A scalable engine for exact multi-point Chowla correlations
Description
This dataset contains the complete numerical results and reproducibility materials for an exact, exhaustive computation of unweighted Liouville correlations through X = 10^13. For the Liouville function lambda(n) = (-1)^Omega(n), the computation evaluated twenty two-point correlations A_k(X) = sum from n = 2 to X of lambda(n)lambda(n+k), for 1 <= k <= 20, and four consecutive multi-point correlations B_r(X) = sum from n = 2 to X of the product of lambda(n+j) for 0 <= j < r, for 3 <= r <= 6. Each terminal sum contains exactly 9,999,999,999,999 terms. The dataset also records all 24 correlations at 81 geometrically spaced prefix endpoints from 10^3 through 10^13. The canonical campaign ran on eight physical cores of an AMD Ryzen 7 5800H. It completed in 27,551.600 seconds, sustained 362.955 million base indices per second, and used 185,204,736 bytes of peak resident memory. The deposit includes exact machine-readable TSV tables, the final JSON state, complete execution log, campaign manifest, SHA-256 checksums, hash-addressed copies of the native source and compiled library used by the campaign, buildable C and Python source code, independent reference tests, benchmark tools, and reproduction instructions. All reported correlation sums are exact signed integers. Floating-point arithmetic is used only for derived presentation values such as normalized ratios.
Files
Steps to reproduce
The data were generated by a deterministic Python and C/OpenMP engine. It computes Liouville values exactly with a segmented factor sieve, then obtains all 24 correlations in one shared XOR/popcount reduction pass. The canonical campaign used eight physical cores, chunks of 100,000,000 base indices, and atomic checkpoints. 1. Verify the download Place all uploaded files in one directory: sha256sum --check SHA256SUMS 2. Unpack the release unzip chowla_exact_source_v1.0.0.zip unzip chowla_1e13_campaign_v1.zip cd chowla_exact_release_v1.0.0 Requirements: Python 3.10+, NumPy, pytest, a C compiler, and an OpenMP runtime. 3. Build and test make native make test The tests compare the native engine with independent direct-factorization and segmented-reference implementations, including high intervals, chunk boundaries, and checkpoint resumption. 4. Run the independent reference validation python3 validation/reference_sequences/generate_bfiles.py \ --limit 1000000 \ --output-dir /tmp/chowla_reference_sequences_1e6 python3 validation/reference_sequences/verify_bfiles.py \ --limit 1000000 \ --input-dir /tmp/chowla_reference_sequences_1e6 The two programs use separate algorithms and compare five sequences at every index through one million: 5,000,000 comparisons. The temporary files occupy about 56 MB. 5. Verify the canonical campaign make verify This checks the manifest, SHA-256 hashes, processed term count, and all 24 terminal exact sums. 6. Run a short campaign PYTHONPATH=src python3 -m chowla_exact run \ --limit 1000000 \ --chunk-size 100000 \ --checkpoint-seconds 0 \ --output runs/reproduce_1e6 7. To repeat the full exhaustive computation, use: OMP_NUM_THREADS=<physical-core-count> \ OMP_PROC_BIND=close \ OMP_PLACES=cores \ PYTHONPATH=src python3 -m chowla_exact run \ --limit 10000000000000 \ --chunk-size 100000000 \ --max-shift 20 \ --output runs/reproduce_chowla_1e13 8. Run the full campaign or another endpoint OMP_NUM_THREADS=THREAD_COUNT \ OMP_PROC_BIND=close \ OMP_PLACES=cores \ PYTHONPATH=src python3 -m chowla_exact run \ --limit ENDPOINT \ --chunk-size 100000000 \ --max-shift 20 \ --output runs/custom_campaign Use ENDPOINT=10000000000000 to reproduce the canonical campaign. Larger endpoints are supported within signed 64-bit limits; for example, ENDPOINT=10000000000000000 requests 10^16. Runtime and memory depend on the endpoint and hardware. The current release uses OpenMP on one shared-memory host; automatic multi-node distribution is not included. Runs resume from atomic checkpoints.