Research Datasets & Information-Theoretic Ledgers
An informational catalog of high-precision mathematical datasets, multi-billion prime ledgers, geometric semiprime fields, and Riemann Zeta zeros used by The Penta-Ledger. Direct public download channels and distribution mirrors are currently being prepared.
Dataset Catalog (14)
Filter by domain or search by schema columns, mathematical theorems, or formats.
PG-CSL Prime Gaps Continuous Sieve Ledger
Massive partitioned continuous sieve ledger recording all consecutive prime pairs up to 1.54 trillion with their exact gap sizes, coordinate indices, and sieve start markers.
- Zhang-Maynard-Tao bounded prime gap analysis and verification
- Elliott-Halberstam distribution level asymptotic bounds (θ = 0.65)
- Maximal prime gap discovery and Cramér/Granville conjecture testing
- Consecutive prime gap clustering and prime constellation frequencies
gap_size: int16p1: int64p2: int64k_start: int64Distilled Primes 54-Column Wave Stack
54-column analytical database capturing 8 cohesive structural layers for integers: 2D spacetime coordinates (u, v, t), exact column sum invariants, harmonic scalings, multiplicative partition signatures, 14 rational continued fraction suites, 50-digit MPFR log/exp strings, and lossless Gauss-Kuzmin horizons.
- Multi-dimensional integer topology and coordinate phase space exploration
- High-precision continued fraction spectrum and divergence analysis
- Exact log-domain floating point precision limits and Gauss-Kuzmin statistics
- Machine learning on number theoretic invariants and resident/gate-crasher classifications
Base Coordinates (8 cols)Row Sums & Envelopes (4 cols)Scalings & Ratios (6 cols)Rational CF Suite (14 cols)50-Digit MPFR Strings (6 cols)5-Billion Prime In-RAM DRAM Bitset & Binary Stream
Zero-copy memory-mapped bitset and contiguous uint64 array providing sub-nanosecond O(1) deterministic primality queries across all odd integers up to 5 billion.
- Sub-nanosecond O(1) in-memory primality testing without trial division
- Large-scale Goldbach conjecture and Hardy-Littlewood circle method checks
- Zero-latency sieving and prime generation pipelines in C++, Rust, and Python
- Cryptographic prime candidate validation and prime density sampling
Bitset: 1 bit per odd integer (2.5B bits)Binary: 234.95M uint64_t valuesRiemann Zeta Non-Trivial Zero Ledger (V1)
High-precision indexed ledger of non-trivial zeros γₙ of the Riemann Zeta function ζ(s) on the critical line Re(s) = 1/2, converted from Odlyzko and Platt calculations.
- Riemann Hypothesis empirical verification and critical line boundary tests
- GUE (Gaussian Unitary Ensemble) Montgomery pair-correlation statistics
- Explicit Riemann-von Mangoldt prime-counting formula evaluation R(x)
- Quantum chaos, random matrix theory, and spectral energy level modeling
zero_index: int64gamma_n: float64 / varchar(50)gram_interval: int32Geometric Primes: Gaussian & Eisenstein Split Ledger
Algebraic number theory dataset classifying primes by Gaussian splits (p = x² + y² ≡ 1 mod 4), Eisenstein splits (p = u² - uv + v² ≡ 1 mod 3), 2-adic valuation ranks, and modulo-12 geometric archetypes.
- Gaussian and Eisenstein integer factorization algorithms
- Quadratic form representations and binary quadratic Diophantine equations
- Elliptic curve point counting and complex multiplication (CM) orders
- Geometric lattice cryptography and Euclidean space partition invariants
p: int64is_gaussian_split: boolx: int32y: int32is_eisenstein_split: boolu: int32v: int32mod12_archetype: stringGeometric Semiprimes & Quadratic Factor Field
Exhaustive ledger of square-free semiprimes recording factor differentials δ = p₂ - p₁, modular archetypes, Gaussian decomposition classes, and harmonic arrival coordinates.
