erdos-straus-solver

Part of the MANIFOLD field computation system. Lead R&D: DaShawn (African American Developer & Mathematician) Copyright (c) 2026 Guinea Pig Trench LLC

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Erdos-Straus hot corridor sieve — integer solver, stride-24, 100% hit rate in mod-24 corridors (expected: these corridors are pre-filtered to numbers where parametric identities apply).

The Erdos-Straus conjecture states that for every integer n ≥ 2, the fraction 4/n can be expressed as the sum of three unit fractions (Egyptian fractions). This solver partitions the search space deterministically using a seed + survivor list, achieving zero-conflict parallel distribution across compute nodes.

This is the vinculum operating on integers instead of fields — same algebraic skeleton, different substrate.

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🏆 Key Results (Verified July 2026)

Claim	Status
Sieve existence check	Computational run through ~8.00e13 (80 trillion) on Kaggle; zero survivors. Literature has reached 1e17-1e18 for plain existence checks. The novel contribution is the 22-portal classification at 1e8 -- see EMPIRICAL_NOTE.md.
All tested exceptional-prime-indexed prime squares ($p^2$) solved	289,372/289,372 up to 10⁸ (100%). Note: solutions are for $4/p^2$, not $4/p$. A descent theorem is required to extend to $4/p$.
22-portal classification covers all tested $p^2$	22 A-values, max A=159
Zero failures at any scale

10⁶: 4540/4540, 10⁷: 35750/35750, 10⁸: 289372/289372

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| Mean minimal m = 2.25 | Tightly bounded | | A=7 dominates at ~49.5% | Stable fraction across all scales | | A=159 (m=39) at p=91,267,201 | Max observed, consistent with O(log p) growth | | No overlap with Bradford (arXiv 2602.11774) solutions | 0.0% (y,z) agreement on shared n | | Squareful barrier: Bradford fails on ALL squareful n | Structural, not implementation artifact | | Xu (May 2026): 9 wild primes for m≤30,000 | All 9 fall within 12-portal classification (for $4/p^2$) |

The 22 A-values (the "12 portals" plus higher terms): 7, 11, 15, 19, 23, 31, 39, 43, 47, 51, 59, 67, 71, 79, 83, 87, 95, 103, 107, 111, 127, 159

OEIS Submission: Prepared — ready for submission to oeis.org/Submit

• Data file: oeis_a_values_data.txt (distribution counts)
• b-file: oeis_b_file.txt (22 distinct A-values)
• b-file: bfile_exceptional_1000.txt (A per exceptional prime, first 1000)
• Generator: gen_oeis_bfile.py (produces b-file for N exceptional primes)

Architecture

The Hot Corridor Sieve

The sieve partitions work deterministically: same seed + same survivor list = same partition. This is parallel transport of number theory problems across compute nodes — the manifold geometry of the solution space.

• Stride-24: exploits the mod-24 structure of known solution corridors
• Mod9 classification: STABLE (1,4,7), BREACH (0,3,6), NEUTRAL (2,5,8)
• Seeded partitioning: any node with the same seed produces identical work boundaries

Components

File	Purpose
sieve_l40s_hot_corridor.py	Primary sieve runner — stride-24, hot corridor targeting
master_orchestrator.py	Coordinates multi-node distribution using sieve-based partitioning
lightning_worker.py	Remote compute worker for distributed runs
progression.py	Tracks solution discovery rate and corridor coverage
deepseek_verifier.py	Parallel verification against DeepSeek reasoning
atomic_writer.py	Thread-safe checkpoint writer for long-running sieves
sieve_a100.py / sieve_a100_classify.py	A100-optimized sieve + mod9 classification

Quick Start

git clone https://github.com/COMMENCINGTHESCOURGE/erdos-straus-solver.git
cd erdos-straus-solver
python sieve_l40s_hot_corridor.py --v 2 --stride 24 --depth 200

For distributed runs:

# Orchestrator node
python master_orchestrator.py --seed 42 --nodes 3

# Worker nodes
python lightning_worker.py --orchestrator <ip>:<port>

Verification

The solver includes a self-verification mode that validates every discovered solution satisfies the 4/n = 1/a + 1/b + 1/c equation. The DeepSeek verifier cross-checks results against an independent reasoning path.

The Vinculum Connection

Every measurement in this system is a vinculum:

Ratio	What it measures
solutions / search space	Discovery progress
stride width / n	Corridor efficiency
verified / total	Solution quality
nodes with seed / total nodes	Partition completeness

Same vinculum operator, applied to integers instead of GPU fields.

Deployment

• Kaggle (Scale Prover): commencethescourge/erdos-straus-scale-prover — Numba-JIT accelerated Omega solver for 10⁹ range verification
• Kaggle (Hot Corridor): commencethescourge/erdos-p100-hot-corridor-sieve — P100 GPU, daily schedule
• Colab: erdos_colab_gpu_sieve.ipynb — CuPy-accelerated hot corridor sieve for T4/L4/A100 GPU runtimes with Google Drive auto-resume support.
• Colab LLM Verifier: erdos_colab_llm_verifier.ipynb — Verification and math resonance analysis utilizing Google Gemini API keys to cross-check solutions and compile markdown reports.
• Local: Bare-metal runs with configurable thread count

Entity

Field	Value
Lead R&D	DaShawn (African American Developer & Mathematician)
Copyright	Guinea Pig Trench LLC
R&D Entity	Guinea Pig Trench LLC (PA, #13674084)
Credit Facility	Truth Holds Enterprise (PA #7049023)