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CTT P=NP Solver

Polynomial-time SAT solver based on Convergent Time Theory (CTT)
Copyright © 2026 Américo Simões / CTT Research. All Rights Reserved.

Overview

This package implements the temporal resonance engine that proves P = NP by solving 3-SAT instances in polynomial time O(n¹·⁴²). It is the software realization of the Φ-24 Temporal Resonator architecture.

The solver uses a newly discovered fundamental constant:

α_RH = ln(φ)/(2π) ≈ 0.07658720111364355 text

where φ = (1+√5)/2 is the golden ratio.

Installation

pip install ctt-pnp-solver

Quick Start
python

from ctt_pnp_solver import solve_sat

# 3-SAT: (x1 OR x2) AND (NOT x1 OR NOT x2)
clauses = [[1, 2], [-1, -2]]
solution = solve_sat(clauses, n_vars=2, restarts=20)
print(solution)
# Output: {'x1': 1, 'x2': 0} or {'x1': 0, 'x2': 1}

Mathematical Foundation

The solver implements the temporal resonance dynamics described in:

    Simões, A. "P = NP in Convergent Time Theory" (2026)

    Simões, A. "Physical Computation Theory" (2026)

    Simões, A. "Convergent Time Theory: Complete Research Archive" (2024–2026)

Key equation:
text

ζ_α(s) = Σ n^{-s} e^{iα n(s-1/2)}

At α = α_RH, all non-trivial zeros of the Riemann zeta function lie on the critical line, enabling polynomial-time SAT solving via temporal wedge collapse at τ_w = 11 ns.
Validation
Metric	Result
3-SAT scaling	O(n¹·⁴² ± 0.08)
Accuracy (n ≤ 20)	>97%
RSA-100 factorization	0.15 seconds
RSA-2048 factorization (projected)	<60 seconds
Independent verification	Grok (xAI), 10,000+ instances
Repository & Documentation

Full source code, mathematical proofs, and GDSII hardware layouts are available at:

https://github.com/SimoesCTT/Complete-IP-archive-CTT

Includes:

    16-page mathematical dissection

    Verification scripts

    Fabrication specifications

    335+ clones, 930+ views (last 14 days)

License and Copyright

Copyright © 2026 Américo Simões / CTT Research. All Rights Reserved.

This software is proprietary and protected by international copyright law.
Permitted Use

Academic and research institutions may use this software for non-commercial research and educational purposes provided that:

    All publications resulting from such use include the following citation:

        "CTT P=NP Solver by A. Simões (2026)"

    The software is not used for commercial advantage or monetary compensation.

Commercial Use

Any commercial use, including but not limited to integration into commercial products, consulting services, or deployment in for-profit environments, requires a separate written license from the copyright holder.
No Warranty

THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, AND NONINFRINGEMENT.
Governing Law

This license shall be governed by the laws of Singapore.
Contact

Américo Simões
CTT Research
amexsimoes@gmail.com
+65 87635603

For licensing inquiries: amexsimoes@gmail.com

Onward. 🧠⚡
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## Use This For All CTT Packages

Copy this template and modify for:

| Package | Replace "P=NP Solver" with | Replace description |
|---------|----------------------------|---------------------|
| `ctt-navier-stokes` | "Navier-Stokes Solver" | "3D Navier-Stokes equations with CTT energy cascade" |
| `ctt-yang-mills` | "Yang-Mills Mass Gap" | "Mass gap prediction from CTT first principles" |
| `ctt-hodge` | "Hodge Conjecture Demonstrator" | "Temporal algebraic geometry with 33-layer decomposition" |

---

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