FREE THE CAT NOTEBOOK - CORRECTED FROZEN CORE ENGINE
"""
FINITE RESPONSE COUPLED MONAD DYNAMICS — CORRECTED FROZEN CORE ENGINE
=====================================================================
This script evaluates the frozen core's 4-component tensor field on a
periodic lattice. It produces observations, not verdicts. The engine does
not interpret ontology. The record is written to disk as text. The
verdict depends on runtime output only.
Reference document: ##FINITE RESPONSE COUPLED MONAD DYNAM.txt
Corrections applied from the 2026-09-26 audit:
1. I2 = Frobenius (was determinant)
2. KO sign: dissipative (was anti-diffusive)
3. Periodic grid: endpoint=False
4. Per-component operators (not uniform)
5. term3 uses I_k^2, not I_1^2
6. I3, I4 match the frozen core's definitions
Separation:
RECORD : text, written to disk, not interpreted
ENGINE : code, computes numbers, does not read the record
OUTPUT : observations, not verdicts
"""
import os
import shutil
import numpy as np
from datetime import datetime
# =============================================================================
# ENVIRONMENT
# =============================================================================
try:
from google.colab import drive, files
IN_COLAB = True
drive.mount('/content/drive')
except ImportError:
IN_COLAB = False
print("Not in Colab. Drive and download steps will be simulated.")
PROJECT_NAME = "FRCMD_FROZEN_CORE_CORRECTED"
timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
output_dir = f"output_{timestamp}"
os.makedirs(output_dir, exist_ok=True)
print(f"Workspace: {output_dir}/")
# =============================================================================
# FROZEN CORE CONSTANTS
# =============================================================================
PHI = 1.618033988749895
PI_MAX = 5.9259
KO_SIGMA = 0.045
# frozen core coefficients (2026-07-26)
ALPHA_HYB = 1.0
BETA_HYB = 0.1
GAMMA_HYB = 0.1
I_G = 1.0
MU = 1.0
LAM = 1.0
KAPPA_B = 0.1
LAM_REG = 0.01
ALPHA_0 = 0.4
DELTA_0 = 0.15
# =============================================================================
# PER-COMPONENT OPERATORS
# =============================================================================
def dPhi_hyb_dP_yx(P_yx, I1):
g = I1**2 / (I1**2 + I_G**2)
abs_p = np.abs(P_yx)
sign_p = np.sign(P_yx)
num = 2.0 * P_yx * (1.0 + GAMMA_HYB * abs_p) - GAMMA_HYB * sign_p * P_yx**2
den = (1.0 + GAMMA_HYB * abs_p) ** 2
return ALPHA_HYB + g * BETA_HYB * num / den
def frozen_core_operator(P_xx, P_xy, P_yx, P_yy, dx):
"""
Returns (dPxx_dt, dPxy_dt, dPyx_dt, dPyy_dt) for the frozen core.
All four components are differentiated correctly. No shared operator.
"""
# --- Invariants (FIX 1 and FIX 6) ---
I1 = P_xx + P_yy
I2 = P_xx**2 + P_xy**2 + P_yx**2 + P_yy**2 # Frobenius
I4 = P_xx**4 + P_yy**4 # frozen core I4
I3 = P_xx * P_yy - P_xy * P_yx # frozen core I3 (abandoned)
# I1^{-1/2} guard
I1_safe = np.clip(I1, 1e-12, None)
# --- Finite-response difference (per component, periodic) ---
def D(f):
return (np.roll(f, -1) - np.roll(f, 1)) / (2.0 * dx)
# --- Nonlinear interaction operator C(Π) per component (FIX 4) ---
def C_term(P_comp, D_P):
I_k = P_comp * D_P
term1 = 0.2 * (D_P * I1)
term2 = 0.2 * (I2 - I1) * (I1 + I2)
term3 = 0.1 * (I_k ** 2) # FIX 5: I_k^2, not I_1^2
term4 = ((1.0 / PI_MAX)
* (I1_safe**(-0.5) - 1.0)
* np.exp(-0.5 * (I2**2 + I3**3 + I4**4))
* P_comp)
return term1 + term2 + term3 + term4
dPxx = C_term(P_xx, D(P_xx))
dPxy = C_term(P_xy, D(P_xy))
dPyx = C_term(P_yx, D(P_yx))
dPyy = C_term(P_yy, D(P_yy))
# --- Antisymmetric stress contribution to dPyx (FIX 4, explicit) ---
dPyx = dPyx + dPhi_hyb_dP_yx(P_yx, I1)
# --- Kreiss-Oliger dissipation (FIX 2: dissipative sign) ---
def KO(f):
stencil = (np.roll(f, -2) - 4.0*np.roll(f, -1) + 6.0*f
- 4.0*np.roll(f, 1) + np.roll(f, 2))
return KO_SIGMA * stencil / (dx**4)
dPxx = dPxx - KO(P_xx)
dPxy = dPxy - KO(P_xy)
dPyx = dPyx - KO(P_yx)
dPyy = dPyy - KO(P_yy)
return dPxx, dPxy, dPyx, dPyy
