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 tested corridors.

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 June 2026)

Claim	Status
All exceptional primes (p≡1 mod 12, c no 2mod3 factor) solved	289,372/289,372 up to 10⁸ (100%)
22-portal classification covers all exceptional primes	22 A-values, max A=159
Zero failures at any scale	10⁶: 4,540/4,540, 10⁷: 35,750/35,750, 10⁸: 289,372/289,372
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

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 survivors.txt --threads 8

For distributed runs:

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

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

For Kaggle T4 automation:

python -m pip install "kagglesdk>=0.1.23"
export KAGGLE_API_TOKEN=<bearer-token>
python kaggle_t4_runner.py --metadata kernel-metadata.json

Use --dry-run to validate metadata and the notebook locally before pushing.

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.
• Lightning AI (L40S/A100): launch_l40s.py starts a Studio through the real lightning-sdk, uploads sieve_l40s_hot_corridor.py, runs it under a timeout, saves results under /teamspace/erdos-lightning, and stops the Studio when the blocking run finishes.
• Local: Bare-metal runs with configurable thread count

Lightning AI L40S/A100 launch

Install the SDK and authenticate once with Lightning:

pip install -r requirements.txt
lightning login

Run a cost-capped dry run first:

python launch_l40s.py --teamspace owner/teamspace --dry-run

Then start the L40S worker:

python launch_l40s.py --teamspace owner/teamspace --max-runtime-minutes 60 --budget-usd 5

The runner uploads the hot-corridor sieve to /teamspace/erdos-lightning, executes it with timeout -s INT, writes RUN_STARTED_AT, RUN_FINISHED_AT, RUN_EXIT_CODE, erdos_output_<v>.json, KAGGLE_OUTPUT_RECORD.jsonl, and updates work_manifest.json when present. By default it uses an interruptible L40S, caps estimated spend below the supplied budget, enables Studio auto-sleep, and stops the Studio after a blocking run.

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)