Coherence Object Calculus Example in Python

coc-example.py

# Computational demonstration of two foundational lemmas in Coherent Object Calculus (COC)
# 1. channel_decomposition_bijective for n up to 1,000,000
# 2. resonance_well_defined for all v in 0..255

# --- Helper definitions mirrored from the spec -------------------------------

def channel_decompose(n: int):
    """Return the base‑256 little‑endian byte list of a positive integer n (n>0)."""
    if n <= 0:
        raise ValueError("n must be positive")
    lst = []
    while n:
        lst.append(n % 256)
        n //= 256
    return lst

def reconstruct(bytes_le):
    """Reconstruct an integer from its little‑endian base‑256 expansion."""
    n = 0
    for i, b in enumerate(bytes_le):
        n += b * (256 ** i)
    return n

# Constants α₁ … α₈
constants = [
    1.0,        # α₁ unity
    1.839287,   # α₂ Tribonacci
    1.618034,   # α₃ golden ratio
    0.5,        # α₄ adelic threshold
    0.159155,   # α₅ interference null
    6.283185,   # α₆ 2π scale transition
    0.199612,   # α₇ phase coupling
    14.134725   # α₈ Riemann resonance
]

def bit_pattern(n: int, i: int) -> bool:
    """Return True if bit i of n is 1."""
    return ((n >> i) & 1) == 1

def resonance(v: int) -> float:
    """Product ∏ constants[i] over active bits of v (0 ≤ v < 256)."""
    prod = 1.0
    for i in range(8):
        if bit_pattern(v, i):
            prod *= constants[i]
    return prod

# --- Lemma 1: channel_decomposition_bijective (finite verification) ----------
MAX_N = 1_000_000
bijective_pass = all(reconstruct(channel_decompose(n)) == n for n in range(1, MAX_N + 1))

# --- Lemma 2: resonance_well_defined (all v in 0..255) -----------------------
resonance_positive_pass = all(resonance(v) > 0 for v in range(256))

# --- Output results ----------------------------------------------------------
print(f"Lemma channel_decomposition_bijective holds for all n in [1, {MAX_N}]: {bijective_pass}")
print(f"Lemma resonance_well_defined holds for all v in 0..255: {resonance_positive_pass}")