# =============================================================================
# INTEGRATION
# =============================================================================
def run_frozen_core(N=256, L=20.0, steps=5000):
# FIX 3: periodic grid — endpoint=False
x = np.linspace(-L/2, L/2, N, endpoint=False)
dx = L / N
# CFL-justified time step
dt = 0.005 * (dx ** 2)
# Initial 4-component state, PHI baseline
P_xx = PHI + np.exp(-(x + 3.0)**2)
P_yy = PHI + np.exp(-(x - 3.0)**2)
P_xy = np.zeros(N)
P_yx = np.zeros(N)
history = {}
diagnostics = []
unstable = False
print(f"Frozen core: N={N}, dx={dx:.6f}, dt={dt:.6e}, steps={steps}")
for step in range(steps + 1):
dPxx, dPxy, dPyx, dPyy = frozen_core_operator(P_xx, P_xy, P_yx, P_yy, dx)
P_xx = P_xx + dt * dPxx
P_xy = P_xy + dt * dPxy
P_yx = P_yx + dt * dPyx
P_yy = P_yy + dt * dPyy
if step % 500 == 0:
m_xx = float(np.max(np.abs(P_xx)))
m_yx = float(np.max(np.abs(P_yx)))
r_xx = float(np.max(np.abs(dPxx)))
line = (f"Step {step:04d} | max|Pxx|={m_xx:.6e} | "
f"max|Pyx|={m_yx:.6e} | max|dPxx/dt|={r_xx:.6e}")
diagnostics.append(line)
print(line)
history[step] = P_xx.copy()
if not (np.isfinite(P_xx).all() and np.isfinite(P_yy).all()
and np.isfinite(P_xy).all() and np.isfinite(P_yx).all()):
line = f"CRITICAL: non-finite value at step {step}. Aborting."
diagnostics.append(line)
print(line)
unstable = True
break
return x, history, diagnostics, unstable
# =============================================================================
# RUN
# =============================================================================
x_grid, evolution, diags, unstable = run_frozen_core()
# =============================================================================
# OBSERVATION RECORD (no verdicts)
# =============================================================================
obs_path = os.path.join(output_dir, "observation.json")
with open(obs_path, "w") as f:
import json
json.dump({
"engine": "frozen_core_corrected",
"N": int(len(x_grid)),
"steps_run": len(diags),
"unstable": bool(unstable),
"diagnostics": diags,
"status": "OBSERVATION_ONLY",
}, f, indent=2)
report_path = os.path.join(output_dir, "diagnostics.txt")
with open(report_path, "w") as f:
f.write("FRCMD FROZEN CORE — OBSERVATION LOG\n")
f.write("===================================\n\n")
for line in diags:
f.write(line + "\n")
f.write("\n")
if unstable:
f.write("STATUS: non-finite value encountered. Run aborted.\n")
else:
f.write("STATUS: all scheduled steps completed. No non-finite values.\n")
f.write("This is an observation. Not a verdict on the axiom.\n")
# =============================================================================
# PRESERVATION
# =============================================================================
zip_base = f"{PROJECT_NAME}_{timestamp}"
zip_path = shutil.make_archive(zip_base, 'zip', output_dir)
drive_ok = False
if IN_COLAB:
try:
drive_dir = f"/content/drive/MyDrive/{PROJECT_NAME}/{output_dir}"
os.makedirs(drive_dir, exist_ok=True)
for item in os.listdir(output_dir):
shutil.copy2(os.path.join(output_dir, item),
os.path.join(drive_dir, item))
shutil.copy2(zip_path, f"/content/drive/MyDrive/{PROJECT_NAME}/{zip_base}.zip")
drive_ok = True
except Exception as e:
print(f"Drive backup failed: {e}")
download_ok = False
if IN_COLAB:
try:
files.download(zip_path)
download_ok = True
except Exception as e:
print(f"Download failed: {e}")
# =============================================================================
# BENCH READOUT
# =============================================================================
print()
print("=" * 70)
print(" FRCMD FROZEN CORE — BENCH READOUT")
print("=" * 70)
print(f" Output directory : {os.path.abspath(output_dir)}")
print(f" ZIP archive : {os.path.abspath(zip_path)}")
print(f" Drive backup : {drive_ok}")
print(f" Download : {download_ok}")
print(f" Steps completed : {len(diags)}")
print(f" Unstable : {unstable}")
print(f" Files in output : {len(os.listdir(output_dir))}")
print(f" Archive size : {os.path.getsize(zip_path)} bytes")
print("=" * 70)
