RandyMcMillan

use num_complex::Complex64;
use std::f64::consts::PI;

/// 1. Schoolbook Multiplication - O(n^2)
/// Base-10 arbitrary-precision multiplication for direct comparison.
pub fn multiply_schoolbook(a: &[u8], b: &[u8]) -> Vec<u8> {
    let mut result = vec![0u8; a.len() + b.len()];

    for (i, &da) in a.iter().rev().enumerate() {
        let mut carry = 0u64;

RandyMcMillan

use bitcoin_hashes::{sha256, Hash, HashEngine};
use bls12_381::{G1Affine, G1Projective, Scalar};
use core::array;
use ff::Field;
use group::Curve;
use rand::{thread_rng, SeedableRng};
use rand_chacha::ChaChaRng;
use std::io::Write;

fn prove<const N: usize, const M: usize, const S: usize>(

RandyMcMillan

use std::f64::consts::TAU;

/// Represents parameters for Gielis' Superformula.
///
/// Formula:
/// r(φ) = (|cos(m_cos * φ / 4) / a|^n2 + |sin(m_sin * φ / 4) / b|^n3) ^ (-1 / n1)
#[derive(Debug, Clone, Copy)]
pub struct SuperformulaParams {
    pub a: f64,
    pub b: f64,

RandyMcMillan

/// Represents parameters for Gielis' Superformula.
///
/// Standard formula (when m_cos == m_sin = m):
/// r(φ) = (|cos(m * φ / 4) / a|^n2 + |sin(m * φ / 4) / b|^n3) ^ (-1 / n1)
///
/// Extended asymmetric formula:
/// r(φ) = (|cos(y * φ / 4) / a|^n2 + |sin(z * φ / 4) / b|^n3) ^ (-1 / n1)
#[derive(Debug, Clone, Copy)]
pub struct SuperformulaParams {
    pub a: f64,

RandyMcMillan

// Tzolkin Matrix Arithmetic, Gregorian Mapping, & Quantum Orch OR Multi-Scale Cascade
// Integrates 613 THz Microtubule Tubulin Dynamics with Tzolkin Matrix Symmetries

use chrono::{TimeZone, Utc};

/// Represents the quantum vibrational frequency bands across the biological hierarchy
#[derive(Debug)]
enum FrequencyBand {
    TerahertzTHz(f64), // Quantum dipole oscillations in tubulin pi-electron clouds (613 THz)
    GigahertzGHz(f64), // Structural lattice vibrations

RandyMcMillan

use std::time::Instant;

/// Checks if a number `p` is prime using Wilson's Theorem.
/// 
/// According to Wilson's Theorem, an integer p > 1 is a prime number 
/// if and only if (p - 1)! + 1 is divisible by p.
/// 
/// Equivalently: (p - 1)! ≡ -1 (mod p) ≡ (p - 1) (mod p).
fn is_prime_wilson(p: u64) -> bool {
    if p <= 1 {

RandyMcMillan

//! # Synthesis: IT³ Paradigm & Ternary Perez Hourglass Framework
//!
//! An executable simulation and mathematical model implementing the discrete, 
//! topological, and algebraic properties presented in the *IT³ Paradigm* paper
//! by Victor Logvinovich & Jean-Claude Perez.
//!
//! ## Theoretical Summary
//! The framework derives fundamental physical properties—such as the proton-to-electron 
//! mass ratio ($m_p/m_e$) and topological confinement barriers—by synthesizing:
//! 1. **Ab Initio Invariants:** Irrational constants derived from algebraic spectral gaps.

RandyMcMillan

use std::time::{SystemTime, UNIX_EPOCH};

pub struct Xorshift32 {
    state: u32,
}

impl Xorshift32 {
    /// Initialize with a non-zero seed.
    pub fn new(seed: u32) -> Self {
        assert!(seed != 0, "Xorshift32 seed must be non-zero");

RandyMcMillan

// Author: Randy McMillan (@RandyMcMillan)
// Model: Sub-Planckian Quantum Entropic Gravity (SQTG) / Bloch-Screen Emergent Gravity
// Theory: Universal Scaling & Singularity Regularization via Exact Binomial Expansion

use std::f64::consts::PI;
use std::time::{SystemTime, UNIX_EPOCH};

pub const HBAR: f64 = 1.054_571_817e-34;
pub const C: f64 = 2.997_924_58e8;
pub const KB: f64 = 1.380_649e-23;

RandyMcMillan

use std::f64::consts::PI;

/// Fundamental Physical Constants (SI Units)
pub const HBAR: f64 = 1.054_571_817e-34; // Reduced Planck constant (J·s)
pub const C: f64 = 2.997_924_58e8;       // Speed of light in vacuum (m/s)
pub const KB: f64 = 1.380_649e-23;       // Boltzmann constant (J/K)
pub const G: f64 = 6.674_30e-11;        // Gravitational constant (m^3·kg^-1·s^-2)

/// Represents a point particle embedded in spacetime geometry
#[derive(Debug, Clone, Copy)]