Random Plancherel geodesic-tree Monte Carlo dataset

A Monte Carlo dataset of random Plancherel geodesic trees: ensembles of infinite geodesic (competition-interface) binary trees of the infinite random standard Young tableau under the Plancherel measure. Each sample is built by applying the Robinson–Schensted–Knuth correspondence to a sequence of independent Uniform(0,1) random variables and reading off the branch points (cusps) of the resulting geodesics. The data accompanies the paper “Jeu de taquin forests and the inverse infinite RSK correspondence” by Dan Romik and Piotr Śniady, and was produced by the software companion (doi:10.5281/zenodo.21361261). Contents. One file per word length n, geodesic_trees_n{n}.jsonl, in JSON Lines format (one tree per line), for several sizes (about 105 to 107), plus a small fully transparent reference set. Each line is a provenance envelope wrapping the tree: the sample index, the RNG and root seed, a per-sample seed fingerprint, and SHA-256 checksums of the input sequence and of the recording tableau. Each dataset has a sidecar *.manifest.json recording the root, the exact seeding formula, the NumPy and SageMath versions, the Git commit, and the file’s SHA-256. Reproducibility and integrity. The samples are the contiguous streams 0…N−1 of a single, publicly recomputable root seed (NumPy PCG64 via SeedSequence), so the whole ensemble — not merely each line — can be regenerated and verified. The bundled auditor regenerates every line from the root and compares it byte-for-byte, checks that the indices form the complete population, and checks the SHA-256; a cherry-picked or altered file fails. Two levels of checking are possible: the per-file SHA-256 recorded in each manifest can be verified with nothing but the data (detecting tampering or truncation), while the full regenerate-and-diff audit runs the bundled generator and auditor inside the software companion, which supplies the RSK engine they import (see AUDIT.md). Using the data with the code. After downloading both the data and the software, either extract the *.jsonl files into the software’s data/statistical_samples/ directory, set the environment variable PLANCHEREL_DATA_DIRto point at them, or regenerate the data from scratch (bit-identical under the recorded NumPy version). The data dictionary in the archive documents every field and the exact checksum definitions.