Mathematical infrastructure for complex systems · Institute for Decision Systems and Number Theory
Research
Research from the ELARA·CORTEX Institute
Our reports give readers the data and methods needed to examine the findings. They cover vehicle routing, number theory, compression and earlier Elara experiments, with the test conditions stated alongside the results.
Built by the ELARA·CORTEX Institute for Decision Systems and Number TheoryMeasured in public: drift proof · benchmarks · research · security
The papers
The paper pages include the abstract, methods, mathematics and references. An introductory note explains the scope of each study. Available PDFs are linked below.
Benchmarking the Elara Route Engine against Google OR-Tools on the CVRPLIB and Time-Window Instances
Kgomotso Lekola · Technical Report TR-2026-01 · 9 June 2026 · ELARA·CORTEX Institute for Decision Systems and Number Theory
This report examines route quality and the cost of replanning when a fleet's day changes. Across nine CVRPLIB X-instances with 100 to 512 customers, the engine finished a mean 3.05% above the published record, using five seconds of single-threaded Python per instance. It produced shorter routes on all six instances also tested with Google OR-Tools, with a wider margin on longer routes. On five small instances, its results matched the optimum certified by Z3.
The study also tested five time-window instances from the Solomon and Gehring and Homberger sets against published records. It excludes an OR-Tools comparison for these instances because a fair encoding could not be certified. On the two clustered instances, Elara matched the record vehicle count at 0.2% more distance. Published route lists allow readers to check feasibility and cost from the public instance files. A separate production API test replanned a 200-stop, ten-vehicle day in about 1.2 milliseconds. The solver method remains proprietary.
Subjects: vehicle routing · combinatorial optimisation · benchmarking · formal verification
Read the report · CiteThe web page is the version of record; no PDF is available.
Significance of the Elara-Cortex founder Kgomotso Lekola on the GIMPS: an efficacy analysis with eight machine-checked statements
Kgomotso Lekola · Analysis · 17 July 2026 · ELARA·CORTEX Institute for Decision Systems and Number Theory
The Great Internet Mersenne Prime Search has operated as a volunteer computing project since 1996. Its leaderboard credits trial-factoring attempts according to their difficulty. Between May and July 2026, the founder's account recorded five attempts: one candidate was factored and four remained unfactored at the time of the study. The paper checks eight arithmetic statements about a frozen leaderboard using Z3. These checks establish the arithmetic; the sample of five does not establish statistical significance.
The paper includes the full comparison cohort, the limits on its claims and an offer to pre-register the next five candidates with predicted outcomes and depth targets before computation begins. Readers can derive the figures from the public leaderboard. The study forms part of the laboratory's work on mathematics used across its routing, compression and context services.
Subjects: number theory · distributed computing · efficacy analysis · machine-checked arithmetic
GPU-Free Online Entropy-Rate Estimation of Text via Lossless Context Mixing in Rapidity Space
Kgomotso Lekola · Preprint · 12 July 2026 · ELARA·CORTEX Institute for Decision Systems and Number Theory
This preprint studies the entropy rate of streaming text on ordinary processors without a graphics card. It estimates how much of the stream is predictable and uses that estimate for lossless compression. The original bytes remain recoverable. Already-compressed files offer little or no further reduction.
A companion note from June 2026 combines published compression benchmarks with estimated company data mixes; it contains no new measurements. The sourced rates include about 92 percent for JSON logs, somewhat less for plain-text logs, similar reductions for columnar analytics, about a fifth for model checkpoints, and almost none for compressed images or video. Using an industry estimate that 78 percent of stored data is unstructured, the note estimates reductions of up to 80 percent across a mixed data estate. Results vary with the mix, from observability data to media archives. A separate laboratory demonstration reduced a five-megabyte log by 96 percent.
Subjects: information theory · lossless compression · context mixing · entropy estimation
View PDFAvailable as a PDF.
Six further papers from the earlier site, including technical reports and an evidence ledger, are awaiting republication with their supporting records.
Earlier Elara experiments
These reports describe earlier systems and test runs. Their results do not establish the performance of the current chat release. Each includes recorded results and commands for repeating the experiment.
The recall experiment placed a sentence and three near-identical decoys at nine depths in a context of just over two million tokens. All 72 trials returned the complete sentence and its code byte for byte. The tested system used relevance-ranked memory mapped to a model; comparator rows are computed fixed-window bounds that assume perfect recall within each window. A second run followed references between facts and gathered related items at two, four and eight million tokens, with no decline in the number of questions answered.
The benchmark report records two public tests through the production API used at the time. On GPQA Diamond, which covers graduate-level physics, chemistry and biology, Elara answered 139 of 156 items correctly: 89.1 percent of answered items, with provider errors reported separately. On HumanEval, it passed 149 of 164 problems on the first attempt, or 90.9 percent. Comparator figures from model laboratories and Epoch AI are reported separately. Item-level records include the question keys and answers needed for independent replication.
Recall experiment
Seventy-two planted facts recalled word for word across a two-million-token context, at nine depths.
Benchmarks
GPQA Diamond and HumanEval results, with test dates, settings and item counts.
Citations and contact
Cite a report by its author, its year, its title and its series number, with the laboratory as publisher.
- Technical report
- Lekola, K. (2026). Benchmarking the Elara Route engine against Google OR-Tools on the CVRPLIB. Technical Report TR-2026-01, ELARA·CORTEX Institute for Decision Systems and Number Theory, New Jersey and Johannesburg.
- Analysis
- Lekola, K. (2026). Significance of the Elara-Cortex founder Kgomotso Lekola on the GIMPS: an efficacy analysis with eight machine-checked statements. ELARA·CORTEX Institute for Decision Systems and Number Theory, New Jersey and Johannesburg.
- Preprint
- Lekola, K. (2026). GPU-free online entropy-rate estimation of text via lossless context mixing. Preprint, ELARA·CORTEX Institute for Decision Systems and Number Theory, New Jersey and Johannesburg.
- Experiment reports
- Cite the page address and the date of the results record named on it.
For questions about methods, requests for the scripts and records cited in a paper, or proposals for independent replication, write to hello@elara-cortex.com. Include the report title.
Reports are added to this page as they are completed. Return to chat · About Elara