- Semiprime factor gap distribution and unbalanced semiprime analysis
- RSA modulus geometry and Fermat factorization boundary conditions
- Quadratic sieve polynomial parameter optimization
- Distribution of square-free composites in residue classes
n: int64p1: int32p2: int32delta: int32mod12_archetype: stringgaussian_type: stringExtended OEIS Offline Mirror & SIMD Codebook Index
Complete offline mirror of the Online Encyclopedia of Integer Sequences with parsed terms, author attribution, formulas, Maple/Mathematica/PARI scripts, b-files, and AVX-512 accelerated fingerprint search codebooks.
- Instant offline integer sequence identification and closed-form matching
- Automated formula discovery and symbolic sequence extrapolation
- Mathematical vulnerability auditing against established sequence literature
- High-throughput term lookup up to N = 4096 via SIMD codebooks
a_number: stringterms: list<int64>formulas: list<string>cross_references: list<string>100 Fundamental Constants High-Precision Library
1,000+ decimal digits and 1-billion-bit binary expansions for the top 100 mathematical and physical constants (π, e, γ, φ, ζ(3), Feigenbaum constants, Khinchin's constant, Glaisher-Kinkelin constant, and more).
- PSLQ integer relation detection and Ramanujan-type formula discovery
- Arbitrary-precision floating point validation and error analysis
- Transcendence and algebraic independence testing
- High-precision numerical integration and special function evaluation
constant_name: stringsymbol: stringvalue_1000dps: stringbinary_bits_path: stringExtended 25-Billion Prime Dataset
Extended sequential prime array and bitset covering the first 1.09 billion primes up to 25 × 10⁹ for large-scale computational number theory.
- Extended prime counting function π(x) error bound verification
- Large-scale prime sieve benchmarking and prime gap record hunting
- High-concurrency OpenMP and GPU parallel number theoretic sieving
uint64 binary sequential array3.0 GB bitmaskB-Smooth Neighborhood Tree Lattice
Multi-radix B-smooth integer tree neighborhoods and coordinate lattices for small prime smooth bases (B ∈ {2, 3, 5, 7}).
- General Number Field Sieve (GNFS) smooth relation matrix generation
- Radix-n Fast Fourier Transform (FFT) parameter optimization
- Smooth integer distribution and Dickman ρ(u) function numerical checks
smooth_base: list<int>tree_depth: intsmooth_elements: list<int64>Prime Gap Markov Transition & Correlation Dataset
Detailed statistical dataset of consecutive prime gap transitions, Markov state transfer matrices (orders 1 through 5), run-length clustering, and Index of Coincidence (IoC) metrics.
- Stochastic modeling of prime gaps as higher-order Markov chains
- Hardy-Littlewood prime k-tuple conjecture empirical testing
- Prime gap run-length clustering and autocorrelation decay analysis
gap_size: inttransition_probs: matrixioc_metric: float64Dodecagonal Quasicrystal R² Metric Graph
Geometric and topological graph dataset mapping 12-fold rotational symmetry quasicrystalline Penrose/Ammann-Beenker type tiling metrics with unit edge lengths in ℝ².
- Aperiodic tiling geometry and non-crystallographic space filling
- Quasicrystal spectral gap and quantum Hall topological insulator edge states
- Graph laplacian spectrum and random walk properties on aperiodic graphs
vertex_coords: (float64, float64)edges: (int64, int64)edge_length: 1.0GPU-Accelerated Binary Gapped Semiprime Tables
CUDA and AVX-512 optimized memory-mapped binary tables designed for ultra-high-throughput semiprime traversal and GPU factorization benchmarking.
- High-throughput GPU semiprime factorization benchmarking
- Vectorized SIMD memory-mapped search algorithms
- Hardware-accelerated mathematical sieve verification
Dense packed binary structCUDA kernel stream-readyFinite Field Irreducible & Primitive Polynomial Catalog
Catalog of irreducible and primitive polynomials across finite Galois fields F₂, F₃, and Fₚ for algebraic coding theory, LFSR generators, and finite field arithmetic.
- Cryptographic S-box and Galois field arithmetic implementation
- Reed-Solomon and BCH error-correcting code design
- Polynomial factorization algorithms and polynomial sieve benchmarking
field: stringdegree: intcoefficients: list<int>is_primitive: boolDataset Index & Future Distribution Roadmap
This page currently serves as an architectural index of the datasets utilized in our epistemic audits. Public downloads, torrent swarms, and partitioned mirror distributions are being architected for an upcoming release.