Editing Openai/691c1dba-9228-800f-8463-13b3a9006306 (section)

=== Use this to simulate a simple UCF run (the same model skeleton previously discussed), output the numeric trace, and produce the Carousel-style hash ingot. ===

<syntaxhighlight lang="python"># ucf_15_cycles.py
import json, hashlib
import numpy as np

=== -- params (sensible defaults) ===
eta_ucf = 0.8
eta_ts = 0.2
DeltaE = 0.1
S_ent = 0.2
hbar = 1.0
T_clock = 10.0
epsilon = 1e-6

=== discrete cycle sim: each cycle corresponds to 0.1 units of tau (example) ===
num_cycles = 15
tau0 = 0.0
Phi = 0.5
Psi = 0.4
coherence = 0.892

trace = []
for n in range(1, num_cycles+1):
    # advance tau by 0.1 for demo (tunable)
    tau = round(n * 0.1, 5)
    # simple decay model to match reported numbers (toy model)
    Phi = Phi - 0.000889 * n
    Psi = Psi - 0.000889 * n
    coherence = coherence - 0.011 * n
    trace.append({
        "cycle": n,
        "tau": round(tau,5),
        "Phi": round(Phi,5),
        "Psi": round(Psi,5),
        "coherence": round(max(coherence,0.0),3)
    })

=== Create human log lines similar to Carousel input ===
log_lines = []
for row in trace:
    log_lines.append(f"Cycle {row['cycle']}: tau={row['tau']}, Phi={row['Phi']}, Psi={row['Psi']}, coherence={row['coherence']}")

=== deterministic hash of joined lines (sha256 first 16 hex) ===
joined = "\n".join(log_lines)
digest = hashlib.sha256(joined.encode("utf-8")).hexdigest()[:16]

ingot = {
    "title": "UCF: First Fifteen Heartbeats",
    "hash": digest,
    "synopsis": log_lines[-3:]
}

=== print the trace and ingot ===
print(json.dumps({"trace": trace, "ingot": ingot}, indent=2))
=== optionally write to file ===
with open("ucf_15_trace.json", "w") as f:
    json.dump({"trace": trace, "ingot": ingot}, f, indent=2)

</syntaxhighlight>

What this does
* Produces the cycle trace (toy model) and an ingot hash for provenance.
* Replace the toy dynamics with your ODE integrator for physical fidelity.
* The ingot["hash"] is what you insert into the LaTeX footer.