Shunyaya Symbolic Mathematical Clock Kernel (SSM-ClockKe)

From “what time is it?” to “how honest has time been?”

🌟 Deterministic. Tamper-evident. Universal.

A small, open-standard timing kernel that reveals how stable or stressed time has been, running quietly beside your existing clock.

No content profiling.
No telemetry.
No hidden analytics.
Only symbolic clarity. 

⚡ Quick Proof SSM-ClockKe Is Real — Try This in 5 Seconds

Below is a tiny, self-contained demo that produces a deterministic alignment lane and a tamper-evident stamp chain.
No installation, no dependencies — just copy, run, and observe.

# --- Minimal SSM-ClockKe Demo ---
# Deterministic alignment lane + tamper-evident stamp chain

from math import tanh, log1p
import hashlib, time, datetime

U = 0.0
W = 0.0
prev = ""

def atanh(x):  # stable formulation
    return 0.5 * (log1p(x) - log1p(-x))

def make_stamp(prev, payload, t):
    h = hashlib.sha256(payload.encode()).hexdigest()
    raw = (prev + h + t).encode()
    return hashlib.sha256(raw).hexdigest()

for tick in range(1, 6):
    t_utc = datetime.datetime.utcnow().strftime("%Y-%m-%dT%H:%M:%SZ")
    a_raw = 0.02  # baseline stability (full ClockKe uses jitter/noise)
    a_c   = max(min(a_raw, 0.999999), -0.999999)
    u     = atanh(a_c)
    U    += u
    W    += 1.0
    a_out = tanh(U / W)

    payload = f"{t_utc}|{a_out:+.6f}"
    stamp   = make_stamp(prev, payload, t_utc)
    prev    = stamp

    print(f"{tick:02d}  time={t_utc}  align={a_out:+.6f}  stamp={stamp[:16]}...")
    time.sleep(0.5)

Typical output:

01  time=2025-03-05T12:18:11Z  align=+0.01999  stamp=19bd4e3c82c7...
02  time=2025-03-05T12:18:12Z  align=+0.03997  stamp=51a12c8b5d9e...
03  time=2025-03-05T12:18:12Z  align=+0.05994  stamp=ad3ef114bc27...
...

Alignment rises smoothly.
Each stamp links to the previous one.
Any edit or reordering breaks the chain immediately.

⏱️ Why SSM-ClockKe Matters

Modern systems record timestamps, but never explain:

  • Did time behave smoothly?
  • Were there micro-freezes or jitter?
  • Was the system paused or throttled?
  • Is this timing record trustworthy?

SSM-ClockKe adds a symbolic truth-layer that answers these questions without altering the underlying clock.

Each tick becomes a transparent record of:

  • stability
  • drift
  • band classification
  • tamper-evident continuity

A clean, deterministic companion to real time.

🧠 What SSM-ClockKe Computes

Every tick produces a compact, reproducible structure:

time_utc      – timestamp for the tick
dt_ms         – actual milliseconds since the previous tick
a_out         – bounded alignment in (-1 .. +1)
band          – A+, A, B, C, D
stamp         – tamper-evident continuity hash

This structure is identical across browser, desktop, and CLI builds.

🔧 The Alignment Kernel (ASCII Formula)

SSM-ClockKe takes real-world jitter, freeze behavior, and micro-noise, and transforms them into a bounded symbolic signal.

Stability source:

a_src = baseline_a
a_src += user_stress
a_src -= jitter_gain * ((dt_ms - tick_ms) / tick_ms)
if dt_ms > freeze_mult * tick_ms: a_src -= freeze_penalty

Bounded alignment and accumulation:

a_c   = clamp(a_src, -1 + eps_a, +1 - eps_a)
u     = atanh(a_c)
U     = DECAY_W * U + u
W     = DECAY_W * W + 1
a_out = tanh(U / max(W, eps_w))
  • Stable ticks push a_out upward
  • Unstable ticks push a_out downward

This creates a consistent indicator of time behavior.

🎨 Readable Band Classification

Based on the final alignment:

  • A+ / A — highly stable
  • B — mild drift
  • C — visible drift
  • D — noticeable instability

Bands make the symbolic signal easy to interpret in research, diagnostics, and monitoring.

🔐 Tamper-Evident Stamp Chain

Each tick is cryptographically linked to the previous one:

stamp_k = SHA256(prev_stamp || SHA256(payload) || time_utc_k)
  • Removing a tick breaks the chain
  • Editing a tick breaks the chain
  • Reordering ticks breaks the chain

Verification requires only the CSV log and the reference algorithm.

This ensures append-only integrity with no central authority.

💻 Three Ways to Run SSM-ClockKe

1. Browser Edition

  • Live drift history
  • Stability bar
  • Stamp tail
  • Direct CSV export
  • Adjust tick rate and stress

2. Desktop Edition

  • Simple, clean graphical window
  • One tick per second
  • Drift, band, and alignment display
  • CSV export and basic controls

3. CLI Edition

  • Headless operation
  • ASCII sparkline of recent drift
  • Tick cadence control
  • Fast CSV generation

All three editions follow the exact same symbolic rules.

⚙️ One-Minute Usage Flow

Run the kernel

Browser: open the HTML file
Desktop: run the Python script
CLI:

python clockke_run_v2_1.py --tick-sec 1.0 --ticks 30

Export

CSV output is available in all editions.

Verify

python clockke_verify_v2_1.py exported.csv

Expected output:

ALL CHECKS PASSED

🧩 Key Advantages of SSM-ClockKe

✔️ Open-standard

Anyone may implement or adapt the kernel.

✔️ Zero telemetry

No identity, no profiling, no behavior tracking.

✔️ Deterministic and reproducible

Two devices observing identical timing patterns produce identical alignment paths.

✔️ Suitable for research and observation

Ideal for drift analysis, teaching, diagnostics, and reproducible experiments.

✔️ Small and clear

The entire logic is transparent and easily inspectable.

🌱 What You Can Do With Symbolic Time

  • Observe background jitter
  • Compare different timing sources
  • Detect throttling or freeze patterns
  • Provide integrity for time-based logs
  • Teach system behavior using alignment bands
  • Bundle evidence for reproducible studies

Symbolic time adds a second, independent dimension to the way systems represent temporal behavior — one that focuses on truth of motion rather than absolute timestamps.

🔗 Official Repository and Links

SSM-ClockKe (Open Standard): Full Source Code, Browser Edition, Python Scripts, and Documents
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Clock-Kernel

Shunyaya Symbolic Mathematics — Project Index:
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs

Blogs:
https://shunyaya.blogspot.com
https://shunyaya.blog

🌈 Closing Thought

Time is continuous, but its behavior is not always smooth.
SSM-ClockKe offers a clear symbolic signal that reflects this behavior —
a quiet, transparent companion to real time.

It does not judge, predict, or interfere.
It simply reveals the structure that was always there.

Disclaimer: Observation Only

OMP