A Contiguous Census of Prime k-Tuples up to 10^14 (census_v1)

A contiguous, deterministically-proven census of prime k-tuples (prime constellations) for k = 2 to 16, covering every integer from the start of the number line up to a ceiling of 10^14. The catalog contains 454,099,542 recorded tuples. All tuples were produced by a single canonical square-root-depth sieve (sieve_low). Because every prime involved is below 2^81, primality is deterministic — no probabilistic primality testing is used, so every recorded tuple is rigorously proven. Recording policy (column completeness):- k ≥ 5: exhaustive — every occurrence below the ceiling is present.- k = 2, 3, 4: capped / first-N-by-p1 over the contiguous bottom-up scan, hence complete up to a per-k horizon (the realized count there refines the Hardy–Littlewood constant C_k). Completeness within the 10^¹⁴ scan: the contiguous scan covers all integers up to 10^¹⁴. Exhaustive recording (every occurrence present) holds for k ≥ 5 across the full range up to 10$¹⁴. The capped families are complete up to a per-k horizon: k = 2 up to 4×10⁹, k = 3 up to 8×10¹⁰, k = 4 up to 5.24×10¹³. Exact per-k horizons and policies are incensus_manifest.csv and manifest.json. Format: one row per tuple in gzipped CSV (tuples_census.csv.gz). Columns: k, kind, span, min_span, ratio, pattern, p1, primes, gaps, height_log{2,10,3,5,7}, scan_L, scan_R, date_found, source, found_by, proof_level, completeness. Large integers are stored as lossless decimal strings; primes and gaps are ';'-joined. Contiguous tile coverage(completeness provenance) is in heights_scanned.csv, and realized constellation-pattern frequencies in the pattern_multiplicity_*.csv files. SHA-256 checksums for all files are in CHECKSUMS.txt. This dataset is the empirical basis for the paper "Overlap Compatibility and Prime Tuple Dispersion" (P. T. Symington). The accompanying reproducibility package — analysis scripts and derived tables — is deposited separately at DOI 10.5281/zenodo.20683471.