CTT Birch–Swinnerton-Dyer Conjecture Solver

Convergent Time Theory — BSD Conjecture Verifier
Copyright © 2026 Américo Simões / CTT Research. All Rights Reserved.

Overview

This package implements the Convergent Time Theory (CTT) approach to the Birch–Swinnerton-Dyer Conjecture — one of the seven Millennium Prize Problems.

It uses temporal decomposition across 33 fractal layers with the fundamental constant: α_RH = ln(φ)/(2π) ≈ 0.07658720111364355

text

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

Mathematical Foundation

The BSD Conjecture

For an elliptic curve E over ℚ, the conjecture states:

1. The rank of E(ℚ) equals the order of vanishing of L(E, s) at s = 1
2. The leading coefficient of L(E, s) at s = 1 is given by the BSD formula involving:
   • Tate–Shafarevich group
   • Tamagawa numbers
   • Regulator
   • Torsion order

CTT Formulation

The L-function is computed with temporal damping: L_α(E, s) = Σ a_n · n^{-s} · e^{-α n / N}

text

where α = α_RH and the sum runs over 33 layers, each with weight e^{-αd}.

Installation

pip install ctt-bsd-conjecture
Quick Start
python
from ctt_bsd import verify_curve, benchmark

# Verify curve 389a (rank 2)
result = verify_curve("389a", (0, 1, 1, -2, 0))
print(f"Rank: {result['analytic_rank']}")
print(f"BSD holds: {result['bsd_holds']}")

# Run benchmark on known curves
results = benchmark()
for curve, data in results.items():
    print(f"{curve}: rank {data['analytic_rank']}")
API Reference
verify_curve(label, coefficients)
Verifica BSD para una curva elíptica.

label: Identificador único (ej. "389a")

coefficients: Tupla (a1, a2, a3, a4, a6)

returns: Diccionario con resultados

benchmark()
Ejecuta verificación en curvas conocidas.

returns: Diccionario con resultados para 37a, 389a, 5077a

BSDVerifier(alpha, layers)
Clase principal para verificación.

alpha: Coeficiente de viscosidad temporal (default α_RH)

layers: Número de capas fractales (default 33)

Examples
Verificar curva 5077a (rank 3)
python
from ctt_bsd import verify_curve

result = verify_curve("5077a", (0, 0, 1, -7, 6))
print(result['analytic_rank'])  # 3
Uso avanzado con la clase
python
from ctt_bsd import BSDVerifier

verifier = BSDVerifier(alpha=0.0765872, layers=33)
curve = verifier.load_curve("389a", (0, 1, 1, -2, 0))
L1 = verifier.compute_L_function(curve, 1.0 + 0.0j)
print(f"L(E,1) = {abs(L1):.6f}")
Validation
El paquete ha sido validado en curvas con rango conocido:

Curva	Rango conocido	Rango CTT
37a	1	1
389a	2	2
5077a	3	3
License and Copyright
Copyright © 2026 Américo Simões / CTT Research. All Rights Reserved.

This software is proprietary and protected by international copyright laws.

Permitted Use
Academic and research institutions may use this software for non‑commercial research provided that:

a) All publications include the citation:

"CTT BSD Conjecture Solver by A. Simões (2026)"

b) The software is not used for commercial advantage.

Commercial Use
Any commercial use requires a separate written license.

No Warranty
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND.

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