Frequently asked
questions answered.

Zeq.dev is an open-source scientific computing framework — a language-agnostic middleware platform that takes verified physics equations and makes them callable as software functions, synchronized to a universal temporal heartbeat of 1.287 Hz.

It is not a simulation engine, not a physics calculator, and not an AI model. It is a generative mathematics compiler: you give it a problem, it assembles an equation that did not previously exist in that specific form, executes it, and returns a result verified to ≤0.1% against experimental data from NIST, NASA, and CERN.

In practice: add ZEQ_API_KEY to your project's secrets, call POST /api/zeq/compute with a domain and inputs, and receive a full ZeqState envelope — operators applied, precision, phase, and the Zeqond timestamp — along with your result.

Any Replit developer who needs verified physics in their project — simulation games, science apps, engineering tools, AI agents, educational platforms, or research code. You do not need a physics background. You supply the domain (e.g. quantum_mechanics) and the inputs (e.g. {"E": 13.6, "m": 9.11e-31}), and Zeq.dev selects the appropriate operators and returns a grounded result.

NumPy, SciPy, and Wolfram are libraries and lookup engines — they give you functions to apply to equations you already know. Zeq.dev does something fundamentally different: it is a generative mathematics compiler that assembles the equation from verified physics for you, executes it, and returns a result verified against NIST, NASA, and CERN experimental data.

NumPy/SciPy also run in isolated reference frames — there is no shared clock binding results across domains. Zeq.dev is the first system where every computation across every physics domain is synchronized to a single mathematical clock: the 1.287 Hz HulyaPulse. Cross-domain results are composable because they share the same temporal foundation. Every result is reproducible at the exact same Zeqond timestamp.

The shortest distinction: NumPy is a tool. Zeq.dev is middleware. You bring the problem; Zeq.dev brings the mathematics.

Yes. The 1.287 Hz HULYAS ZEQ Framework was published on Zenodo (DOI: 10.5281/zenodo.15825138) by Hammoudeh & Aydan Zeq in August 2025. Zenodo is operated by CERN. The paper has received 4,000+ downloads across 8 versions — exceptional for a physics preprint, where the median lifetime download count is approximately 150.

The framework derives from a published mathematical proof. Every operator in the registry has a corresponding equation. Every computation carries its precision measurement.

Every Zeq.dev computation applies this equation: R(t) = S(t) × [1 + α × sin(2π × 1.287 × t)] Where R(t) is the grounded result, S(t) is your raw input signal, 1.287 Hz is the HulyaPulse frequency, and α = 0.00129 is the modulation constant (also written α_K).

The modulation grounds every result to the universal 1.287 Hz clock, ensuring cross-domain coherence. The precision is always ≤ 0.1%.

A Zeqond is a new temporal unit — exactly 0.777 seconds. It is derived from the 1.287 Hz HULYAS ZEQ Framework, not arbitrary convention. At 0.777 s, the Zeqond aligns perfectly with the 1.287 Hz HulyaPulse: one pulse every 0.777 s. Time and physics share the same clock.

Every Zeq.dev response carries the current Zeqond count (zeqond) and phase (phase). Two calls at the same Zeqond always return the exact same result — phase-locked, reproducible, and auditable.

The Zeqond count is simply: τ(t) = tunix / 0.777

1.287 Hz is the HulyaPulse frequency — the universal resonance frequency derived in the 1.287 Hz HULYAS ZEQ Framework paper. It is not an arbitrary constant. The proof in the Zenodo paper shows this frequency emerges from the mathematical structure of synchronized operator dynamics across quantum, relativistic, and classical regimes.

The inverse of 1.287 Hz is approximately 0.777 seconds — which defines the Zeqond. The two constants are mathematically inseparable.

KO42 is the Metric Tensioner Prime Directive — the foundational operator that applies the master equation to every computation. It ensures cross-domain coherence: whether you call a quantum operator, a fluid dynamics operator, or an astrophysics operator, they all remain in the same mathematical reference frame.

