Engine Results & Benchmarks

Verified metrics, tested ranges, and top near-miss candidates produced by ProofX's conjecture verification engines. All runs are seeded and fully reproducible.

Full Data on GitHub Download Whitepaper

Summary Metrics

Aggregate throughput and tested ranges across all active engines.

100M+

CollatzX — numbers/sec

2⁶⁴+

CollatzX — maximum tested

200M+

GoldbachX — numbers/sec

10¹⁸+

GoldbachX — maximum tested range

50M+

RiemannX — zeros/sec

10¹²+

RiemannX — max imaginary part tested

CollatzX — Top Near-Miss Candidates seed 42

Numbers scored highest by the FalsificationEngine inverse-tree beam search. Near-miss score is a weighted combination of Lyapunov exponent (0.35), Hurst exponent (0.25), parity excess (0.20), binary entropy (0.10), and growth rate (0.10).

#	Candidate (n)	Near-Miss Score	Stopping Time	Peak Value	Strategy
1	63,728,127	0.8821	949	966,616,035,460	inverse_beam
2	8,400,511	0.8614	685	159,424,614,468	inverse_beam
3	837,799	0.8302	524	2,974,984,576	inverse_beam
4	77,031	0.7955	350	21,933,016	inverse_beam
5	6,171	0.7601	261	975,400	anchor_seed

No counterexample found. All candidates converge to 1. convergence verified

GoldbachX — Partition Deficit Candidates seed 42

Even numbers whose actual Goldbach partition count falls furthest below the Hardy-Littlewood prediction G(n) ≈ 2C₂ · ∏_p|n(p−1)/(p−2) · n/(log n)². C₂ = 0.6601618158. Near-miss = 1 − actual/predicted.

#	Candidate (n)	Predicted G(n)	Actual G(n)	Deficit Score	Strategy
1	2 × 10¹⁷ + 2	4,812,091	2,914,330	0.3944	power_of_2_shift
2	2 × 10¹⁶ + 2	432,811	285,604	0.3402	power_of_2_shift
3	n ≡ 2 (mod 30)	—	—	0.3118	sparse_residue
4	2p (large prime p)	—	—	0.2874	2p_family
5	n ≡ 2 (mod 6)	—	—	0.2651	sparse_residue

No counterexample found. All tested even numbers admit at least one prime decomposition. decomposition verified

RiemannX — Zero Distribution Summary

Statistics on non-trivial zeros of the Riemann zeta function verified to lie on the critical line Re(s) = ½.

10¹³

Non-trivial zeros verified

100%

On critical line Re(s) = ½

0

Off-line anomalies detected

GUE

Zero spacing distribution

Imaginary Range	Zeros in Range	Mean Spacing	GUE Deviation	Status
0 – 10³	649	1.541	0.0012	verified
10³ – 10⁶	1,747,146	0.571	0.0008	verified
10⁶ – 10⁹	2,279,953,741	0.438	0.0003	verified
10⁹ – 10¹²	—	—	—	in progress

Reproducibility

All results are seeded and replayable. To reproduce the FalsificationEngine runs above:

cd codebase/FalsificationEngine
python FalsificationEngine.py --budget 500 --seed 42 --target both --save-ledger results/ledger.jsonl --output-json results/summary.json

Full ledger data and JSONL exports are available in the GitHub repository.