1+EPS, 1-EPS)
    a2_c = clamp(a2, -1+EPS, 1-EPS)
    u1 = math.atanh(a1_c)
    u2 = math.atanh(a2_c)
    return math.tanh(u1 + u2)

class SymbolicInfinity:
    def __init__(self, sign, align):
        if sign not in (+1, -1):
            raise ValueError("sign must be +1 or -1")

        self.sign = sign
        self.align = clamp(align, -1+EPS, 1-EPS)

    def __repr__(self):
        s = "+∞" if self.sign == +1 else "-∞"
        return f"<{s}, a={self.align:.6f}>"

    # unary negation
    def __neg__(self):
        return SymbolicInfinity(-self.sign, self.align)

    # addition
    def __add__(self, other):
        if isinstance(other, SymbolicInfinity):
            if self.sign == other.sign:
                a_out = merge_align(self.align, other.align)
                return ("infinite-class", SymbolicInfinity(self.sign, a_out))
            else:
                a_out = merge_align(self.align, other.align)
                return ("zero-class", a_out)

        if isinstance(other, (int, float)):
            return ("infinite-class", SymbolicInfinity(self.sign, self.align))

        return NotImplemented

    __radd__ = __add__

    # subtraction
    def __sub__(self, other):
        if isinstance(other, SymbolicInfinity):
            return self + SymbolicInfinity(-other.sign, other.align)
        if isinstance(other, (int, float)):
            return ("infinite-class", SymbolicInfinity(self.sign, self.align))
        return NotImplemented

    # multiplication
    def __mul__(self, other):
        if isinstance(other, (int, float)):
            if other == 0:
                return ("zero-class", 0.0)
            sign_out = self.sign * (1 if other > 0 else -1)
            return ("infinite-class", SymbolicInfinity(sign_out, self.align))
        return NotImplemented

    __rmul__ = __mul__

    # division
    def __truediv__(self, other):
        if isinstance(other, SymbolicInfinity):
            if self.sign != other.sign:
                return ("finite-class", merge_align(self.align, other.align))
            else:
                return ("finite-class", merge_align(self.align, other.align))

        if isinstance(other, (int, float)):
            if other == 0:
                return ("undefined", None)
            sign_out = self.sign * (1 if other > 0 else -1)
            return ("infinite-class", SymbolicInfinity(sign_out, self.align))

        return NotImplemented

    # power
    def __pow__(self, exponent):
        if isinstance(exponent, (int, float)):
            if exponent < 0:
                return ("zero-class", 0.0)
            else:
                return ("infinite-class", SymbolicInfinity(self.sign, self.align))
        return NotImplemented