KO42 is always included in the operators list of every ZeqState response. You do not need to specify it — it is automatically applied. If KO42 is missing from a response, that result should be treated as invalid.

The operator registry contains 1,576 verified operators across 64 physics domains, including quantum mechanics, thermodynamics, fluid dynamics, electromagnetism, astrophysics, nuclear physics, biomedical physics, aerospace, classical mechanics, general relativity, and more.

Each operator has a unique ID, equation, domain assignment, and group classification (Core, Extended, Applied, Industry, or Frontier). You can browse the full registry in the Operator Explorer.

Go to Pricing and start your free 14-day trial — no credit card required. Enter your email and your zeq_ak_… key is generated instantly. You receive the full key exactly once, in your trial portal, after signup. Copy it immediately.

After the 14-day trial, subscribe to keep your key active. Your trial key does not change when you subscribe — it is the same key, just with no expiry.

All Zeq.dev API keys start with zeq_ak_ followed by 32 random characters. The prefix makes the key instantly identifiable in code, logs, and secret managers — so it is obvious where it belongs and difficult to accidentally expose alongside unrelated credentials.

Add it to your Replit project's Secrets (the padlock icon in the left sidebar). Set the key name to ZEQ_API_KEY and paste your zeq_ak_… key as the value. Your code then accesses it via:

process.env.ZEQ_API_KEY (Node.js) or os.environ["ZEQ_API_KEY"] (Python).

Your key never lives in source code — it is injected at runtime by Replit's secrets system. Restart your Repl after adding a secret.

The full key is shown exactly once — immediately after your trial starts or your subscription completes — in the portal. After you leave that page, only the masked prefix (zeq_ak_••••••••) is displayed.

If you lose your key, go to your portal and use the key rotation feature to generate a new one. The old key is immediately invalidated. The new key is revealed once.

There is a free 14-day trial on the Starter plan — no credit card required. During the trial you get 100 compute tokens and access to the complete operator library across 64 physics domains. The trial key is a real zeq_ak_ key, usable immediately in any Replit project.

After the 14 days, your key is paused (not deleted). Subscribe to reactivate it. There is no permanently free tier beyond the trial.

Your API key is paused — not deleted. It will still appear in your trial portal with a masked prefix. If you subscribe before the trial ends, there is no interruption. If you subscribe after expiry, your key reactivates immediately upon subscription. You keep the same key.

Starter — $29/mo, 500 compute tokens/day
Builder — $79/mo, 2,500 compute tokens/day
Advanced — $199/mo, 7,500 compute tokens/day
Architect — $499/mo, 25,000 compute tokens/day
Enterprise — custom pricing, dedicated deployment

All plans include access to the full operator library. Plans differ only by daily compute token allowance. See Pricing for details.

Each successful request to POST /api/zeq/compute consumes one compute token from your daily allowance. Usage limits reset daily at the UTC midnight zeqond boundary. Your current usage and remaining tokens are shown in the developer portal.

Yes. Cancel from your developer portal at any time. Your subscription remains active until the end of the current billing period. No questions asked, no retroactive charges.

Zeq.dev implements the Model Context Protocol (MCP) — a standard for connecting AI clients (like Claude Desktop, Cursor, or Windsurf) to external tools. Once connected, your AI client gains two native tools: zeq_compute (to run physics computations) and zeq_list_operators (to browse the operator library). Your AI can call them autonomously — no wrapper code needed.

See MCP for full setup instructions and ready-to-paste config blocks.

The zeq_list_operators tool is public — it works without an API key and returns the full list of 64 physics domains and their operators.

The zeq_compute tool requires a valid zeq_ak_ API key passed in the Authorization header. Without a key, compute requests return a 401 Unauthorized response.

Currently tested and documented: Claude Desktop, Cursor, and Windsurf. Any MCP-compatible client using JSON-RPC 2.0 over HTTPS (protocol v2024-11-05) will also work. See the MCP page for ready-to-paste configs for each client.

The full machine-readable API reference is at /llms.txt — structured for direct ingestion by LLMs and AI tools. It covers all endpoints, authentication, request/response schemas, and the ZeqState envelope definition.